MD-OS

Verified Solver Transport Model

Status and claim boundary

This model defines a bounded candidate mechanism for generality: transport a verified solver structure between explicitly different frames, instantiate a frame-local solver under equal budgets, and admit the transport only after independent hidden verification.

The repository contains controlled synthetic evidence for one two-step invariant across five finite frames. It does not establish open-world generalization, a universal representation of intelligence, a general tensor of AGI, externally replicated learning, or AGI.

Core objects

A frame is

F = (P_F, A_F, R_F, V_F)

where P_F is the problem space, A_F the answer or action space, R_F the domain relations and assumptions, and V_F an independent verification contract.

A frame-local talent is a solver

s_F : P_F -> A_F

that may be strong inside F without transferring outside it.

A candidate frame transformation

tau : F -> F'

contains a problem encoder, a result decoder, the structure claimed to be preserved, and a verifier. A transported result is admissible only when the transformed solver is generated before hidden evidence is exposed and the decoded result passes the original-frame verification contract.

The candidate generality operator is

G(C_t, F, p) -> (F', tau, s_F', a, evidence)

where C_t is persistent operational context. The operator is not admitted as general merely because it changes representations: the transformation, result, budget, contamination boundary, and claimed invariant all require readback.

Verified transport contract

For problem p, encoder E_tau, target solver s_F’, and decoder D_tau, the bounded preservation condition is

V_F(p, D_tau(s_F'(E_tau(p)))) = pass.

Textual equality is not required; preservation of the declared operational relation is. Persistent context commits the transport only on pass:

pass    -> retain transformation, solver structure, scope, evidence, verdict
fail    -> retain the falsification; do not promote the transport
unknown -> retain the hypothesis as unverified; do not promote it

Finite transport tensor

The controlled fixture defines a binary rank-three tensor

T[frame, solver_step, operator_kind]

with shape [5, 2, 3]. Its axes are five finite synthetic frames, two ordered solver positions, and three operator kinds: filter, map, and reduce.

The observed invariant is filter>map. Components depend on the frame basis, while the tested operator sequence survives a reversal permutation of that basis. For permutation matrix P, the implemented transformation law is

T_prime[i,p,o] = sum_j P[i,j] * T[j,p,o].

Applying the inverse permutation reconstructs T exactly. This establishes a finite permutation-equivariant tensor representation of solver structure in the fixture. It does not establish covariance under arbitrary changes of basis, a tensor field over open domains, or a tensor representation of AGI.

Controlled experiment

Experiment verified_solver_transport_20260823_v1 uses repository-local, deterministic tasks.

Source frames:

Wholly different target frames:

The source frames independently admit the same structural solver sketch, filter>map. Target primitive identifiers and semantic domains are absent from the admitted source solvers. Candidate generation receives public task examples but no target program, hidden test, evaluator-only expected value, or oracle object.

Each target is evaluated under the same 12-candidate budget:

memory disabled:    no prioritized solver structure
reversed sham:      map>filter
verified transport: filter>map

An independently coded target oracle runs only after candidate generation. The preregistered closure condition requires:

Observed result

The deterministic report returns:

status:                              ok
memory-disabled success:             0/3
reversed-sham success:               0/3
verified-transport success:          3/3
verified hidden cases:               6/6
delta over memory-disabled control:  1.0
tensor shape:                         [5, 2, 3]
tensor nonzero components:            10
frame-permutation equivariance:       pass
contamination audit:                  ok
report hash:                          a079b062412a1546b951a0aa83afbade4955b15545026e1e1e73d6665c665fd6

The causal interpretation is bounded: under the fixture’s fixed enumeration order and equal candidate budget, prioritizing the source-induced invariant is the changed condition that makes all three target solvers reachable; disabling it or reversing it removes the advantage.

Falsifiers and limits

The bounded result is falsified if a control solves a preregistered target, verified transport fails a target or hidden case, evaluator-only data enters the learner request, budgets differ, the source invariant is not independently present in both source frames, or inverse frame-basis transformation fails.

The experiment has only three target frames and six hidden cases. It has no population-level statistical claim, external replication, real-world noise, continual frame discovery, arbitrary solver depth, or open-world evaluator. The tensor uses one discrete permutation family. The result supports a mechanism inside a controlled finite family, not AGI.

Implementation and evidence

The experiment runs once and starts no autonomous loop. A future extension must separate frame discovery from evaluator labels, add composed unseen transports, precommit a larger sealed cohort, and obtain independent external replication before widening the claim.

This experiment is bounded evidence for one transported solver invariant. The general runtime contract that now governs candidate-law induction, relative tensor transformations, cognitive-unity state, and APFC promotion is defined separately in the Cross-Domain Cognitive Unity Model. The two results must not be conflated: the solver-transport tensor records one finite mechanism, while the cognitive-unity model defines how future cross-domain claims must be constructed and verified.