DIVERGE-PL1: Branch-Local Verified Plasticity

Status: oracle-typed mechanics lane only. SRP1 closed negative, so raw-language PL1 is not admitted. The exact gate below may test branch-local plasticity with an oracle-typed referent interface, but cannot qualify a language architecture, Shohin integration, or continuation pretraining.

1. Question and prior-art boundary

PL1 asks one narrow question:

Can a small model-owned policy state improve later, context-free attempts by committing only verifier-certified, branch-local eligibility writes, while every protected semantic and execution owner remains bit-identical?

Inference-time mutability, Hebbian updates, eligibility traces, fast weights, metaplasticity, test-time training, transient LoRA, and multi-timescale memory are established families. PL1 does not claim any of them individually. The only candidate contribution is the conjunction of coherent DIVERGE branches, copy-on-write policy state, verifier-gated local credit, exact rollback, and measured improvement after the demonstrations and feedback text are removed.

PL1 is not a replacement for source compilation. Plasticity cannot recover a referent that the compiler discarded. It is also not continuation pretraining, durable consolidation, structural growth, pruning, or full-backbone updating.

2. Admission boundary

Before PL1 can consume natural text, SRP1 must satisfy its frozen gate and the following owners must be hash-bound:

1. WORLD compiler;
2. numeric EVIDENCE compiler;
3. semantic REFERENT owner shared by EVIDENCE and QUERY; and
4. exact typed executor/verifier.

All four are immutable throughout PL1. Only POLICY_PLASTIC may change. A pre-write manifest binds every protected model-state hash. Every attempted commit recomputes those hashes and fails closed on any difference.

SRP1 missed. REFERENT_ORACLE therefore replaces only item 3. A result may qualify the plastic update mechanics, but cannot qualify natural-language PL1 or a Shohin integration.

3. Episode family

Each episode defines a new eight-symbol mini-language. The symbols denote a hidden permutation of eight noncommuting, invertible transforms over a pair of registers modulo 97. The transform set is fixed, but symbol aliases, mapping, initial registers, programs, and surface order are episode-local and disjoint across train, development, and confirmation.

An episode contains:

• eight shallow acquisition programs of depth 3--5;
• twelve feedback attempts, each with eight complete branch proposals;
• sixteen transfer programs of depth 12--20;
• four poison/rollback probes; and
• four unrelated-task interference probes.

The verifier exposes only PASS or the index of the first invalid transition. It never exposes the correct transform, state, answer, mapping, or gradient. Each branch therefore receives delayed, deterministic, executable feedback, but no answer label.

The transfer programs use the same episode-local rules at held-out depths and compositions. Before transfer, all demonstrations, branch transcripts, verifier messages, source residuals, and textual context are deleted. The runtime retains only the fixed owners and the bounded plastic policy state.

4. Plastic owner

The owner has a fixed symbol feature map, fixed transform feature map, and a mutable low-rank score correction:

logit(symbol, transform) = base(symbol, transform) + u(symbol)^T F v(transform)

u and v are immutable. F is the only mutable session tensor. Version 0 uses rank 8 and one owner, not six layer-local ranklet banks. This is the smallest test of the proposed causal mechanism.

At attempt t, branch b receives copy-on-write F[t,b]. It samples one complete bijective symbol-to-transform assignment and executes every acquisition program coherently under that assignment. Its eligibility record contains the chosen symbol/transform pair for each executed transition and the branch-local state hash at that transition.

On PASS, the write proposal potentiates all used assignments. On a verified first-error certificate, it depresses only the assignment active at that transition. Unverified, malformed, stale, or cross-branch certificates cannot write. Branch proposals are combined only after verification; fields from different complete assignments are never averaged into a synthetic mapping.

The commit is:

proposal -> certificate check -> write-budget projection -> protected-hash check
         -> atomic session commit or exact rollback

The Frobenius norm of each attempt write is capped, the cumulative session write budget is fixed, and the singular values of F are clipped to the frozen homeostatic envelope. The transaction log stores pre-state hash, certificate, branch identity, eligibility hash, update norm, effective rank, and post-state hash.

5. Matched arms

Every arm receives the same episodes, branch count, proposal count, verifier calls, mutable-scalar allowance, and total update FLOPs. No arm may retain raw episode text at transfer.

1. STATIC: frozen policy; matched no-op update compute.
2. CONTEXT_ONLY: feedback remains available during acquisition but is deleted with all text before transfer.
3. DIVERGE_ONLY: eight coherent complete branches per attempt with no persistent policy write.
4. FAST_WEIGHT: one session matrix updated from all branch outcomes without branch-local eligibility or first-error localization.
5. TRANSIENT_GRAD: the same mutable-scalar budget updated by a standard transient policy-gradient/LoRA-style step on complete branch reward.
6. PL1: branch-local eligibility, verified local credit, bounded atomic commit, and rollback.

The static arm receives extra recurrent policy evaluations so total forward FLOPs match PL1. Update FLOPs, verifier calls, wall time, peak memory, and mutable bytes are reported separately rather than hidden in a single total.

6. Causal controls

The unchanged PL1 checkpoint is evaluated under:

• shuffled verifier outcomes;
• correct outcome assigned to the wrong branch;
• plastic-state reset before transfer;
• unrelated-episode plastic-state transplant;
• one poisoned certificate followed by atomic rollback;
• eligibility trace removed;
• write/homeostatic budget removed; and
• protected-owner mutation injection, which must fail closed.

The poison probe records behavior before poison, after poison, and after rollback. Rollback must restore the exact pre-poison plastic hash and outputs.

7. Data and split custody

The CPU builder first materializes train, development, and unopened confirmation episodes from separately frozen seeds. It reports exact identity, alias, mapping, program, transition, and composition overlap. Development is used only to verify that the board is nondegenerate and to measure random and oracle ceilings. Quantitative gates are frozen after that calibration and before fitting or opening confirmation.

The independent assessor re-enumerates every hidden mapping and executes every program without importing candidate runtime code. It verifies unique episode solutions, verifier certificates, first-error indices, transfer depth, poison validity, and split disjointness.

8. CPU calibration

The fixed development board contains 256 oracle-typed episodes. The runtime uses eight complete branches, twelve acquisition attempts, seed 2026080799, rank 8, per-write norm cap 4, score clip 8, and sixteen context-free transfer programs per episode. Before confirmation, development transfer counts are:

PL1's assessor-only context-free transfer probe rises from 1/4,096 after attempt 1 to 3,657/4,096 after attempt 12. Reset, shuffled credit, wrong-branch credit, and no eligibility score 1, 2, 0, and 1 of 4,096. Removing the write cap and score clip is identical to PL1 on development, so homeostasis is retained as a safety envelope but explicitly excluded from the candidate causal claim.

9. Frozen confirmation gate

The five confirmation seeds contain exactly 256 episodes each. All conditions are conjunctive:

1. PL1 transfer exactness is at least 85% aggregate and 80% on every seed;
2. PL1 exact mapping recovery is at least 80% aggregate and 75% on every seed;
3. PL1 exceeds every matched arm by at least 10 absolute transfer points in aggregate and by at least 5 points on every seed;
4. deterministic 5,000-resample paired 95% bootstrap intervals for PL1 minus every matched arm have a lower bound above zero;
5. assessor-only transfer exactness after attempt 12 exceeds attempt 1 by at least 50 points;
6. plastic-state reset loses at least 25 points and does not beat STATIC by more than 3 points;
7. shuffled reward, wrong-branch credit, and unrelated transplant do not beat STATIC by more than 3 points;
8. poisoned state differs from pre-poison behavior in at least 95% of episodes, and rollback restores the exact pre-poison hash and outputs in every case;
9. removing eligibility loses at least 5 points; the no-homeostasis arm is stable and fully reported, but is not required to lose;
10. protected mutation injection fails closed on every seed and normal runs have zero protected-owner hash changes, unauthorized writes, stale-certificate commits, cross-branch commits, false verifier acceptances, or rollback mismatches; and
11. all arms report per-attempt accuracy, transfer exactness by depth, update norm, write budget, verifier calls, mutable bytes, operation receipts, and wall time.

A failure closes this exact PL1 update rule. Do not retry rank, width, layer, branch count, seed, duration, optimizer, or write budget. Attribution may be read-only. A mechanics pass under oracle referents authorizes one natural integration only after a semantic compiler separately qualifies; it is not a reasoning or language claim by itself.