The axiom-independence audit: eight inherited invariants compress to a minimal, irreducible five
A post-program compression audits which inherited invariants are load-bearing. The eight (brain B1–B5, physics P1–P3) compress structurally onto five operational L0 axioms — data-encoded field, symmetry, nonlinearity, settling, metastable band — with theta-gamma capacity deferred as a higher-layer realization. Nulling each axiom while the rest stay intact collapses a core capability: all five are load-bearing, the set irreducible.
Each axiom is nulled in isolation and judged by one non-circular probe (recover an independently-drawn stored pattern from a corrupted cue), paired and sign-stable across six seeds, gated by a passing intact control (cap 0.967). Every one collapses: AX1 0.90→0.00, AX2 graded 0.867→0.000 as reciprocity breaks, AX3 0.90→0.00 (linear flow scrambles), AX4 1.00→0.00 (no-settle = corrupted cue), AX5 0.967→0.00 as R→1.000 (over-coherence carries zero stored information). redundant_axioms = [] — the five-axiom core is minimal, with no further compression.
This is the compression continuation: not a new layer, but an audit of the foundations the whole program inherited. It asks which invariants are genuinely load-bearing versus derivable, and answers it by knocking each one out (session v0.12, digest 7f59ced6…). The L0 substrate is never edited — every knock-out is a deliberately broken substitute built beside it.
Eight invariants compress to five operational axioms
The structural step (C0) maps the eight inherited invariants onto five operational L0 axioms, with theta-gamma capacity deferred to a higher layer rather than treated as a substrate axiom.
| axiom | meaning | compresses |
|---|---|---|
| AX1 | data-encoded coupling field | B1 + B4 |
| AX2 | field symmetry / reciprocity | B4 + P3 |
| AX3 | coupling nonlinearity | B2 |
| AX4 | settling / clock-free relaxation | P2 + B2 |
| AX5 | metastable operating band | B3 + P1 |
B5 (theta-gamma capacity ~7) is deferred: it is an L2/L3 realization, not an L0 axiom — a clean structural distinction that the empirical test then confirms is the right cut.
Every axiom is load-bearing
The empirical step (C1–C5) nulls each axiom while the others stay intact, judged by one non-circular probe — recover an independently-drawn stored pattern from a corrupted cue — paired and sign-stable across six seeds, gated by a passing intact control (cap 0.967).
| null | capability | why it collapses |
|---|---|---|
| AX1 | 0.90 → 0.00 | a non-encoding field holds the patterns as non-attractors |
| AX2 | 0.867 → 0.000 (graded) | breaking reciprocity removes the Lyapunov guarantee (tolerance κ ≈ 1.0) |
| AX3 | 0.90 → 0.00 | linearization removes the wells; linear flow scrambles, R stays low ~0.08 |
| AX4 | 1.00 → 0.00 | no settling = the corrupted cue; the stored field alone is inert |
| AX5 | 0.967 → 0.00 as R→1.000 | forced coherence swamps structure; one global state = zero stored info |
The verdict
redundant_axioms = [] and axiom_set_irreducible = True — the eight inherited invariants compress to a minimal five-axiom operational core, and no axiom in it is redundant. AX2’s graded result is itself informative: a little asymmetry is tolerated (κ ≈ 1.0) before a strong break collapses recovery. An earlier “syncs to the wrong answer / R high” reading of AX3 was corrected to “scrambles, R low” — an honest in-place fix. With this and the A3 closure, both named post-program continuations are executed. new_tuned_constants = 0.