C(P112) >= 64: complete reduction to stated conjectures

[DreamingOfClouds]

Adds research/p112-reduction-to-conjectures/ only; nothing existing is changed. Pure finite combinatorics on the E8 root lines and the unit P112, in the line of #2832 (K1/K2 split), #2985, #3049, #3074 (one-sided), #3029, #3040, #3045, #2854 (two-sided). No kappa claim, no window, no supplier word.

What it does

• One-sided: updates Research: one-sided residue closures, part 2 — Lemma Q4, count lemma + E6 dim-cover and rerunnable span passes close 78 more of the 116 open residues (38 open; no kappa claim) #3049's ledger (38 open) by closing 37 further rows with per-row certificates and both (mostly three) implementations: 19, 113, 262, 159, 302, 398, 263, 399, 602, 596-601, 169, 332, 333, 424, 426, 427, 464, 312, 316, 418, 420, 430, 435, 303, 315, 400, 401, 402, 409, 411, 417, 425. Audit fixes are built in (E6A1 via KILL-A8 (a); 399's s=6 scenarios; G3 dependency and target-completeness for 596-601). Row 579 is CONDITIONAL: Theorem K5 and Lemmas K5^-, K5^-2 (each double-implemented) reduce it to the finite conjecture DEG2 (C6). The 7 rows of the earlier (6,6,5) s0@T7 span run (381, 384, 576-578, 580, 581) are now KILLED by two implementations (s3y and an independent s3z rerun, 192/192 slices, 0 cracks). Ledger: 602 KILLED of 603.
• Two-sided: BUDA11 ((1,1), all m, with the sound P2 minus n01), Theorem DR', Theorem S with -n01, TWOSIDE Lemma BK, F7 and the BX extension, FINITE alpha and beta (R = 6, p = 2; R = 7, p = 2, two implementations, max span 4), CONJG2 reductions (x >= 1 empty; d = 0 shape; d >= 1 finite lists of 35 and 280, reproduced by an independent filter chain).
• PROOF_MAP.md maps every claim to a rerunnable check; verify.sh (default: manifest, ledger recomputation, 15 reruns, ALL PASS; FULL=1 for the heavy ones); data/ledger3_consolidated.csv is recomputed.

Dependency map. #2832 split -> #2985 / #3049 / #3074 (one-sided) and #3029 / #3040 / #3045 / #2854 (two-sided) -> this PR -> conjectures C1-C7 (CONJECTURES.md).

Remaining conjectures (each stated with what would close it in CONJECTURES.md): C1 Conjecture G (d = 0 branch, kappa in 3..8; d >= 1 lists of 35 / 280); C2 R-dep for s >= 2 and the s = 1 N2 pattern; C3 tight configurations inside Theorem S's slack budget; C4 Theorem DR' residues; C5 FINITE beta R = 7, p = 4; C6 DEG2 (row 579); C7 the d = 0 sliver Z = ker rho cap S != 0.

Caveats. Claims marked R in the proof map ship sources and hash-pinned recorded outputs but are not re-executed by the default verify (heavy SAT/DRAT/table runs regenerate under FULL=1). The DP/LP filters behind the d >= 1 lists are shared imports. Row 579 is CONDITIONAL on DEG2 (C6). The heavy FULL=1 reruns are recorded in evidence/ (full_a/b/c logs, PRIOR7 slices).

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code; Apache-2.0.

🤖 Generated with Claude Code