Conditional κ = 0.001661960547713947: T37 owner map on PR890's U8 word (independent cross-check of #942)

[GamingPuzzled]

Independent, concurrent; same κ as #942 (jon314159), posted 20 min earlier. This construction was developed independently and reaches the identical κ, idle profile {48:11086,1:6} and 1024-bit charged-prefix premise; credit for first publication goes to jon314159 (#942). It is offered as an independent cross-check, not a new record.

Raises the conditional exponent from PR890's 0.001661957774647029 to 0.001661960547713947 (+2.773066918e-9). The U8 local word, its widths, the PR589 bit supplier, both moment engines and the 47-inequality outer recipe are unchanged.

Idea. κ depends only on the global paid rank profile, through the complex moment root b. Here the bit side does not bind, and finite invoice counts enter only as strict admission inequalities. PR890's fixed-family bound stops at T ≤ 22 only because of the charged 512-bit prefix (113+18T < 512). That payload is paid in three places and nowhere else: the prefix reserve, the row reserve (2*payload) and the bootstrap cutoffs (2*(4+payload)). Charging 1024 bits gives prefix 779 < 1024, row 17495 < 20161, and recomputed cutoffs. Without the T cap, PR890's own signed dual (PR795 prices) is tight at T37 with idle {48:11086, 1:6}: six rank-1 remainders give credit 5550 = 150·37 and mass ≡ 30·37 (mod 48). This is the best normalized profile at any replica count.

Construction.

• PR890's T21, plus PR858's T16 relabelled into replicas 21..36, both rebuilt by their unchanged constructors.
• The two call sequences are merged proportionally: key (i+1)/189 against (j+1)/144.
• Eight frozen whole-role edits give a credit-neutral (44,3,2) → (48,1) trade: a two-step width-4 chain, then bins (20,14,111) and (27,15,0) are repacked to {8,4×6}=32 and {9,9,9,4}=31. Every move is cross-component.

All 167,832 roles in 333 calls pass the independent window/family/chart/slice audit. All eight omitted edits are rejected, and so is the sequential (non-interleaved) schedule. The 8+8+8+8+5 bank envelope passes a literal audit with eight mutations. The full PR870 controller chain runs with explicit cardinality and payload edits.

Validation.

• Strict replay PASS_STRICT_U8_T37_PR589_COMPOSITION 0.001661960547713947. It reused a PR799 baseline that was cold-rebuilt in this session, with ancestry re-bound.
• A fresh git archive cold replay of commit 50c6ae8 passed: PASS_STRICT_U8_T37_PR589_COMPOSITION 0.001661960547713947 (cold PR589/PR741/PR799 rebuild plus all 19 stages, macOS, Python 3.11).
• PR890's own cold replay also passed on the same machine (macOS, Python 3.11).

python -B research/complex-t37-owners/verify.py --work /tmp/t37-cold

Credits.

• Chafik Boukhalfa (chafreaky), Conditional κ = 0.001661957774647029: T21 whole-owner packing and fixed-family bound #890 (T21, T5, bank lift, owner bound and driver) and Independent exact certificate of PR741 owner-profile optimality #795 (signed dual).
• Hao Yan (@FanPUYen), Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858 (T16 constructor, windows, independent checker).
• Conditional κ = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word #869/Conditional κ = 0.001661956299899884: PR858's sixteen-replica owner controller on the U8 word #870 U8 (NewBArch, ColdWitness/icekylinx).
• Jeremy Kothe Conditional κ = 0.001661634653669567: four paired read exchanges on PR741's frame-coalesced word #799, Chafik Boukhalfa Conditional κ = 0.001661202643272239: eight B-frame coalescences after SW4 #741, and the PR589 bit supplier (DreamingOfClouds/eumemic lineage).
• The PR514/484/507/635/645 controller lineage.
• jon314159, Conditional κ = 0.001661960547713947: T37 whole-owner packing and all-T bound #942: the same T37 construction and κ, published first (independent, concurrent work).

Scope. This is a finite conditional composition. All-size compiler, realization, hosting, precision/tape, analytic transfer and bit H1–H5 remain inherited. The new explicit premise is the 1024-bit charged prefix.

AI disclosure: prepared with Claude Opus 5.5 (Anthropic) via Claude Code, directed by Joel Pulikkan (GamingPuzzled). No independent human review is claimed.

🤖 Generated with Claude Code