# R12 EFC Source-Sealed Quotient-Algebra Compiler Protocol ## Status **REJECTED FOR SOURCE FREEZE / CPU FALSIFIER ONLY.** No neural fit, scored development access, confirmation generation, reasoning claim, or pretraining is authorized by this document. The protected step-300k Shohin checkpoint remains immutable. The user pretraining hold remains active. The candidate is named **Source-Sealed Quotient-Algebra Compiler (SSQAC)**. Its first fixed-solver draft was rejected because a host-authored Macaulay/border-basis circuit would own the substantive reasoning. The revised primary treatment must compile both constraints and a source-deleted algebra microprogram executed by only primitive field/register operations. The fixed exact algebra engine remains a gold ceiling and favorable control. JASEC and hardcoded SLRA remain additional controls. ## Current implementation gate (2026-07-24 EDT) SSQAC remains **NO-GO for source freeze and reasoning claims**. The current implementation has established: - an exact sparse F_257 quotient compiler with portable RREF/provenance, complete-prolongation, order-ideal, commuting-multiplication, Boolean idempotence, consequence, and status certificates; - bounded adaptive closure from emitted-generator degree at most four through closure degree at most eight. This closes the concrete degree-four failures: both `xyz-1` and a six-variable one-hot ideal stabilize and independently replay at closure degree five; - an independently implemented verifier in `pipeline/verify_ssqac_quotient_artifact.py` that does not import the producer and accepts real degree-five producer artifacts while rejecting digest, source, row, provenance, span, query, value, domain, and evidence tampering; - an independently supplied intended-Boolean-zero-set gate in addition to the F_257/F_263 consistency check; - a primitive branch-free row ALU and a 2,317,847-parameter recurrent neural controller with deterministic coordinate encodings and content-addressed row/column pointers; and - a generated 32-unit/128-cell law-collision CPU family spanning eight geometries and 32 late-query addresses. Every unit has exactly two direct completions, opposite laws select opposite completions, and fact worlds have incompatible complete-action cycle invariants. Majority, stump, depth-two tree, and logistic held-out attacks are 50%; nearest-neighbor is 56.25%. The generated family is now connected to the gold quotient engine through a strictly assessor-side bridge. For all 128 cells it independently enumerates the two direct completions, creates one Boolean one-hot variable per completion, translates the source law to a completion-selector constraint, translates the fresh late query to an answer polynomial, checks its independently enumerated zero set over F_257/F_263, exports the consequence, and passes the standalone verifier. Law deletion returns `AMBIGUOUS`; opaque key and completion-variable recoding preserve the result. The bridge receipt hash-binds source, query, completion set, generators, intended semantics, certificate, outcome, and artifact. Completion variables and bridge artifacts are gold-oracle data and are forbidden candidate inputs. The controller result is negative outside its training geometry. The original absolute-index controller reached `60/64` closed-loop certificates on fresh same-geometry matrices, but only `2/64` when trained on at most `3x4` and evaluated on `4x5--4x6`. Replacing untrained absolute row/column/step tables with deterministic coordinates and pointer heads improved unseen-geometry teacher-forced instruction accuracy from `85.475%` to `91.258%`, yet produced `0/64` autonomous certificates (`57` invalid, `7` overlong). This is an exposure-bias/control-stability failure, not evidence of an algorithm. The first H100 launch (`700847`--`700849`) failed before fitting because a rank-deficient reverse-pivot matrix exposed premature “settled row” detection in the preparation-only trace oracle. No model result was produced. The exact counterexample was reduced to 2x3 and 3x3 reverse-identity matrices; the oracle now checks later leading columns before accepting a settled row, and focused tests pass. Corrected three-seed jobs `700853`, `700854`, and `700855` are isolated one-H100 variable-geometry development fits. They do not load or write the flagship and cannot authorize pretraining. Their purpose is only to distinguish undertraining from architectural instability. No result is admitted until exact reports are complete and reviewed. ## Question Can a compact model compile raw anonymous source into a finite algebra of episode-local constraints, preserve correlations among multiple legal machine completions, and prove a query or machine cell only when it is invariant across that algebra? The intended distinction is: - JASEC predicts one binding and one machine, then iteratively makes them self-consistent; - hardcoded SLRA receives a fixed permutation/balance residual whose unique zero already identifies the answer; - SSQAC predicts source constraints, then a learned source-deleted controller constructs and checks their joint solution set through a counted algebra microprogram, sealing only consequences that are algebraically forced. This would still be bounded reasoning. It does not establish unrestricted general reasoning unless the same mechanism later transfers across natural task families and direct interaction. ## Prior-Art And Novelty Boundary Neural prediction of Groebner bases, neural guidance of exact border-basis algorithms, differentiable theorem proving, and probabilistic algebraic constraint layers already exist. Relevant primary references include: - [Learning to Compute Groebner Bases](https://arxiv.org/abs/2311.12904); - [Computational Algebra with Attention](https://arxiv.org/abs/2505.23696); - [Learning Reasoning Strategies in End-to-End Differentiable Proving](https://proceedings.mlr.press/v119/minervini20a.html); and - [A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction](https://proceedings.mlr.press/v286/kurscheidt25a.html). Therefore SSQAC may not claim novelty merely for combining a neural emitter with polynomial constraints, Groebner/border-basis computation, or a symbolic executor. The only potentially distinct empirical claim is the complete contract: raw anonymous law text is compiled into exact constraints; the source and compiler are destroyed; a learned controller constructs a certificate using only primitive field/register operations; later consequences are sealed only when forced across all legal completions; and the same learned mechanism transfers across paired opposite laws, unseen law topologies, variable ontologies, renderers, and task families under matched controls. Novelty remains unclaimed until that full contract passes and a dedicated literature review finds no equivalent system. ## Claim Boundary A positive SSQAC result may support: > bounded, architecture-native compilation and composition of unseen > episode-local laws after irreversible source deletion. It may not support: - unrestricted general reasoning; - a claim that the 125M Shohin trunk alone acquired reasoning; - reasoning attribution to parameter count; - natural-language transfer without a separate held-out task-family result; or - source deletion if the compiler process, source mount, GPU state, or temporary workspace remains available to the query process. ## Mathematical Object Let `z = (z_1, ..., z_d)` contain Boolean physical-key assignment atoms and categorical transition/observer atoms. A source-attached neural emitter maps each raw record to a sparse bounded-degree polynomial over `F_257`: `f_r(z) = sum_alpha c[r, alpha] z^alpha`. The source-defined ideal is: `I_S = < z_i^2-z_i, one_hot(z), f_1, ..., f_m >`. The retained semantic object is the finite coordinate algebra: `A_S = F_257[z] / I_S`. The first implementation is bounded: - at most 128 source generators; - at most 4,096 admitted monomials; - maximum **emitted-generator** degree four; - maximum adaptive complete-closure degree eight; - quotient dimension at most 256; - exact arithmetic modulo 257; - no floating rank decision; - overflow, incomplete closure, ambiguity, or inconsistent constraints fail closed with distinct statuses. The degree-four bound does not cap the degree needed during closure. Admitted square-free monomials may have higher degree. The runtime must either prove that its admitted monomial set is closed under every quotient generator multiplication needed by the board or abstain. A degree-truncated Macaulay span is not the quotient algebra and may not support a certificate. Because every variable is Boolean and `257 != 2`, the base quotient `F_257[z] / ` is a finite product of fields indexed by Boolean assignments. Every further ideal in that product is radical. The implementation may therefore use rootwise constancy as an equivalent assessment oracle, but the candidate runtime must establish the same equality by a complete exact algebra certificate. One-hot constraints are additional generators inside this Boolean quotient; they do not relax the closure requirement. Every board law must pass exhaustive Boolean truth-table equivalence between its intended semantics and its `F_257` polynomial encoding. A second-prime audit over `F_263` must preserve the Boolean zero set. A law whose coefficient reduction changes its intended semantics, including a coefficient that vanishes modulo the field characteristic, is rejected before any split is created. A fixed exact sparse Macaulay/border-basis engine computes the CPU gold ceiling and favorable fixed-solver control: - closure under admitted monomial multiplication; - exact row reduction over `F_257`; - a quotient basis; - multiplication operators; - normal forms for machine and query polynomials; and - optional ideal-membership certificates. This engine is not the primary reasoning treatment, even when implemented in Torch/CUDA. Reimplementing a solver as tensor operations does not make its algorithm model-owned. The claim-bearing runtime exposes only a fixed-shape register file and these primitive operations: 1. copy or clear a row/register; 2. add a selected row multiplied by one selected `F_257` scalar; 3. swap two selected rows; 4. request one public square-free monomial prolongation; 5. multiply one retained normal form by one selected variable; 6. compare one register to zero or another register; 7. append one bounded certificate record; and 8. `HALT_SUCCESS`, `HALT_AMBIGUOUS`, `HALT_UNSAT`, `HALT_INCOMPLETE`, or `HALT_OVERFLOW`. A tied learned controller selects the opcode, row/register addresses, coefficient, and halt decision at every cycle from only the current sealed algebra registers, public masks, and its private recurrent state. Host code may validate types and bounds but may not select pivots, prolongations, row operations, basis order, or stopping time. The controller must generate the closure/reduction/certificate schedule after the source compiler has exited. Its maximum cycle count and every field operation are included in the resource receipt. The claim-bearing implementation may not import or invoke SymPy, Sage, a Groebner/border-basis package, a SAT/SMT solver, a Python semantic search loop, the board generator, the label oracle, the gold engine, or assessor feedback. For every successful seal, the receipt must contain enough source-free information for an independent exact checker to verify: - the admitted monomial order and multiplication closure; - every pivot and modular inverse used in row reduction; - reduction of every source generator to zero; - reduction of each Boolean/one-hot schema generator to zero; - the quotient dimension and multiplication-table consistency; and - the claimed answer or cell equality in the quotient. Failure to emit or independently verify this certificate is abstention, not an incorrect answer and not a successful reasoning case. Completeness additionally requires an order ideal connected to `1`, unique rewrites for every border monomial, pairwise commuting multiplication matrices, `M_i^2=M_i` for every Boolean variable, all generators reducing to zero, `1` not reducing to zero, and stable rank under one complete prolongation beyond the retained border. Any failed condition is `INCOMPLETE` or `UNSAT`; it may never be converted to a certified answer. ## Behavioral Uniqueness For answer polynomial `g[q,y](z)`, answer `y` is certifiable only when: `NF_I(g[q,y]) = 1` and every other answer normal form is zero. A machine cell may be sealed only when its category is constant over every root of `I_S`. If several machines remain but every legal late query has the same answer, that behavior may be sealed with an explicit quotient receipt. If two roots are distinguishable by a legal late query, the compiler must abstain. The runtime statuses are disjoint: - `AMBIGUOUS`: complete certified algebra, multiple query-distinguishable roots; - `UNSAT`: complete certified algebra with `1` in the ideal; - `INCOMPLETE`: closure or certificate could not be established; - `RESOURCE_OVERFLOW`: a registered dimension, monomial, row, or cycle bound was exceeded; and - `CERTIFIED`: the claimed behavior is constant in the complete quotient. Only the first status is epistemic abstention. `INCOMPLETE` and `RESOURCE_OVERFLOW` are coverage failures and can never satisfy an ambiguity gate. This is an information boundary, not an optimization preference. No deterministic source-deleted system can recover information absent from the source-defined version space. ## Law-Collision Board The decisive board must prevent finite-template and marginal shortcuts. Every paired episode contains: 1. a partial anonymous machine whose direct records admit at least two completions; 2. an episode-local law that selects exactly one completion; 3. an opposite-law twin with byte-identical non-law evidence and a different selected completion; and 4. fresh late queries generated only after the source-side artifact is sealed. Every primary unit is a balanced counterfactual quadruple, not only a law pair: 1. facts `F0` with law `L0`; 2. the same facts `F0` with opposite law `L1`; 3. counterfactual facts `F1` with law `L0`; and 4. the same counterfactual facts `F1` with law `L1`. All four target combinations must be equally represented. This prevents a law template alone or a fact template alone from identifying the completion. Candidate completion indices, enumeration order, and canonical labels are never model features or training labels. The deterministic four-state `F0/F1 x L0/L1` fixture is only the smallest CPU mechanics falsifier. It is explicitly **ineligible for neural training, development, confirmation, or promotion**: its four targets admit a shallow fact-bit XOR law-bit rule, `F0` and `F1` are state-isomorphic, and its fixed late-query address breaks that symmetry. Passing it proves only exact enumeration, law deletion, clause deletion, and counterfactual plumbing. The claim-bearing board must contain many independently generated, nonisomorphic quadruples with varying queries and must separately prove that fact-only, law-only, rank/marginal, positional, and learned direct classifiers remain at chance. Primary collision pairs must match: - state/action/observer/answer cardinalities; - all unary and row marginals; - key frequencies and occurrence counts; - direct visible records; - source length and record count; - depth-zero, depth-one, and depth-two behavior multisets; - renderer statistics; and - candidate-completion cardinality. They may differ only through a determining degree-three or degree-four relation. The law must therefore require joint composition rather than reading one marginal or one candidate-local zero. ### Variable Geometry The full qualification board varies: - 5--13 states; - 2--5 actions; - 1--4 observers; - 2--6 opaque answers; - one to four hidden rows; - transition, observer, coupled transition-observer, and independent trajectory-identification task families; and - DSL, equations, controlled English, and an independently implemented confirmation renderer. Padding and maximum geometry are fixed before training. Geometry values, family IDs, renderer IDs, split IDs, source hashes, and canonical program IDs are not model inputs. ### Split Rules Before rendering, reject overlap in: - canonical machine isomorphism; - canonical Boolean zero set and law ideal under variable permutation, Boolean complement, and machine isomorphism; - law circuit topology; - generator lineage; - task family; - renderer implementation; - semantic program; - query behavior signature; and - paired target fiber. Training may use simple degree-two/three laws and two renderers. Development holds out deeper compositions, one renderer, ontology sizes, and machine families. Confirmation is generated once after source, executable, weights, optimizer decision, and assessor are frozen; it holds out complete law families, one task family, a separately implemented renderer, and depths 4--12. The confirmation family definition, generator executable, count bounds, and seed derivation must be committed before the weights are frozen. The seed itself is derived from a later public beacon. This prevents selecting a confirmation distribution after inspecting the trained model while preserving post-freeze unpredictability. ## Zero-Parameter Gates Before any neural code or board labels enter a candidate process: 1. Exhaustively enumerate the bounded version space for every CPU fixture. 2. Without the law, prove that at least two behaviorally distinguishable completions remain. 3. With the law, prove that exactly one completion or one query-equivalence class remains. 4. Law twins must share exact non-law bytes and select opposite completions. 5. Law deletion must make the gold compiler abstain. 6. Removing a determining clause must make the gold compiler abstain. 7. Adding a redundant generator already in the ideal must change nothing. 8. Opaque-key recoding must conjugate the quotient representation and preserve every answer. 9. A direct rank/marginal classifier must remain at chance on collision pairs. 10. The gold quotient-algebra ceiling must solve 100% or SSQAC is killed before a neural fit. 11. Every registered gold case must remain inside all monomial, quotient, workspace, and cycle bounds; overflow is a failed coverage case. 12. Intended-law truth tables and zero sets must agree over both `F_257` and `F_263`. The first mandatory falsifier uses three Boolean variables: `I_facts = `. It has roots `{000,111}`, so query `x` is `AMBIGUOUS` while `x-y` is certifiably zero. Adding `L0=` must leave only `000`; adding `L1=<(1-x)(1-y)(1-z)>` must leave only `111`. Law deletion restores ambiguity; adding generator `1` returns `UNSAT`; omitting `xyz` from the admitted closure returns `INCOMPLETE`; and a semantic law containing a coefficient that vanishes modulo 257 is rejected by the field-semantics validator. Variable permutations preserve every decision and simultaneous Boolean complement swaps `L0` with `L1`. The reference generator and exhaustive oracle are preparation/assessment tools. They must be absent from the candidate runtime closure. ## Neural Architecture The provisional complete system replaces JASEC's 19,013,524-parameter assignment-machine equilibrium rather than adding to it: | Component | Parameters | |---|---:| | Protected Shohin trunk | 125,081,664 | | Gauge-invariant source/witness encoder | 44,658,064 | | Detached query parser | 748,033 | | Clause-to-polynomial emitter | 3,400,000 | | Typed monomial/gauge router | 1,600,000 | | Tied source-deleted algebra microcontroller | 12,000,000 | | Certificate/query/intervention heads | 2,000,000 | | **Complete provisional system** | **189,487,761** | | **Headroom below 200M** | **10,512,239** | These counts are a design budget, not an admission. A live constructor must implement masked variable geometry, opaque-answer binding, the sealed quotient wire, and the late-query parser; recompute unique parameters; and remain strictly below 200,000,000. The current fixed `8/3/2/4` JASEC runtime and detached hard-machine worker do not instantiate this system. No parameter receipt is valid until the new constructor and artifact format exist. The complete resource vector must report more than trainable parameters: fixed-runtime source bytes, monomial-table bytes, field-inverse bytes, peak workspace, sealed-artifact bytes, primitive field operations, controller cycles, sequential depth, wall time, and peak device memory. The fixed-solver control receives the same representation bounds and its full algorithmic resource vector is reported rather than treated as free. The score-bearing emitter receives only raw source bytes or their ordinary tokenization, position/mask tensors, and the frozen Shohin residuals computed from those bytes. It must infer record boundaries, occurrence identity, coreference, and law roles itself. Host-provided physical-key incidence, equality partitions, record-role tensors, candidate completions, or parsed schema fields are oracle diagnostics and are ineligible for treatment. The emitter must not receive: - parsed law ASTs; - host-provided key incidence or equality matrices; - record, clause, witness, or law-role labels at inference; - SLRA residuals; - target machine probabilities; - supervisor tensors; - target categories; - candidate scores from an oracle; - query answers; - split/family/renderer IDs; or - source/canonical hashes as features. The algebra circuit receives emitted coefficients and fixed public Boolean / one-hot schema generators. It may not receive target labels or reference solutions. ### Discrete coefficient learning Exact modular row reduction is intentionally outside the gradient path. Training may supervise a bounded sparse sequence of monomial indices and `F_257` coefficients derived solely from the training source law, with all machine completions, query answers, recurrent states, and executor outcomes withheld. At inference, logits are hardened once into exact coefficients before the algebra circuit runs. Straight-through gradients, soft modular arithmetic, or gradients through an oracle completion are forbidden in the primary arm. Each emitted term uses categorical heads for generator boundary, monomial index, coefficient in `{0, ..., 256}`, and sequence `STOP`. Duplicate monomials inside one generator are merged modulo 257 after hardening. Missing `STOP`, support overflow, invalid schema type, an all-zero required generator, or a top-two logit margin below the frozen hardening threshold produces `INCOMPLETE`. Generator ordering is canonicalized only by source occurrence order and public type; target/candidate order may not enter canonicalization. Development and confirmation report three separate levels: 1. soft term/support accuracy before hardening; 2. exact hardened generator multiset accuracy; and 3. independently certified behavior after controller execution. Only the third level is a reasoning score, and it is credited only when the complete certificate verifies. This makes the first SSQAC candidate a neural source-to-constraint compiler followed by a learned source-deleted algebra controller and a primitive field ALU. It is not an end-to-end differentiable discovery claim. A favorable equal-parameter sequence compiler that emits the final machine directly must receive the same source-side supervision budget. ### Late-query semantics The first claim-bearing query language contains only public predicates over the sealed ontology: value/category of one anonymous cell, equality of two cells, or one public bounded composition of those predicates. The counted late-query parser may emit only predicate kind and anonymous codebook addresses. It may not emit answer coefficients, a target category, a normal form, or a certificate. After hard pointer/type selection, a source-independent public constructor maps the typed query to Boolean answer-indicator polynomials. Those indicators must each be Boolean in the quotient, pairwise exclusive, and sum to one. The same constructor and costs are shared by treatment and controls. Gold query pointers are an oracle diagnostic only. ## Source Deletion Claim-bearing evaluation uses three processes: 1. the compiler process receives source bytes, emits the hardened exact constraint tensor and anonymous symbol codebook, then exits; 2. the learned algebra-controller process receives only that tensor, codebook, fixed controller weights, and primitive ALU runtime; it emits a complete quotient/certificate artifact, destroys its constraint/workspace/private state, and exits; and 3. only then is the late query generated. The detached query process receives the quotient/certificate artifact, anonymous codebook, query parser, and query bytes. Each successor starts only after the predecessor's cgroup, GPU context, shared memory, mount namespace, temporary files, and writable artifact handles are destroyed. The claim-bearing runtime is independently packaged; it may not add the repository to `sys.path` or import from a writable checkout. A closed file-descriptor inventory, mount/pivot-root receipt, process-death receipt, and network-denial receipt are mandatory. The final detached process receives only: - the fixed quotient/certificate artifact; - a bounded model-emitted anonymous symbol codebook included in that artifact; - the counted late-query parser/runtime; and - late query bytes. It must not receive source tokens, KV cache, residuals, record states, constraint-emitter state, hardened source generators, algebra-controller state, Macaulay workspace, labels, or compiler diagnostics. Literal source keys may not be copied across the boundary as a host dictionary. The late-query parser must match query bytes to the sealed anonymous codebook through its counted neural path. A gold string/equality matcher is an oracle ceiling only. Codebook deletion, permutation, collision, and donor transplantation are required causal controls. ## Matched Controls All neural controls must match train examples, optimizer, updates, parameters, batching, and candidate runtime where applicable. 1. **Gold full ceiling:** exact generators plus fixed exact algebra engine. This is an oracle ceiling, never a reasoning result. 2. **Gold constraints plus learned controller:** isolates source-deleted execution planning. 3. **Emitted constraints plus fixed exact engine:** favorable semantic-compiler control. It may establish source-to-law compilation but not model-owned algebraic execution. 4. **Current JASEC:** factorized point-estimate equilibrium. 5. **Equal-parameter unstructured compiler:** predicts machine logits directly from the same source states. 6. **Generator derangement:** precommitted source-independent permutation of generator-to-record alignment. 7. **Rank-one/factorized algebra:** removes generator interactions while preserving coefficient marginals. 8. **Controller-program derangement:** replays a type-valid action schedule from another same-shape instance. 9. **Fixed pivot/closure schedule:** same primitive ALU and maximum cycle budget, no learned controller. 10. **Closure truncation:** stops before degree-three/four consequences. 11. **Law-masked and same-length law-shuffled sources.** 12. **Zero/random logits through any hardening/projector diagnostic.** 13. **No-projector unconstrained predictions.** 14. **Real Shohin trunk, zero trunk, random frozen trunk, and fixed feature-permuted trunk.** 15. **Source-retained diagnostic:** explicitly ineligible for promotion. The treatment must beat the strongest eligible control. Beating only a broken or information-poor control is not evidence. ## Causal Interventions The following are required: - opaque-key recoding; - redundant-generator insertion; - determining-generator deletion; - `do(z_i=c)` ideal extension; - law-twin swap with fixed non-law source; - donor sealed-algebra swap between identical non-law completion fibers; - source-record reorder and distractor insertion; - renderer paraphrase; - closure-depth truncation; and - compiler-to-query process destruction. Donor swaps are valid only when no donor completion index, target tensor, candidate packet, source state, or query answer crosses with the sealed algebra. The recipient's final machine and every distinguishing query must follow the donor law. ## Promotion Gates The CPU mechanics phase advances only if: - gold exact machine/query result is 100%; - every underdetermined or determining-clause-deleted case abstains; - all recoding, redundant-generator, `do`, and source-deletion tests are exact; - fixed-width workspace bounds never overflow; and - no candidate runtime dependency imports an external solver. The neural development phase advances only if all preregistered seeds achieve: - at least 95% `CERTIFIED` coverage on information-complete cases and zero `RESOURCE_OVERFLOW` on the registered gold distribution; - at least 95% exact unconstrained sealed programs in every held-out cell; - at least 95% law/fact counterfactual consistency; - at least 95% donor-law following; - at least 95% detached depth-4--12 query exactness; - at least 99% gauge/renderer invariance; - 100% abstention on information-insufficient cases; - the learned controller certifies at least 95% of cases certified by the same emitted constraints through the fixed exact engine; - controller-program derangement and fixed-schedule controls each trail the learned controller by at least 20 points; - at least 20 points over current JASEC on collision cases; - at least 10 points over the strongest eligible matched control; and - paired 99% confidence lower bound above five points. Confirmation remains sealed unless every development gate passes without threshold changes. ## Direct Behavior Inspection Before scoring, freeze a separate nonconfirmation inspection split of at least 32 researcher-readable episodes. For each, preserve: - raw source; - direct-fact completion fiber; - emitted sparse generators; - quotient dimension and closure status; - algebraic certificate or abstention receipt; - sealed machine; - late queries and answers; and - matched law deletion, law swap, fact mutation, paraphrase, key recoding, reorder, and distractor transcripts. The model should preserve semantics under paraphrase/recoding/reorder, change under law or determining-fact interventions, and abstain when the source no longer determines behavior. Sealed confirmation sources, generators, answers, and transcripts remain unreadable until an immutable score, independent assessment, and decision artifact exist. Post-decision transcript release cannot authorize adaptation or rescoring on that board. ## Path To General Reasoning Passing this board establishes only bounded unseen-law reasoning. The same sealed algebra mechanism must then be evaluated without architecture changes on held-out natural task families: - finite-state procedural instructions; - symbolic algebra and equation constraints; - multi-step logic; - program-state and code contracts; and - ordinary language questions requiring source-defined rules. Public math/code benchmarks and direct conversation remain final capability gates. A synthetic pass with no natural-family transfer is retained as a scientific component, not reported as genuine general reasoning. ## Immediate Work Order 1. **PASS:** exact finite-field gold compiler and primitive row ALU. 2. **PASS as mechanics / rejected as board:** the three-variable and minimal quadruple fixtures; the minimal quadruple is permanently shortcut-tainted. 3. **PASS at CPU gold boundary:** adaptive closure, intended semantics, disjoint statuses, and independent artifact verification. 4. **PASS as CPU falsifier only:** generated 32-unit collision family and preregistered shallow-classifier audit. Promotion remains false. 5. **FAIL:** learned-controller transfer from `<=3x4` to `4x5--4x6`; await the bounded H100 scale falsifier, then change training dynamics or architecture rather than interpreting teacher forcing. 6. **PASS at gold boundary:** connect all 128 generated cells to the independently verified quotient oracle with complete source/query/outcome receipts; law deletion is ambiguous and recoding is exact. 7. **PASS as user-space custody mechanics:** the compiler, candidate, and assessor now run as separate processes. The source workspace is deleted before candidate launch; closed-world manifests, file hashes, process ordering, guarded reads, and network-denial audit hooks fail closed. This is not a hostile-kernel isolation claim. 8. **PASS as exact structural accounting:** an independent resource receipt replays quotient artifacts and primitive instruction streams, counts variables, generators, terms, ranks, RREF/provenance support, opcode schedules, abstract cycles, sequential depth, and declared peak workspace. Wall time and device memory remain external observations and cannot be fabricated by the structural receipt. 9. **FAIL in bounded CPU smoke:** reactive step-free DAgger produced 0/8 closed-loop certificates on strict larger geometry after two correction rounds; expert-state accuracy fell from 46.3% to 33.7%. The mechanics and zero-oracle final rollout pass, but this is evidence against naive on-policy aggregation, not a reasoning result. 10. **FAIL at H100 imitation boundary:** standard recurrent jobs `700853` and `700854` certified 0/512 and 1/512 larger-geometry programs at 90.863% and 91.562% teacher-forced instruction accuracy. Reactive step-free jobs `700857` and `700858` both certified 0/512 at 88.314% and 89.141%. Replacement seed `700859` certified 1/512, making the standard aggregate 2/1,536 = 0.1302%. Paired larger-data/batch jobs `700873` and `700874` remain active only as utilization/scale measurements. Jobs `700855` and `700856` were lost to or stopped on anomalous `evc33`; neither provides a model result. No job read or wrote the flagship checkpoint. 11. **FAIL under strict endpoint:** a bounded equivariant defect-energy treatment reached 96/96 unordered-basis certificates but only 1/96 under the original canonical RREF verifier; energy-only reached 2/96 and random-label 0/96. Endpoint weakening explains the apparent win. 12. **PASS as counted host-search ceiling only:** bounded structural search reaches 16/16 at `4x5--4x6` and 8/8 at `5x7--5x8`, while randomized guidance reaches 1/16 and 0/8. It uses up to 3,771 expanded nodes, 55,791 edges, and depth 22. This is a conventional external algorithm and is not native reasoning. 13. **FAIL despite solved utilization:** a corrected vectorized reactive policy has exact row/column recoding tests, no recurrent state or step signal, and a strict matrix-only final rollout. Three H100 seeds reached 97--99% sampled GPU utilization but certified 0/1,536 aggregate at approximately 83% teacher-forced full-instruction accuracy. Efficient reactive imitation is closed as a sufficient mechanism. 14. Implement the sealed quotient wire, anonymous codebook, and late-query parser. 15. Hostile-audit the complete CPU/controller boundary and matched controls. 16. Freeze a neural emitter only if all prior gates pass. Do not generate scored confirmation data or start pretraining.