R12 Autocatalytic Hysteretic Relation Field Preregistration

Status: architecture and matched controls frozen at source commit c67d945; no score-bearing AHRF result exists.

Pre-artifact launch b4dcbf0 exhausted local MPS memory in a dense parent-by-child membrane expansion before an optimizer update or output write. Source 4fc5a11 replaces it with an exact gather after adding a fail-closed one-child-per-typed-role validator. The full-geometry MPS canary completed without OOM; this is a systems repair, not a score.

Pre-artifact launch 84eec59 was then stopped before any output or optimizer update after a structural audit proved that its recurrent field propagated only same-cell child state. It therefore had no path that could combine relation cells (i,k) and (k,j) to update (i,j), making exact relational composition unrepresentable regardless of optimization. Source c088261 adds a learned object-equivariant dynamic triadic contraction over the two typed argument-role membranes. The corrected full-geometry MPS canary wrote a checkpoint and report with 291,666 added parameters and 125,373,330 total parameters. Its one-update scores are not evidence and will not be reused.

The first launch after preregistration commit 26cb046 was stopped and its ephemeral optimizer state destroyed before it wrote an output directory. An independent structural audit found two more decisive faults: no runtime path could transpose a live child relation for a converse node, and clamping exact hard events before binary cross entropy killed the intended straight-through terminal gradient. The same audit showed that the 16-step safety cap was below the conservative propagation envelope of the proposed board.

Source 0dccab5 adds a generic direct/transposed channel for every typed child role, uses an MSE terminal surrogate only during exact hard-event updates, adds learned/false/zero triad modes with identical parameter counts, records the transitive source set before and after training, and derives a fail-closed minimum safety horizon from expression depth and fixed-point updates. Source 1dd7a5d additionally keeps the generic control's card encoder active through object-marginal features and removes all primitive-classifier-head layers from the warm start. A full-geometry 64-step MPS canary completed in 56 seconds with 316,824 standalone parameters and a hypothetical integrated total of 125,398,488. Its one-update scores are systems evidence only and will not be reused.

A real-board batch-four canary then reached the local MPS 9.07 GiB memory cap before any output write. Batch two completed the full 80-train/50-development geometry without OOM or source drift. Source c67d945 therefore freezes 2,000 field updates and 400 halt updates at batch two, preserving the intended 4,000 and 800 sampled examples respectively. Unsafe MPS watermark overrides are forbidden.

Question

Can a standalone architecture that fits within a sub-200M Shohin integration budget infer fresh episode-local relation laws, propagate their consequences through a host-compiled, source-deleted recursive graph, preserve facts as write-once state, and decide when to halt without a host executor, operation labels, an execution schedule, or a host convergence test?

This is a test of a bounded synthetic relational reasoning mechanism. A pass is not evidence of unrestricted language reasoning, and AHRF is not yet connected to the protected Shohin trunk.

Architecture

The treatment is the Autocatalytic Hysteretic Relation Field (AHRF):

1. an object-equivariant opaque witness-card encoder with row, column, transpose, and triadic pair messages;
2. a node-equivariant recurrent graph field;
3. two typed operation-argument edge roles and one distinct equation-feedback edge role;
4. a learned object-equivariant dynamic triadic membrane contraction that combines (i,k) state from the first argument role with (k,j) state from the second argument role to drive (i,j);
5. direct and generically transposed fact/membrane channels for every typed child role, allowing an opaque card to select relation orientation without a named converse primitive;
6. exact write-once fact and evidence latches with straight-through gradients;
7. continuous membrane state;
8. a learned event-triggered absorbing halt latch; and
9. a fixed maximum recurrence used only as a safety bound.

The runtime score path receives structural node kinds, graph links, equation feedback links, root masks, constants, opaque witness cards, and object masks. It receives no primitive identity, operation name, target relation, answer, trajectory, iteration count, schedule, host-executor output, or convergence flag. Every active node must reach a root, every opaque card must be used, and padding/unused card arguments must be exactly zero.

Default hidden_dim=64, card_rounds=2, max_steps=64 has 316,824 standalone parameters and leaves 74,601,512 parameters under a hypothetical 200M flagship-integration cap. This is budget accounting, not evidence that the trunk and reasoner are integrated. The exact receipt is checkpointed and independently testable.

Initialization

The card encoder may warm-start only from a hash-bound CWEB treatment trained after this source freeze with:

• width 64;
• two learned triadic rounds;
• no statistics-only architecture;
• no false- or zero-triad control; and
• exact source/config/checkpoint receipts.

Only the pair input, pair rounds, and witness encoder are copied. No primitive classifier layer or output, target relation, host program, or halt parameter is transferred.

Board

The first pilot uses the hardened source-deleted Bekić board:

• factorial train orbits;
• held-out in-range, motif, scale, depth, and joint development cells;
• P, P-prime, equivalent P, constant-only rewire, and compose-only reversal;
• split-disjoint individual depth-two and depth-three motif receipts;
• held-out motif absent from every training arm;
• canonical recursive pressure requiring both variables to change, at least two convergence updates, and at least three total variable-change events;
• a fail-closed propagation envelope max(depth * (updates + 1)), with every admitted board required to fit within the frozen 64-step safety bound;
• fresh opaque slot IDs, node IDs, card order, witness order, object order, and varied input densities; and
• exact independent simultaneous and nested set oracles used only outside the model score path.

The clean source commit precedes the board/training seed. Development is score-bearing for this pilot; no confirmation claim is authorized.

Optimization

The frozen local pilot budget is batch two, 2,000 field updates, and 400 halt updates. Every matched learned control receives the same sampled-example, update, and recurrence budget.

1. Fit terminal root relations from final-state supervision only.
2. Use continuous monotone write events for the first 90% of field updates.
3. Use exact straight-through write events for the final 10%. Binary cross entropy is used for the continuous phase and MSE for the exact hard phase so incorrect hard bits retain a finite nonzero gradient.
4. Keep halt absorption disabled during field fitting.
5. Freeze the field and fit only the halt head from whether the model's own hard per-step root facts exactly equal the training target.
6. Evaluate with exact write events and learned halt enabled.

No intermediate node target, primitive label, host execution trace, or fixed halt deadline may supervise the field.

Frozen Controls

Every promoted run requires same-board, same-budget controls:

1. no feedback: remove equation-root-to-variable feedback links;
2. no hysteresis: replace write-once fact latches with ordinary overwrites;
3. shuffled cards: permute opaque cards between slots while preserving arity and all graph statistics;
4. generic recurrence: parameter/FLOP-matched recurrent field without aligned card-conditioned pair messages; the same card encoder remains trainable and supplies only object-marginal card features;
5. false triad: same-parameter, same-cost contraction using the wrong object-equivariant A-transpose times B alignment;
6. zero triad: evaluation ablation only; it is not a matched learned control because its triad parameters receive zero gradient; and
7. fixed deadline: disable learned halt and read only at the safety bound.

Identity-delay twins are a mechanics falsifier: terminal semantic facts must remain equal while learned halt latency increases by the inserted relay depth.

Gates

All must pass on at least five independent seeds before promotion:

• at least 99% exact terminal packets on train and development;
• at least 99% exact in every development cell and score-bearing arm;
• at least 99% learned halt with at most 1% safety exhaustion;
• 100% object, node-storage, card-order, and witness-order equivariance;
• 100% P/equivalent-P terminal agreement;
• treatment exceeds each nontrivial control by at least 20 percentage points in exact development packets;
• no source/target/covert-state validation failure;
• exact complete-system parameter receipt below 200M; and
• independent replay from the frozen source/checkpoint hashes.

Failure rejects the treatment on this board. Passing authorizes only a fresh, preregistered transfer board spanning at least Horn closure, dataflow analysis, and one non-relational family. No synthetic Bekić result, by itself, may be called genuine general reasoning.

Existing Evidence Boundary

The contextual witness-equivariant binder is a useful warm-start component but not a decisive law-learning result: its exploratory shifted score is 99.61%, while a statistics-only control reaches roughly 97.8%. The current card ontology is therefore strongly marginal-solvable. AHRF must win through recursive terminal execution and model-owned halt, not by citing the binder classification score.