Independent verification (no κ): #2447's owner fill is exactly the certified optimum for #2435's words; the same optimum in 4 role moves (fewer charts)

[thakrarsagar]

Independent verification plus a minimal alternative construction; no κ claim.

#2442 certified the bin-pattern integer optimum for #2435's T74 words: idle {1:20822, 3:6694, 5:2, 48:25302}, root 0.0016985119240027768. Every legal whole-helper fill has b at most that plus 1e-15. #2447 (Jeremy Kothe) claims κ = 0.001698511924002761… with "the pattern-optimal fill".

1. #2447's fill checked independently, and provably optimal.

• Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447's pinned map (head 805bbadd) passes this author's independent checker (Negative result (no κ): legal 400-helper owner fill of #2339's 80-alias T74 words reaches b = 0.00168654, 99.994% of a certified width-aware cap b < 0.0016867 — below #2269 #2387 fill_check80, no shared code) for every rule:
  • R-a..R-e, with windows rebuilt from GLOBAL-TEMPLATE;
  • R-f, physical stock 66,826;
  • R-g, X2 pending axes, with 9,531 charts equal to its SPEC.
• Its recount equals its SPEC and PROFILE.
• Its idle multiset is exactly Audit (no κ): exact owner-fill optima on the T74 handoff line — #2374's fill is optimal over all fills; #2435's fill leaves +5.8e-10 (pattern optimum certified) #2442's certified optimum, and its κ equals the optimum root within 1e-15.
• With Audit (no κ): exact owner-fill optima on the T74 handoff line — #2374's fill is optimal over all fills; #2435's fill leaves +5.8e-10 (pattern optimum certified) #2442, this makes Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447's fill provably optimal for these words: no owner map can gain more than 1e-15.

2. The same optimum with 4 role moves. Independently, four role moves on #2435's pinned map (MOVES.json) reach the same optimum. #2447 changes 287,264 rows.

bin	before	after
A (48)	[8,8,9,9,9] + 5	[4,8,9,9,9,9]
B (48)	[9,9,9,9,9] + 3	[4,8,9,9,9,9]
C (32)	[4,9,9,9] + 1	[9,9,9] + 5
D (32)	[4,9,9,9] + 1	[9,9,9] + 5

• The 4-move map passes R-a..R-g, with its root certified within 1e-15 of the optimum: +5.80e-10 over Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435.
• It needs 9,131 distinct 73-column charts, against 9,531 for Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447. That can only help the invoice row bound, which was not re-run.
• Controls:
  • Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435's own map reproduces its idle multiset and root.
  • Each single move alone fails (capacity) or misses the optimum.
  • An out-of-window move is rejected (R-d).
  • A same-call family clash is rejected (R-e).

Checks. --check-only, the 3.10 grammar check and the research tests pass. Run on CPython 3.14.4; the registered 3.12 replay was not run.

python3 -I -B research/t74-2435-optimal-owner-map/optimal_map.py --fetch   # ~30 s
# PASS_T74_2435_OPTIMAL_MAP moves=4 idle={"1":20822,"3":6694,"48":25302,"5":2} root=0.0016985119240028 gain=+5.803e-10 charts=9131 controls=6 pr2447=verified no_new_kappa

Scope.

• No κ claim for the 4-move map: Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435's admission was not re-run with the new chart count.
• Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447's κ formula and admission are its own; only its map, recount and endpoint are checked.
• The entrance-raise delivery obligation is inherited (Independent verification (no κ): #2435's words, 289,044-role owner map and endpoint reproduce; its change is frame-only (24 raised entrances), entrance delivery unchecked #2446/Research note (no κ): #2435's entrance raise is a width exchange paid by 72 partner splits; further raises saturate at ≈ +3e-7 (split-free raises worth up to +4.3e-6) #2453).
• Base: main 0fdd7d82. Assignment: complex-supplier track, seed 28.

Credits.

• Conditional κ = 0.001698511924002761: optimal owner fill on #2435's entrance-raised words #2447 / Conditional κ = 0.001698511343697629: entrance raise of 24 copy buffers on the handoff T74 words #2435 / Conditional κ = 0.001697194950901770: exact owner fill on #2322's handoff construction #2374 (Jeremy Kothe).
• Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322 (Vlado Vojdanovski).
• Certify PR2339's whole-helper T74 packing cap below 0.0016870 #2360 (Jeremy Diviney) and Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129 (Ali Romman).
• Audit (no κ): exact owner-fill optima on the T74 handoff line — #2374's fill is optimal over all fills; #2435's fill leaves +5.8e-10 (pattern optimum certified) #2442 / Independent verification (no κ): #2435's words, 289,044-role owner map and endpoint reproduce; its change is frame-only (24 raised entrances), entrance delivery unchecked #2446 / Negative result (no κ): legal 400-helper owner fill of #2339's 80-alias T74 words reaches b = 0.00168654, 99.994% of a certified width-aware cap b < 0.0016867 — below #2269 #2387 (this author).

Prepared with substantial AI assistance (Claude Code, Anthropic, Claude Opus 5.5). No independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code