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Apical-Basal Critical Resonance

Shohin's current reasoning experiments expose three separable bottlenecks:

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Apical-Basal Critical Resonance

Status: architectural hypothesis; no capability claim

Problem

Shohin's current reasoning experiments expose three separable bottlenecks:

  1. learned local operations can be strong while autonomous composition fails;
  2. monotone recurrent fields cannot retract a defeated hypothesis; and
  3. rewrite search without a query enumerates possibilities but does not decide which computation answers the problem.

Apical-Basal Critical Resonance (ABCR) is a query-directed, reversible neural proof field. It combines bottom-up support, top-down demand, transient episode-local bindings, conflict backflow, and exchangeable hypothesis lanes. The proposal is inspired by two-compartment cortical models, concurrent belief propagation, competitive constraint networks, and focused proof search. Those ingredients are not individually novel. The hypothesis under test is their specific source-deleted, equivariant, model-owned combination.

ABCR must not use a host matcher, symbolic scheduler, branch enumerator, executor, semantic verifier, target state, or convergence oracle.

Operational Claim

Given:

  • an anonymous typed rule hypergraph;
  • anonymous evidence records;
  • one anonymous query record; and
  • fixed recurrent compute,

ABCR should:

  1. propagate evidence forward as basal support;
  2. propagate the query backward as apical demand;
  3. form episode-local variable/object bonds;
  4. activate only rules whose support and demand agree through the same bond;
  5. maintain competing hypotheses in exchangeable lanes;
  6. inhibit and revise bonds responsible for contradictions;
  7. commit only stable support-demand closures; and
  8. halt or abstain when its own obligations are resolved or irreducibly conflicted.

A clean cross-family pass would establish a bounded general reasoning mechanism. It would not establish unrestricted intelligence or natural-language reasoning.

State

For batch b, lane l, record i, rule r, and variable v, recurrent state contains:

S[b,l,i,h]     basal support
D[b,l,i,h]     apical demand
T[b,l,i,h]     tentative state
C[b,l,i,h]     conflict/inhibition
B[b,l,r,v,i]   transient variable-to-record bond
J[b,l,r,h]     rule resonance
Q[b,l,h]       lane query state
H[b,l]         lane halt potential

Rule and graph geometry are source-deleted tensors. Every symbol, rule, variable, record, and lane identity is freshly reindexed per episode.

S, D, T, and C have no privileged slot order. B is an episode-local soft partial matching with explicit unbound capacity. Lanes share all weights.

Recurrent Dynamics

Let premise(r) and conclusion(r) be typed anonymous incidence tensors, not host-executed semantics.

Basal support

Evidence and tentative conclusions send forward proposals:

support_match[r] =
    MatchPremises(S, B, premise(r))

MatchPremises is a learned equivariant contraction. It receives incidence, types, equality structure, support state, and bonds. It receives no legal mask or host binding.

Apical demand

The query initializes D. Active conclusions send obligations backward:

demand_match[r] =
    MatchConclusion(D, B, conclusion(r))

Demand is not an answer hint. It specifies which consequences are relevant. Query-shuffle twins must redirect the activated proof field.

Multiplicative resonance

A rule becomes active only when support and demand agree through the same binding:

J[r] = sigmoid(
    Wj(
        support_match[r]
        * demand_match[r]
        * binding_consistency[r]
        - conflict_pressure[r]
    )
)

The elementwise product is causal, not decorative. An additive dual-stream control receives the same tensors, parameter count, and compute but replaces the product with a learned sum.

Transient bonds

Bindings update through evidence, demand, and resonance:

B_next = PartialSinkhorn(
    leak_b * B
    + proposal_b(S, D, J, rule_graph)
    - conflict_to_bond(C)
)

The partial normalization enforces only competition and an explicit unbound state. It does not match a rule. Equality and repeated-variable constraints are learned from anonymous incidence twins.

Tentative and committed state

Tentative conclusions are reversible:

T_next =
    leak_t * T
    + forward_proposal(J, B, rule_graph)
    - retract(C)

Committed support uses a differentiable hard event after stability:

stable = agreement(S, D, T, B) * low_conflict(C)
write = straight_through(stable > threshold)
S_next = max(S_evidence, S, write * T)

Only evidence and stable closures are monotone. Tentative hypotheses and bonds remain retractable.

Critical conflict

Incompatible overlapping proposals induce inhibition:

C_next =
    leak_c * C
    + incompatible(T, B, rule_graph)
    + duplicate_lane_pressure(T)

Conflict flows to the bindings and rules that caused it. A no-conflict-backflow control keeps the same conflict computation but prevents it from changing B, J, or T.

Lane exchange and coalescence

Lanes are exchangeable phase states, not host-created branches. A learned competition mechanism amplifies distinct low-conflict hypotheses and coalesces equivalent lanes:

lane_affinity = EquivariantStateSimilarity(S, D, T, B)
lane_gate = compete_and_coalesce(lane_affinity, C, Q)

No canonical graph hash or host equivalence test is available in the model process.

Halt and abstention

Halt is a learned function of:

  • unresolved demand;
  • tentative activity;
  • conflict energy;
  • bond motion;
  • rule resonance;
  • lane diversity; and
  • state velocity.
energy_t =
    unresolved(D)
    + activity(T)
    + conflict(C)
    + velocity(S,D,T,B)

halt = hard_event(H > threshold)

Terminal/nonterminal delay twins, cyclic twins, and underdetermined twins are required. A fixed recurrence cap is only a fail-closed safety bound.

Energy Interpretation

ABCR is not required to minimize one scalar energy, but a useful diagnostic is:

E =
    E_unmet_demand
    + E_unsupported_claims
    + E_binding_inconsistency
    + E_conflict
    + E_duplicate_lanes
    + E_state_velocity

Successful reasoning should reduce all terms except during deliberate hypothesis splitting. Energy is never used as a host convergence test. It is logged for causal diagnosis and may supervise the learned halt head.

Parameter Budget

The protected Shohin trunk has 125,081,664 parameters. The initial ABCR budget is 32,000,000 added parameters:

ComponentCeiling
record/rule encoders6M
support and demand dynamics8M
bond dynamics6M
conflict and lane dynamics6M
state reader and halt2M
Shohin interface adapters4M
complete system157,081,664

The complete system remains below 200M. Larger size is not evidence; every promoted treatment needs a parameter- and compute-matched generic recurrence.

Training

Training is staged without exposing a privileged full proof trace to the autonomous score path:

  1. Bond mechanics: anonymous repeated-variable, type, and occurrence twins.
  2. One-rule resonance: set-valued valid activations under query changes.
  3. Reversible composition: two-to-six-rule episodes with hard recurrent state and decaying teacher forcing.
  4. Critical competition: forks, delete effects, contradictions, cycles, and underdetermined queries.
  5. Autonomous closure: final-answer, abstention, and halt supervision only.
  6. Cross-family confirmation: five fresh seeds with two entire held-out families.

Training may use independent-oracle labels in an offline process. Evaluation may not contain the oracle, its source, its traces, or any derived legal-action mask.

Families

The first rotation uses:

  • Horn closure;
  • forward and backward dataflow;
  • typed occurrence rewriting;
  • delete-effect planning; and
  • algebraic normalization.

For each confirmation, two families are absent from all optimization. Every local operator must appear in training, while the held-out family changes its composition, state topology, and query semantics.

Controls

  1. forward-only AHRF-style support;
  2. additive support/demand without multiplicative resonance;
  3. no conflict backflow;
  4. no persistent transient bonds;
  5. one hypothesis lane;
  6. shuffled query;
  7. shuffled rule cards preserving statistics;
  8. parameter/FLOP-matched generic recurrent slots;
  9. reset recurrent state each step;
  10. fixed-deadline readout; and
  11. Shohin trunk-zero intervention.

Gates

All five seeds must achieve:

  • at least 95% exact in every held-out family;
  • at least 90% exact at doubled depth and increased graph width;
  • at least 95% halt or abstention on cyclic and underdetermined cases;
  • 100% storage, symbol, rule, lane, and branch-order reindex invariance;
  • at least 99% correct query, donor-state, binding, and RHS intervention responses;
  • treatment at least 20 percentage points above every causal control;
  • paired 95% lower confidence bound above a 10-point advantage;
  • no host repair, family-specific inference head, evaluation fine-tuning, source access, or custody failure; and
  • complete parameter count below 200M.

Reject ABCR if:

  • a generic recurrent control matches it;
  • it requires gold schedules or host matching;
  • conflict backflow is causally inert;
  • query interventions do not redirect computation;
  • tentative states never retract on counterfactual twins;
  • family-specific adapters are required; or
  • language integration succeeds only by bypassing the frozen runtime.

Evidence Ladder

  1. deterministic mechanics and tensor-custody tests;
  2. isolated one-rule causal interventions;
  3. autonomous within-family composition;
  4. held-out renderer and depth transfer;
  5. held-out task-family transfer;
  6. frozen Shohin language compilation and reading;
  7. natural-task confirmation with manual transcript review.

No rung may be described using the claim of a later rung.