Independent verification: PR869's U8 word and κ with a code-disjoint checker (no new kappa)

[SethBurkart123]

Independent verification of PR869's U8 complex word; no new κ claimed.

I wrote a checker from the word semantics. It shares no code with audit_local.py, the PR799 verifiers or PR869's builders. It accepts PR869's U8 word (090fd574…) and PR799's selected X4 word (1e1d99ba…), and recounts exactly the claimed local profiles:

• X4: {1:2548, 2:338, 3:430, 4:194, 5:56, 8:8}
• U8: {1:2548, 2:338, 3:446, 4:162, 5:72, 8:8}

Both have width 3778. The checker also re-derives PR869's κ = 0.001661948695165034 from its PLAN with interval arithmetic.

Methods (different from audit_local)

• Exact scalar map: residues mod 16 primes plus a rigorous height bound. The certified height is below 2^91, against a 2^492 limit.
• Compensation is solved, not propagated: Comp = Rest⁻¹·E·Pre⁻¹ must be the identity plus a target←helper block that avoids every entering and low-end helper.
• Frames: subspaces are held as 512-bit membership sets.
• Low-end cones: exact nonzero patterns of the prefix and its inverse.
• κ: mpmath interval moments at both grid endpoints, plus the bootstrap closed form. Positive control: it reproduces PR799's κ and that PR's recorded residuals.

Controls

• All 36 of PR869's mutant words are rejected, and its C0/recipe words pass.
• Six further single mutations of U8 are each rejected for the intended reason.

Reproduction note for #869: its README runs reproduce_jx.py --frames-dir, but the script only accepts --sw4-dir. With that flag, the rebuilt X4 and U8 words match the pins byte for byte.

PY=python3 bash research/u8-independent-xcheck/verify.sh OUT   # → PASS_U8_INDEPENDENT_XCHECK (~50 s)

• Pins: base f567884a, PR869 head 73e86f69. The full log is in VERIFY.log.
• Not covered: owner admission, hosting, the invoice, the 47 outer constraints (see Independent verification: Bernstein certificates for all 47 outer inequalities #813), the PR589 bit supplier and PR870. The inherited all-size, realization, hosting, precision and analytic assumptions remain. This is a finite replay, not a formal proof.
• Credit and track: the modular-CRT idea parallels Independent verification: exact bounded modular replay of #741 backward endpoint #835. Assignment seed 80 (track 75–84).

Prepared with substantial AI assistance.

🤖 Generated with Claude Code