# ECCR Next-Architecture Preregistration **Status:** preregistered proposal; no result and no capability claim **Date:** 2026-07-23 **Proposed treatment:** Monotone Counterexample-Transport Fiber Reactor (MCTFR) ## 1. Frozen evidence and diagnosis The score-bearing boundary is the source-deleted physical tensor bundle: complete deterministic transitions, observation-equality tensors, and active record/generator/query masks. No quotient, class identifier, path certificate, family, motif, renderer map, or assessor output may enter `forward`. ### Existing round-8 results | Run | Train exact | Dev exact | Dev hard-valid | Legal but wrong | First hard-failure counts | |---|---:|---:|---:|---:|---| | pairwise, seed `2026072303`, data `2026072304` | 250/256 | 40/64 | 46/64 | 6 | observation 10, generator 4, transitivity 4 | | pairwise, seed `2026072305`, data `2026072306` | 254/256 | 45/64 | 45/64 | 0 | observation 7, generator 11, transitivity 1 | | record-fiber, seed `2026072305`, data `2026072306` | 254/256 | 44/64 | 44/64 physical; 64/64 equivalence | 0 | 10 observation-invalid and 20 descent-invalid; the former are a subset of the latter | The two pairwise runs therefore give 85/128 exact and 91/128 valid development decodes. Of 43 total misses, 37 (86.0%) are rejected before quotient scoring and 6 (14.0%) are legal refinements of the target. The six legal errors have coarseness precision 1.0 and reduced recall: they split a true class rather than inventing a legal coarser quotient. Reported pairwise failure reasons are ordered first failures because the decoder checks transitivity, then observations, then generators; they are not guaranteed to be disjoint latent causes. The matched record-fiber result is the decisive architectural control. It guarantees reflexivity, symmetry, transitivity, and exact projector laws on 64/64 examples, but exactness falls from 45/64 to 44/64. It makes 59 false-collision ordered pairs, zero false splits, and reaches only 44/64 generator-descent-valid examples. Its 16 noncommuting-context examples score 3/16, with 41 false collisions. Structural equivalence decoding is therefore not the missing capability; the shared encoder is merging records before it has transported all observation and generator counterexamples. ### Exact implementation causes 1. **Universal constraints are represented by means.** The current encoder averages query evidence, outgoing generator evidence, incoming evidence, and global record evidence. A single violating query or generator is diluted as `Q` or `G` grows. Development uses `G,Q in {3,4}`, while train uses `G,Q in {1,2}`. All 17 pairwise observation first-failures occur in the unseen multisensor family. 2. **The final pair head has no persistent pair state.** It must reconstruct `R(T_g i,T_g j)` from two compressed unary record embeddings. The required greatest-fixed-point operator lives on record pairs, not individual records. 3. **Generator composition is collapsed before comparison.** Generator states begin identically and are updated from pooled transition marginals. Systems with matched unary marginals but different ordered compositions can remain indistinguishable. The shared 3/16 noncommuting-context result across the pairwise and record-fiber decoders is the clearest symptom. 4. **The current physical residuals are weak averages.** Observation and descent residuals each have weight `0.05` and average over every active constraint. They do not impose a count-invariant worst-case margin. 5. **Record-fiber replicas are correlated, not independent error correction.** Five votes share the encoder and head input. Equality of thresholded rows guarantees an equivalence relation, but a systematic row collision merges an entire class. The fresh run's minimum absolute vote margin is only `0.00743`. 6. **The corpus does not identify architecture from coverage.** Train and development simultaneously change geometry (`N/G/Q`), latent-state count, family, and motif. The results prove failure on the frozen held-out distribution, but not whether larger geometry or unseen semantics is the dominant causal variable. A factorial control is mandatory. ## 2. Mathematical target For records `X`, observations `o_q`, and deterministic generators `T_g`, the coarsest causal congruence is the greatest fixed point ```text Phi(R)(i,j) = [AND_q o_q(i) = o_q(j)] AND [AND_g R(T_g(i), T_g(j))]. ``` Equivalently, distinction is the least fixed point obtained by propagating an observational counterexample backward through aligned generator transitions. The architecture should learn this local transport law and its stopping geometry, rather than infer a global relation from pooled unary summaries. ## 3. Preregistered treatment: MCTFR ### 3.1 State and routing - Maintain a tied recurrent pair state `z_t[i,j]` for every active ordered record pair. Use exactly eight rounds, matching `N <= 8`; no host-observed adaptive loop or retry is allowed. - Initialize `z_0[i,j]` from the full per-query equality pattern `observation_equal[i,q,j,q]`, using shared query encoders plus both log-sum-exp and max channels. Do not use a mean-only summary. - At round `t`, gather the aligned successor-pair states `z_t[T_g(i),T_g(j)]` directly with the physical one-hot transition tensor. A shared generator-equivariant cell aggregates them with max/log-sum-exp, preserving the universal-constraint scale as `G` changes. - Update with a tied monotone residual cell: the designated distinction channel may increase but not decrease across rounds. Nonnegative parameterization applies only to that channel; auxiliary channels remain unrestricted. - Ordered generator composition is represented by recurrence: round `t+1` sees the same-generator successor pair whose round-`t` state already summarizes all length-`t` continuations. No generator identity embedding or canonical generator numbering is introduced. ### 3.2 Observation-safe anonymous fibers The hard signature for record `i` concatenates: 1. immutable observation-fiber bits `B_obs[i,q,a] = [o_q(i) = o_q(a)]` for every active query and record anchor; 2. learned dynamical fiber bits produced from `z_8[i,a]`. Hard equivalence is equality of complete active signature rows. This retains the record-fiber guarantee of an equivalence relation. The immutable observation fibers additionally guarantee observation preservation: if two signature rows match, the anchor bit at each query forces their observations to match. These bits use only input equality structure, are invariant to injective value recoding, and transform equivariantly under record/query reindexing. Generator descent is deliberately **not** repaired or hard-coded. It remains the primary learned and falsifiable gate. ### 3.3 Objective Use final target-relation supervision only; intermediate oracle partitions or distinction paths are prohibited. ```text L = L_balanced_fiber + 1.0 * L_max_descent + 0.5 * L_fixed_point + 0.5 * L_orbit + 0.1 * L_margin. ``` - `L_balanced_fiber`: separately normalized positive/negative supervision for the anonymous final relation and learned fiber bits. - `L_max_descent`: per-episode smooth-max hinge over `p(i~j) - p(T_g(i)~T_g(j))`; no averaging over generators or pairs. - `L_fixed_point`: consistency between the final two recurrent relation proposals, without changing the hard output or invoking a closure operator. - `L_orbit`: mapped-logit consistency across matched reindex, value-recode, split, and merge presentations; mappings are offline training metadata and never enter `forward`. - `L_margin`: keep all active hard bits at least one logit unit from zero. The added module is capped at 24,000,000 parameters. With the protected 125,081,664-parameter Shohin base, the complete system is capped at 149,081,664 parameters, below the 200M ceiling. ## 4. Controls and identifiability Every treatment comparison uses identical packets, optimizer updates, batch order, threshold, and seed. 1. Existing round-8 pairwise encoder/head. 2. Existing round-8 record-fiber model. 3. Parameter-matched generic pair-state reactor with mean pooling. 4. MCTFR without successor-pair transport. 5. MCTFR with the observation-fiber skip but the old unary encoder. 6. MCTFR with generator alignment independently permuted on one transition side; it must lose descent competence. 7. Frozen random MCTFR and shuffled final targets; neither may pass. 8. A non-neural Boolean partition-refinement oracle is reported only as a mechanics ceiling and is excluded from every neural claim. The corpus analysis must add an equal-budget 2x2 diagnostic board: seen/unseen geometry crossed with seen/unseen family/motif. Exact, latent, action, path, and orbit leakage gates remain unchanged. This board determines whether remaining error is cardinality extrapolation, semantic transfer, or their interaction; it cannot replace the frozen 256/64 score. ## 5. Frozen gates Run the frozen 256/64 board on three fresh model/data seed pairs. Promotion requires **every** seed to satisfy: - train exact relation at least 99%; - development equivalence validity exactly 100%; - development observation validity exactly 100%; - development generator-descent and total physical validity at least 95%; - development exact target relation at least 90%, with median at least 95%; - conditional exactness among physically valid relations at least 98%; - false-collision and false-split rates each at most 0.5%; - noncommuting-context exactness at least 80%; - reindex and value-recode orbit consistency 8/8, all-orbit consistency at least 7/8; - at least 15 percentage points exact improvement over the matched record-fiber control and a paired two-sided McNemar `p < 0.05`; - all source-deletion, source-hash, split-isolation, parameter, and single-hard- decode custody gates pass. Kill or redesign the treatment if any seed is below 85% exact, below 90% physical validity, or below 60% noncommuting-context exactness. Do not scale a failed pilot to the 48k/4k board. Diagnostic interpretation is frozen: - observation validity below 100% means the observation-safe fiber contract is incorrectly implemented; - high equivalence/observation validity but low descent validity rejects the counterexample-transport cell; - high physical validity but low exactness, with precision 1 and recall below 1, identifies conservative under-merging/coarseness failure; - good seen-geometry and bad unseen-geometry cells identify count transfer; - good geometry-complete but bad unseen-motif cells identify semantic composition failure. ## 6. Why this is not external symbolic execution MCTFR performs one fixed differentiable forward pass from physical tensors to model-owned pair states and anonymous fibers. The host never computes a partition, chooses a candidate, supplies a certificate, executes a path, checks an intermediate state, retries, closes, or repairs the proposal. Generator routing is a neural architectural adjacency operation, analogous to convolutional routing; the recurrent transition and dynamical signature are learned checkpoint parameters. A single frozen threshold decodes the final fibers once. The immutable observation-fiber skip enforces only an input-preservation law; it does not determine generator closure or the coarsest quotient. Therefore a random, no-transport, or mean-pool model can still fail the primary descent and exactness gates. A pass would establish bounded source-deleted neural quotient induction, not language reasoning or genuine general reasoning. ## 7. Pre-score hostile-audit amendment This amendment was written after implementation review and before any MCTFR development score was opened. It does not relax any gate above. 1. **Duplicate-idempotent universal aggregation.** The proposed max/log-sum-exp channels are replaced by max/min channels over encoded query and generator evidence. Log-sum-exp changes when a semantically duplicate query or generator is inserted, so it violates the required duplicate-idempotence. Max/min preserves permutation and exact duplicate invariance while retaining two-sided extremal evidence. 2. **Counterexamples cannot appear from a clock.** The first implementation added an unconditional positive softplus increment to every off-diagonal distinction. That creates distinctions even for bisimilar records. The corrected channel can only inherit an already present observational or successor counterexample through a learned gate, followed by a monotone max with its previous value. 3. **Worst-case descent is taken before smoothing.** The original normalized log-sum-exp hinge could hide one positive descent violation among many safe constraints. The corrected objective takes the exact maximum active violation per episode, then applies a smooth hinge. Generator or pair count can no longer dilute a witness. 4. **The fixed-point term is relation-level.** It compares the penultimate and final anonymous soft relation proposals produced by the same dynamical head, rather than comparing one raw state coordinate. 5. **Soft and hard fibers share one semantics.** Soft relation probability is the product of sign-aligned Bernoulli bit-match probabilities, masked by immutable observation compatibility. Hard decoding still thresholds each learned bit once and compares complete rows. 6. **Fail-closed tensor and numeric contracts.** Transition rows must be partial one-hot maps; semantically duplicate query/generator axes must leave states and hard output bit-identical; floating features inherit model parameter dtype; bisimilar pairs must retain exactly zero transported distinction. FP64/BF16, malformed-transition, source-deletion, and pure soft-fiber gradient tests are mandatory. 7. **The scored fiber is transport-bound.** A hostile audit showed that a strictly positive sigmoid gate made nonzero counterexample support propagate exactly even in a random model, while an unconstrained output MLP could ignore that support. The corrected treatment uses a fixed confidence threshold on the transported distinction itself. The learned gate determines whether a counterexample remains above threshold at each depth, and the hard dynamical fiber is exactly that thresholded state. There is no separate learned answer head. 8. **The soft surrogate is extremal, not multiplicative.** Multiplying Bernoulli bit-match probabilities made self-relation less than one and decayed exponentially with record count. The corrected relation uses the minimum signed logit agreement over active fibers, is set to one on the active diagonal, and is invariant to duplicate fibers. 9. **Primary optimization is renderer-blind.** Orbit-paired sampling and mapped renderer-logit supervision are removed from the primary arm. They use assessor-side morphisms and therefore cannot support a strict final-relation- only attribution. The optimizer samples unique train packets using only partition length. Orbit consistency remains assessment-only; a renderer-supervised arm, if ever run, must be labeled as a separate augmentation ablation. 10. **The frozen 256/64 board is tuning-only for MCTFR.** Its development packets and seed have already been inspected by earlier architectures and tests. The first MCTFR result on this board can kill or refine the architecture but cannot confirm it. Any confirmation claim requires a source/config commit followed by one independently generated, previously unopened manifest and one evaluation receipt. The amendment narrows the intended mechanism to counterexample transport that is extremal, duplicate-idempotent, and witness-conservative. It does not add oracle paths, target partitions, host convergence, closure, repair, retry, or development-informed selection. ## 8. Attribution result and closure The first tuning-board treatment and its deterministic matched shuffled-target arm both completed 800 CPU updates from the same source commit, seed, corpus, optimizer configuration, and protected-base receipt. | Arm | Train exact | Development exact | Development physical | False splits | False collisions | |---|---:|---:|---:|---:|---:| | True target | 256/256 | 64/64 | 64/64 | 0 | 0 | | Shuffled target | 256/256 | 64/64 | 64/64 | 0 | 0 | The true-target checkpoint and report SHA-256 values are `a56b0a320c367cdc26ddd541c635d593efa458a425d68e3574f36604cb502d93` and `46eb592ad7fd018b21af9d7cd1c7fc4590b5cafcc601d5ba5be853da5cb8539b`. The shuffled-target checkpoint and report SHA-256 values are `768ef9c8f418239a3120cf9301a68ab96c71eebd722e4b21293f1b3207880b38` and `d8de5fdc46ae18974177b08dc81086b7cd2b9183b251cce89a92da65bfc371d6`. Both atomic bundles pass manifest verification. This falsifies learned-target attribution. The board is exactly solved whenever counterexample evidence is kept above the fixed threshold, including by a constant-high gate and by a gate optimized against shuffled relations. The learned relation objective in the shuffled arm remains high (`2.2779269 -> 2.2730541`) while its true assessment score is still perfect. Therefore the architecture, not correct label learning, determines the hard answer on this board. MCTFR is closed as a learned reasoning mechanism. It may remain available as a fixed, audited bounded partition-refinement primitive, but it is not eligible for fresh-seed confirmation, Shohin integration, H100 scale, or a reasoning claim. The next experiment must make episode-specific state discovery, action binding, operator selection, and noncommuting order causally necessary, with an all-actions/constant-high control bounded near chance by construction.