VeriLLM

Formulate the problem before choosing the machinery

VeriLLM begins with a decision problem, not a framework. Wrap cached GPT inference in Merkle commitments and spot checks, then simulate a decentralized committee with rewards and slashing. Restate that sentence as an observable input, a desired output, and a criterion for preferring one output over another. Identify who or what supplies supervision, whether feedback is immediate or delayed, and whether examples can be considered independent. These choices determine what can be learned and what remains an assumption. The implementation is honest only when those assumptions are visible near the data contract rather than buried in training code.

The raw material becomes a token representation. Representation decides which distinctions the system can express and which distinctions disappear. List categorical domains, numerical units, missing-value semantics, sequence or spatial axes, masks, player or client perspective, and precision. Then consider invariances: should translation, permutation, rescaling, token position, client identity, or board symmetry change the answer? An architecture that ignores the required invariance wastes data; one that imposes the wrong invariance makes the target impossible to represent.

Finally define the baseline and the abstention point. A baseline can be a constant predictor, random policy, linear rule, naive kernel, synchronous algorithm, or human heuristic. It anchors complexity in evidence. The abstention point describes inputs for which the system lacks support and should decline, defer, or fall back. Together they prevent VeriLLM from being judged only by an impressive end-to-end demonstration while basic correctness, calibration, robustness, or operational usefulness remains unknown.

Connect the objective to the behavior you actually want

An objective compresses preferences into a scalar, but no scalar captures every product or scientific goal. For VeriLLM, distinguish the training objective from the evaluation metric and the deployment utility. The training objective must provide a usable signal to parameters or state; evaluation must estimate generalization under a controlled protocol; deployment utility includes latency, cost, safety, and the consequence of errors. When these three disagree, optimization can succeed while the system becomes less useful.

Study each term dimensionally and statistically. Ask what happens if one term is multiplied by ten, one class becomes rare, a sequence becomes longer, a client contributes more samples, or rewards are shifted. Determine whether averages are per token, example, client, action, spatial position, or batch. Regularization is not decorative: it encodes a preference over solutions and changes units unless normalized consistently. A correct derivation names the population quantity of interest, its finite-sample estimator, and the approximation introduced by minibatches, replay, sampling, or surrogate losses.

Identifiability is the deeper constraint. Data may not contain enough information to separate competing explanations. Merkle trees, Spot checks, Slashing can improve computation or inductive bias, but they cannot manufacture missing evidence. State causal assumptions, observability limits, support conditions, and equivalence classes of solutions. Use sensitivity analysis and targeted interventions where possible. When identification is impossible, report uncertainty or a set of plausible answers rather than converting an arbitrary modeling choice into unwarranted confidence.

Make mathematical equivalence survive finite precision

Paper algebra assumes exact real numbers; the implementation uses finite precision, bounded memory, and discrete execution order. In VeriLLM, audit exponentials, logarithms, divisions, reductions, norms, probabilities, recursive values, and accumulated updates. Rewrite unstable expressions with max subtraction, log-sum-exp, compensated accumulation, safe denominators, or higher-precision reductions. Track where a mathematically harmless reordering changes rounding and where mixed precision needs scaling or master copies.

Shapes are part of the proof. Annotate each intermediate with semantic axes rather than only dimensions: batch, token, head, channel, client, action, expert, feature, row, column, or sample. Broadcasting should be intentional and verified with asymmetric dimensions so an accidental match cannot hide. Record contiguous layout and stride assumptions when performance code depends on them. For every reshape or transpose, write both the precondition and the inverse operation needed during backward, decoding, aggregation, or reconstruction.

Build a numerical ladder: scalar example, tiny vector or matrix example, batched reference, optimized path, then realistic workload. At each rung compare values and invariants before increasing scale. This catches defects while they are still interpretable. The acceptance test should specify absolute and relative error, exceptional values, deterministic modes, and the hardware or library versions used. Numerical stability is not a final cleanup task; it is part of the algorithm’s definition.

Design evidence that can falsify the implementation

Evaluation is an experiment. For VeriLLM, specify the unit of analysis, split strategy, temporal boundary, randomization, baseline, metric, and uncertainty before viewing final results. Prevent duplicates, transformed copies, future information, opponent leakage, and shared-client information from crossing the boundary. A single aggregate score can hide subgroup collapse, unstable seeds, poor calibration, tail latency, or rare catastrophic behavior, so pair it with distributions and stratified slices.

Ablations connect outcomes to mechanisms. Remove or replace Merkle trees, Spot checks, Slashing one at a time while controlling data, compute, and evaluation. Compare equal wall-clock or equal resource budgets when efficiency is part of the claim. Repeat stochastic runs and report variation rather than selecting the best seed. Inspect learning curves and intermediate metrics because two systems with the same final score may differ radically in sample efficiency, stability, or cost.

The test suite and the benchmark answer different questions. Unit and property tests prove local contracts; integration tests prove components agree; benchmarks estimate behavior at scale; task evaluation estimates usefulness. Preserve all four. A benchmark that bypasses validation or uses a different code path from production is weak evidence. The strongest release gate reruns the exact packaged implementation with recorded configuration and produces an artifact that another person can inspect.

Turn the learning artifact into an operable system

Production structure separates pure computation from orchestration, configuration, persistence, and interfaces. Package the core of VeriLLM behind typed contracts. Keep data loading, model or state construction, training, evaluation, serialization, and serving independently invocable. Configuration should be validated, versioned, and printable. Random seeds, data identifiers, source commit, dependency lock, hardware, and metric definitions belong in the run record so an apparent regression can be reproduced instead of guessed at.

Capacity planning follows the critical path. Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage across representative input sizes and concurrency. Report warm-up separately, distinguish throughput from latency, and include tail percentiles. Define memory ownership and lifetime so caches, activations, buffers, replay, or optimizer state cannot grow without a bound. Backpressure and admission control are preferable to unpredictable collapse. Where hardware-specific acceleration exists, preserve a portable reference path for correctness and degraded operation.

Observability must explain decisions and failures without exposing sensitive content. Log stable identifiers, shapes, versions, summary statistics, timings, and error categories. Monitor input drift, output distribution, task quality, saturation, retries, and fallback rate. Establish rollback and shadow-evaluation procedures before the first risky change. A production-grade implementation is not merely more abstract than a notebook; it makes dependencies, state, failure, and evidence explicit enough for another engineer to operate safely.

Read claims as reproducible hypotheses

The research surrounding VeriLLM improves representations, objectives, algorithms, systems, or evaluation protocols. Classify each paper by which lever it changes. Then identify the comparison budget: data, parameters, tokens, environment steps, hardware, communication, wall-clock time, and tuning effort. A claimed improvement may disappear when budgets are normalized or when the baseline receives equal tuning. Read methods and appendices for details that determine reproducibility, not only the abstract and headline table.

Reproduction begins with the smallest claim. Recreate one table row or ablation before attempting the entire system. Preserve the authors’ preprocessing and metric definitions, then deliberately vary one assumption. Document deviations, failed attempts, and environment details. When a result does not reproduce, distinguish an implementation defect from missing procedural knowledge, stochastic uncertainty, and genuine sensitivity. Negative evidence is useful when it narrows the conditions under which the method works.

Extension should start from a mechanism and a falsifiable prediction. The skills developed here—Verifiable compute, Transformers, Protocols—suggest multiple directions, but change one major factor at a time. Predict which metric and intermediate signal should move if the explanation is correct. Use confidence intervals and preregistered stopping rules for expensive experiments where possible. Publish code, configuration, data provenance, and failure cases so the work contributes more than another isolated score.

Maintain a chain of evidence from equation to outcome

A proof ledger for VeriLLM links each important claim to the smallest evidence that could disprove it. For a mathematical claim, keep a hand-worked example and a high-precision reference. For a software contract, keep unit and property tests. For an optimization claim, keep profiler traces and equal-budget baselines. For a learning claim, keep per-seed results, confidence intervals, and ablations. For a production claim, keep load tests, failure injection, monitoring queries, and rollback evidence. This structure prevents one successful end-to-end run from being treated as proof of every layer beneath it.

Record evidence beside the versioned artifact it evaluates. A metric without its dataset revision, configuration, dependency lock, hardware, and commit cannot reliably settle a regression. Likewise, a screenshot or generated sample is qualitative evidence, not a distribution. Name the claim, evidence type, acceptance threshold, owner, and date. When the implementation changes, rerun the smallest affected evidence first and then the downstream integration gates. The ledger becomes a map of confidence: it shows what is known, what is assumed, what has become stale, and where another experiment is required.

Use the ledger during review. Ask whether each test would fail for a realistic defect, whether each benchmark measures the packaged code path, whether every aggregate retains inspectable raw values, and whether uncertainty is reported at the correct independent unit. Include counterexamples and failed experiments because they define the boundary of the method. Over time this habit turns Verifiable compute, Transformers, Protocols from isolated implementation skills into a reproducible engineering practice that survives new data, new hardware, new collaborators, and changing product constraints.

Build Char Vocab — from contract to production evidence

Build Char Vocab is the construction at milestone 1 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between tokenizer and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Build Char Vocab as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Build Char Vocab depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Build Char Vocab needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Build Char Vocab can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Build Char Vocab changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Tokenizer. Build a character-level vocabulary and encode/decode strings to and from token ids.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Embed Tokens — from contract to production evidence

Embed Tokens is the transformation at milestone 4 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between embeddings and causal self-attention with kv cache and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Embed Tokens as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Embed Tokens depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Embed Tokens needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Embed Tokens can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Embed Tokens changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Embeddings and Causal Self-Attention with KV Cache. Implement token and positional embeddings, the linear projection primitive, and a single-head causal self-attention module that reads and writes a KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Compute Attention Scores — from contract to production evidence

Compute Attention Scores is the measurement at milestone 7 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between embeddings and causal self-attention with kv cache and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Compute Attention Scores as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Compute Attention Scores depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Compute Attention Scores needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Compute Attention Scores can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Compute Attention Scores changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Embeddings and Causal Self-Attention with KV Cache. Implement token and positional embeddings, the linear projection primitive, and a single-head causal self-attention module that reads and writes a KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Softmax Attention Weights — from contract to production evidence

Softmax Attention Weights is the transformation at milestone 10 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between embeddings and causal self-attention with kv cache and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Softmax Attention Weights as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Softmax Attention Weights depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Softmax Attention Weights needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Softmax Attention Weights can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Softmax Attention Weights changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Embeddings and Causal Self-Attention with KV Cache. Implement token and positional embeddings, the linear projection primitive, and a single-head causal self-attention module that reads and writes a KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Append Kv Cache — from contract to production evidence

Append Kv Cache is the pipeline boundary at milestone 13 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between embeddings and causal self-attention with kv cache and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Append Kv Cache as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Append Kv Cache depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Append Kv Cache needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Append Kv Cache can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Append Kv Cache changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Embeddings and Causal Self-Attention with KV Cache. Implement token and positional embeddings, the linear projection primitive, and a single-head causal self-attention module that reads and writes a KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Single Head Causal Self Attention — from contract to production evidence

Single Head Causal Self Attention is the pipeline boundary at milestone 16 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between embeddings and causal self-attention with kv cache and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Single Head Causal Self Attention as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Single Head Causal Self Attention depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Single Head Causal Self Attention needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Single Head Causal Self Attention can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Single Head Causal Self Attention changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Embeddings and Causal Self-Attention with KV Cache. Implement token and positional embeddings, the linear projection primitive, and a single-head causal self-attention module that reads and writes a KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Compute Mean Variance — from contract to production evidence

Compute Mean Variance is the pipeline boundary at milestone 20 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between feed-forward, layernorm, and transformer block and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Compute Mean Variance as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Compute Mean Variance depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Compute Mean Variance needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Compute Mean Variance can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Compute Mean Variance changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Feed-Forward, LayerNorm, and Transformer Block. Assemble the position-wise feed-forward network, layer normalization, residual add-and-norm sublayer, and the full transformer block that updates the KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Transformer Block — from contract to production evidence

Transformer Block is the transformation at milestone 23 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between feed-forward, layernorm, and transformer block and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Transformer Block as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Transformer Block depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Transformer Block needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Transformer Block can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Transformer Block changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Feed-Forward, LayerNorm, and Transformer Block. Assemble the position-wise feed-forward network, layer normalization, residual add-and-norm sublayer, and the full transformer block that updates the KV cache.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Run Prefill — from contract to production evidence

Run Prefill is the pipeline boundary at milestone 26 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between lm head, prefill, and autoregressive decoding and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Run Prefill as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Run Prefill depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Run Prefill needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Run Prefill can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Run Prefill changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: LM Head, Prefill, and Autoregressive Decoding. Project hidden states to vocabulary logits, run prefill over a prompt, and generate tokens one decode step at a time while recording per-step state.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Hash Tensor — from contract to production evidence

Hash Tensor is the pipeline boundary at milestone 29 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between merkle commitments over decode steps and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Hash Tensor as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Hash Tensor depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Hash Tensor needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Hash Tensor can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Hash Tensor changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Merkle Commitments over Decode Steps. Hash tensors and decode-step states into leaves and build a Merkle tree with inclusion-proof generation and verification.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Build Merkle Level — from contract to production evidence

Build Merkle Level is the construction at milestone 32 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between merkle commitments over decode steps and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Build Merkle Level as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Build Merkle Level depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Build Merkle Level needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Build Merkle Level can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Build Merkle Level changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Merkle Commitments over Decode Steps. Hash tensors and decode-step states into leaves and build a Merkle tree with inclusion-proof generation and verification.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Merkle Inclusion Proof — from contract to production evidence

Merkle Inclusion Proof is the pipeline boundary at milestone 35 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between merkle commitments over decode steps and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Merkle Inclusion Proof as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Merkle Inclusion Proof depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Merkle Inclusion Proof needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Merkle Inclusion Proof can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Merkle Inclusion Proof changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Merkle Commitments over Decode Steps. Hash tensors and decode-step states into leaves and build a Merkle tree with inclusion-proof generation and verification.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Sample Audit Positions — from contract to production evidence

Sample Audit Positions is the decision at milestone 39 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between prover transcript and spot-check verification and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Sample Audit Positions as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Sample Audit Positions depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Sample Audit Positions needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Sample Audit Positions can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Sample Audit Positions changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Prover Transcript and Spot-Check Verification. Run the prover to produce outputs and commitments, assemble the public transcript, and implement seeded spot-check verification that re-executes audited decode steps.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Check Commitment Against Proof — from contract to production evidence

Check Commitment Against Proof is the verification at milestone 42 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between prover transcript and spot-check verification and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Check Commitment Against Proof as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Check Commitment Against Proof depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Check Commitment Against Proof needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Check Commitment Against Proof can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Check Commitment Against Proof changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Prover Transcript and Spot-Check Verification. Run the prover to produce outputs and commitments, assemble the public transcript, and implement seeded spot-check verification that re-executes audited decode steps.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Tamper Transcript Flip Token — from contract to production evidence

Tamper Transcript Flip Token is the pipeline boundary at milestone 45 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between tampering, detection probability, and verifier cost and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Tamper Transcript Flip Token as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Tamper Transcript Flip Token depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Tamper Transcript Flip Token needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Tamper Transcript Flip Token can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Tamper Transcript Flip Token changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Tampering, Detection Probability, and Verifier Cost. Tamper with transcripts, derive the detection probability under k audits and a corruption fraction, and quantify verifier cost as a fraction of full re-execution.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Show Tampered Transcript Rejected — from contract to production evidence

Show Tampered Transcript Rejected is the pipeline boundary at milestone 48 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between tampering, detection probability, and verifier cost and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Show Tampered Transcript Rejected as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Show Tampered Transcript Rejected depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Show Tampered Transcript Rejected needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Show Tampered Transcript Rejected can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Show Tampered Transcript Rejected changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Tampering, Detection Probability, and Verifier Cost. Tamper with transcripts, derive the detection probability under k audits and a corruption fraction, and quantify verifier cost as a fraction of full re-execution.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Aggregate Votes Majority — from contract to production evidence

Aggregate Votes Majority is the pipeline boundary at milestone 51 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between decentralized committee, incentives, and end-to-end evaluation and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Aggregate Votes Majority as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Aggregate Votes Majority depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Aggregate Votes Majority needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Aggregate Votes Majority can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Aggregate Votes Majority changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Decentralized Committee, Incentives, and End-to-End Evaluation. Sample verifier committees, aggregate votes by majority, implement rewards and slashing, and run honest and malicious rounds reporting end-to-end verification cost.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.

Assign Dual Role — from contract to production evidence

Assign Dual Role is the pipeline boundary at milestone 54 of VeriLLM. Its purpose is not merely to make the next function run. It establishes a contract between decentralized committee, incentives, and end-to-end evaluation and every downstream stage. Begin by naming the accepted inputs, their axes, units, legal ranges, ownership rules, and whether mutation is permitted. Then name the output with the same precision. In this project the surrounding ideas—Merkle trees, Spot checks, Slashing—only compose correctly when this boundary preserves those invariants. A useful implementation note records one representative shape, one smallest valid example, one boundary example, and one invalid example before any optimization is attempted.

From first principles, treat Assign Dual Role as a mapping from available information to a new token representation. Ask which information is genuinely known at this point and which information would leak from the future, evaluation set, opposing player, held-out client, or later pipeline stage. Write the transformation symbolically before translating it into array operations. Every reduction must state its axis; every probability must state its normalization set; every random choice must state its distribution and seed; every learned quantity must state the objective that changes it. This discipline turns an appealing formula into an executable specification that can be challenged with small counterexamples.

The reference implementation should favor clarity over cleverness. Separate validation, the mathematical core, and state updates so each can be tested independently. Use explicit intermediate names that correspond to the derivation rather than compressing the work into one expression. Confirm dtype promotion, broadcasting, device placement, and empty-input behavior. If Assign Dual Role depends on randomness, pass a generator instead of reading hidden global state. If it owns mutable state, return or document the updated state explicitly. The optimized implementation may later fuse operations or reuse buffers, but it must remain numerically comparable with this small version on deterministic fixtures.

Verification for Assign Dual Role needs more than a happy-path assertion. Prove a hand-computable normal case, a boundary case, an invalid case, and at least one invariant. Compare against loss curves, held-out generations, ablations, and human or automated evaluations. Add metamorphic tests when an exact answer is awkward: permutation, scaling, symmetry, conservation, monotonicity, or equivalence under a harmless representation change. Run the test repeatedly under fixed seeds to distinguish deterministic defects from statistical variation. When floating-point arithmetic is involved, justify tolerances from expected rounding error instead of choosing a loose threshold simply because the test passes.

Failure analysis asks how Assign Dual Role can look plausible while being wrong. Inspect data leakage, exposure bias, hallucination, unstable preference signals, and unsafe deployment behavior. Trace one example through every intermediate value and preserve enough logging to reproduce it. Distinguish a contract violation from an optimization failure and from an evaluation-design failure; each requires a different repair. A numerical answer within range is not automatically meaningful, and a rising training metric is not proof that the intended signal is being learned. The strongest debugging move is usually to shrink the input until the complete computation fits on paper, then compare the paper trace with the program line by line.

Productionizing Assign Dual Role changes the question from “does it work once?” to “does it remain trustworthy under load and change?” Measure tokens, parameter memory, attention work, decoding latency, and evaluation coverage. Define observability for inputs, outputs, latency, failures, drift, and resource saturation. Decide what happens on malformed data, cancellation, partial worker failure, unavailable accelerators, or a distribution outside the training envelope. Version configuration and schemas with the code, preserve reproducible seeds where appropriate, and expose a safe fallback. Optimization is accepted only when the reference tests, numerical comparisons, and task-level metrics remain within an explicitly documented budget.

• Part: Decentralized Committee, Incentives, and End-to-End Evaluation. Sample verifier committees, aggregate votes by majority, implement rewards and slashing, and run honest and malicious rounds reporting end-to-end verification cost.
• Normal case: choose the smallest input that exercises the intended transformation.
• Boundary case: use an empty, singleton, saturated, masked, terminal, or maximum-size input as appropriate.
• Invariant: verify shape, range, conservation, normalization, symmetry, immutability, or monotonicity.
• Production evidence: record correctness, latency, memory or cost, and the exact configuration.