[DreamingOfClouds]

Claim. Conditional κ = 0.00341603 (raw crossing 0.00341603288178402), up from 0.00339993013239573 of #6883 by +1.610e-5, +0.4736%. Package research/p104-hosted-shared-cover. Root, caller and hosted pair are those of #6883 (t = -1/2, S = 1520); only the native word and the BIT pin change. Not claimed as a frontier change.

Conditional on the five framework assumptions of #6833, on A6 (owned ascent) exactly as declared in #6883, and on the BIT pin 0.00376669 taken from the open #6726, because this κ is above main's admitted 0.0034. The admission file is pinned and not re-derived. Main's ordinary BIT 0.0034363538396 is also above this κ but is admitted conservatively as 0.0034 (docs/research/bottleneck-brief.md:17-18); the ledger lines pass at 0.00343, with the BIT verifiers not re-run.

What changes against #6883.

• Helper sharing between the forward network and its contragredient mirror is chosen by an exact optimum on whole-word tax rather than one greedy order: dD per call 7663.4 to 7546.61, 116.80 R0 better. All T and P differences are in ranks 1 to 9, multiples of 18.
• 342 core ADD events are deleted and 22 silent helpers dropped (public registers 1403 to 1385). The forward network is no longer the Conditional κ = 0.00330823 (+9e-8 over #6805): lift two helper inputs onto one shared carrier #6824 word verbatim, so the black-box argument of Conditional κ = 0.00339993 (+2.813e-5, +0.834% over #6833): host a pair at every root call with a mirrored native, declared owned ascent #6883 does not apply. The deletions are not no-ops: none leaves T unchanged on its own, the changes fall in blocks the rebuilt gates correct, and correctness rests only on the exact replay. Controls reject removing or duplicating an ADD.
• Owned ascent has the same scope: 23 rises, mass 56, 54 lifetimes, 51 roles.

Scope and caveats.

• Peak owned fields rise from 13 to 25; events are 222,128. No ledger or invoice term reads them.
• Raw totals are 948,952,288 (literal), 999,138,736 (actual per-call work, margin 0.1%) and 1,052,149,312 (review's conservative count, 5.2% over 10^9). No outer-ledger term reads 10^9; it is a parameter of the precision and tape contract, not re-examined here.
• κ rests on pricing the hosted-stage idles as whole H8 jobs (else 0.002995), and IDLE_ONE and LAMBDA come from open PRs, as in Conditional κ = 0.00339993 (+2.813e-5, +0.834% over #6833): host a pair at every root call with a mirrored native, declared owned ascent #6883.
• Logarithm power 2100 suffices (minimum 2073), following the p-form at research/balanced-query-tree/pricing.py:95-107.
• Not independently examined: an adjoint replay and tensor width 3. Optimality of the sharing assumes conflicts persist in supersets; that affects only whether it's optimal, not correctness. The inherited precision-tape and compiler assumptions are not discharged.

How to verify. python3.12 -B scripts/research_package.py --package research/p104-hosted-shared-cover prints PASS_REGISTERED_RESEARCH_PACKAGE (about 2 min). The comparison controls rebuild #6883 and #6833 by the same code.

Question for review. Is the BIT pin of #6726, or a higher admission of main's ordinary saving, accepted for the outer statement above 0.0034?

Credit: builds on #6883 and its lineage: #6833, #6726 (zxv), #6716 (thu-nmrc), CubeJerry (#6805), Ali Romman (#6349, #6353, #6372), Jacob Alan Sussman (compiler), #6702 and #6824.

Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

🤖 Generated with Claude Code