test: adinkra codewords as society-member identity — why N=8, self-correcting identity - #9157
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…rrecting identity (shadow*)
Push-forward on the adinkra thread (Aaron: "the James Gates adinkras fit in with mod
2 … secret/generator code words for society members based on purpose … push forward,
it's very valid, time will be the ultimate judge").
IMPORTANT (honest note): the doubly-even self-dual code is ALREADY a full module —
Zeta.Core.AdinkraCode ([8,4,4] extended Hamming) with 14 tests. I initially
overwrote its test file by mistake, caught it (git showed it Modified not new),
and RESTORED the original. This adds a COMPLEMENTARY file that builds ON the existing
module rather than duplicating it.
tests/Tests.FSharp/AdinkraIdentity.Tests.fs — what the existing tests don't cover +
what Aaron's framing needs:
• WHY N=8: the MINIMAL doubly-even self-dual length — exhaustive search shows none
at N=2/4/6, one at N=8 (Gleason/Mallows–Sloane N≡0 mod 8) — the E8/Clifford floor
the adinkra→Clifford→E8 ladder stands on;
• MEMBER IDENTITY SELF-CORRECTS: a purpose-codeword corrupted in any 1 bit decodes
back to itself (nearest-codeword; min distance 4) — identity as an ECC (Gates);
• distinct purpose = distinct identity (the 14 weight-4 codewords are ≥ distance 4
apart — purposes don't collide);
• ζ tie-in: the weight enumerator 1 + 14y⁴ + y⁸ is a partition function over member
identities by weight (the ζ name-audition shape), on the SAME GF(2)^8 as the
scheduler round-map (#9151). 4/4 green.
RESUME updated (adinkra step landed). Anchors: S. James Gates Jr. et al. (adinkras ↔
doubly-even codes); Gleason/Mallows–Sloane; Conway–Sloane (E8); CayleyDicksonDoublyEven.lean.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
AgencySignature-v1:
persona: otto
actor: zeta-otto
surface: tests
topology: shadow-clone
intent: adinkra-codewords-as-member-identity-why-n8-self-correcting-built-on-existing-module
authorization: aaron-explicit-push-forward-on-adinkra-2026-07-02
uncertainty: low
measure: adinkra-identity-why-n8-minimal-doubly-even-self-dual-none-below-8-member-identity-self-corrects-1-bit-weight-enumerator-partition-function-4-tests-restored-clobbered-original
delta-u: adinkra-thread-lands-member-identity-as-ecc-why-8-e8-floor-complements-existing-module
seed: S4
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…e-preserving map (shadow*) (#9163) Next-rung #3 (Aaron: 2→3→1). Ties the adinkra member-identity thread (#9157) to the scheduler dynamical zeta (#9151): a CODE-PRESERVING round-map on GF(2)^8 keeps every member's purpose-codeword a valid identity, and the Artin–Mazur zeta of that map — restricted to the [8,4,4] adinkra code — has periodic ORBITS that partition the 16 member-identities into PURPOSE CLASSES. The round-map is a code AUTOMORPHISM: a coordinate permutation π with π(C)=C (found by exhaustive search over Zeta.Core.AdinkraCode). Identity-preserving dynamics — no member is ever mapped to a non-identity. tests/Tests.FSharp/AdinkraOrbits.Tests.fs (3/3): • the round-map is a code automorphism (preserves the code; every identity stays one); • its dynamical zeta self-verifies: exp(Σ Fix(π^k)u^k/k) = Π_orbit 1/(1−u^|O|) — the same Fix-count-vs-orbit-decomposition discipline as #9151; • the orbits partition the 16 members into purpose classes (Σ lengths = 16, a genuinely dynamical orbit ≥ 2, the quiescent all-zero identity its own fixed class). Confirms the exact machinery next-rung #1 (formalize the CHIP-8/IScheduler predictor) needs — a finite map's Artin–Mazur zeta whose orbits classify its configs. RESUME updated (#3 landed). Anchors: Gates (adinkras ↔ doubly-even codes); Artin–Mazur 1965; the [8,4,4] automorphism group AGL(3,2). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> AgencySignature-v1: persona: otto actor: zeta-otto surface: tests topology: shadow-clone intent: adinkra-orbits-classify-members-dynamical-zeta-over-code-preserving-automorphism authorization: aaron-explicit-2-then-3-then-1-2026-07-02 uncertainty: low measure: code-automorphism-preserves-adinkra-code-dynamical-zeta-fix-eq-orbit-product-orbits-partition-16-members-into-purpose-classes-3-tests delta-u: adinkra-identity-tied-to-scheduler-dynamical-zeta-orbits-classify-members-machinery-for-chip8-confirmed seed: S4
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Push-forward on the adinkra thread (you: "push forward on the adinkra stuff, it's very valid, time will be the ultimate judge").
Honest note
The doubly-even self-dual code is already a full module —
Zeta.Core.AdinkraCode([8,4,4]extended Hamming, 14 tests). I initially overwrote its test file by mistake, caught it (git showed it Modified, not new) and restored the original. This PR adds a complementary file building on the existing module, not duplicating it.What's new (what the existing tests don't cover + your framing needs)
4/4 green. RESUME updated (adinkra step landed). Anchors: Gates et al.; Gleason/Mallows–Sloane; Conway–Sloane (E8); .
🤖 Generated with Claude Code