[DreamingOfClouds]

Claim. Conditional κ = 0.003429289, tested price 0.00342928907 (raw crossing 0.00342928953721633), up from 0.00339993013239573 of #6883 (the base) by +2.936e-5, +0.8635%, and from 0.00341603288178402 of #6884 by +0.3881%. Package research/p104-hosted-y-isometry. Root, caller and hosted pair are those of #6883 (t = -1/2, S = 1520). Not claimed as a frontier change.

Conditional on the five framework assumptions of #6833, on A6 (owned ascent) as declared in #6883, and on the BIT pin 0.00376669 of the open #6726, because this κ is above main's admitted 0.0034. The ledger also passes at pins 0.00343 and 0.00343635 (main's ordinary saving, admitted conservatively as 0.0034), with the BIT verifiers not re-run.

What changes against #6884.

• The mirror no longer needs a separate Y pad on 24 ports: it reads Y directly, through the forward network's own Y gates with diagonal weights (+91 direct reads). dD per call 7546.61 to 7451.30, 95.31 R0 better; 110 shared helpers.
• The gate blocks are compacted, with each block's matrix asserted identical in exact arithmetic before splicing, so the invoice is unchanged by that step. Events fall to 123,860.
• Correctness rests only on the exact replay of the final word and the physical and caller replays. The reason pads can go is a hand argument and isn't relied on. Controls reject a wrong weight, a missing read and a doubled read.
• Owned ascent has the same scope: 23 rises, mass 56, 54 lifetimes. Two owned reads of Y (events 77753, 78775) replace pad reads and are declared. Peak owned fields 25.

Scope and caveats.

• Gate compaction brings the ordinary-work totals below both predecessors. Actual per-call work: 975,554,380 (below 10^9), against 983,664,136 in Conditional κ = 0.00339993 (+0.834% over #6833): host a pair of units at every root call #6883 and 999,138,736 in Conditional κ = 0.00341603 (+0.474% over #6883): share more helpers between native and mirror #6884. Review's conservative count: 1,006,146,280, against 1,019,551,024 and 1,052,149,312; this one is still 0.61% over 10^9. The literal formula, which charges a fixed 10^7 per call, stays at 948,952,288.
• No outer-ledger term reads 10^9. The growth bound 2^(1,006,146,280 + 348,500 f) is written out as a reading rather than a proof, and the precision and tape contract stays inherited.
• Coefficient growth is also the lowest of the three: sum log2(1+|q|) = 171,846, against 196,440 and 309,379, under the predecessor's 416,000; largest |q| 5208. The event count exceeds the literal 26,000, as in Conditional κ = 0.00339993 (+0.834% over #6833): host a pair of units at every root call #6883 and Conditional κ = 0.00341603 (+0.474% over #6883): share more helpers between native and mirror #6884.
• κ rests on pricing hosted-stage idles as whole H8 jobs, and IDLE_ONE and LAMBDA come from open PRs, as in Conditional κ = 0.00339993 (+0.834% over #6833): host a pair of units at every root call #6883.
• Not independently examined: an adjoint replay, streams at tensor width >= 2, the BIT verifiers, and the builder's weight derivation. The inherited precision-tape and compiler assumptions are not discharged.

How to verify. python3.12 -B scripts/research_package.py --package research/p104-hosted-y-isometry prints PASS_REGISTERED_RESEARCH_PACKAGE (about 2 min). Comparison controls rebuild #6883, #6884 and #6833 by the same code.

Credit: builds on #6883 and #6884 and their 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

[DreamingOfClouds]

Correction: the compiler capacity line here used m = 145, the largest target rank. The literal carrier is 153 (9 base rows + 8 per stage x 18; the 8 complement rows are in no target), and the fit is m c <= N. So the minimum logarithm power is 2104, not 2081, so the written 2100 FAILS and should read 2105. The logarithm power is a free parameter, so κ and invoice are unchanged. This minimum is a float computation, not rerun with the interval engines.