[DreamingOfClouds]

Claim. Conditional κ = 0.003519487, tested price 0.00351948707 (raw crossing 0.00351948708416676), +0.154% over #6902. Package research/p104-mixed-port-root.

What it is. A per-port mix: 96 ports keep the two-chain form of #6902, 8 ports use the hosted form of #6889. The root is a pair of roots, block-diagonal over 78 roles, with one stage variable per stage and 18 joint contacts.

Conditional on #6902's assumptions (the five of #6833, A6 owned ascent, the BIT admission of open #6726) and its departures, plus the per-port root.

New to review.

• A root whose form varies by port. I found no quoted requirement that ties a root to one form, but no text names this either.
• Cross-type traffic: 180 ADD or COPY events couple mains of different port types, 96 involving a second main, and 279 helpers touch both types. The endpoint rows of all 400 mains hold no foreign-type input.
• 8 hosted ports with gauge SCALE 1/2 and no second mains. Owned reads of mains: 8 of Y2, 7 of X, 1 of X2. Peak owned 30. LAMBDA 206 events; if paid rank 1 per port, S = -11,040 and there is no crossing.

Scope and caveats.

• Logarithm power 2160 written (minimum 2159, using the literal carrier 153; an earlier version of this package used m = 145 and was too low, with no κ change). Raw 962,308,192 / 968,225,044 / 978,594,376, all below 10^9. Events 59,918.
• An algebraic all-columns check gives 0 wrong, using the method of Prove the selected P104 all-column caller algebra (no new κ) #6890 (CubeJerry). No width >= 2 streams were run.
• Not examined: an adjoint replay, the BIT verifiers. Theorem 1G and the compiler were not re-derived.
• Correction to earlier packages: their "peak row denominator 2^N" lines are one too high (Conditional κ = 0.00351406 (+1.652% over #6889): one native word serves two root chains #6902's 2^8 is 2^7). No κ, raw count or ledger value depends on it.

How to verify. python3.12 -B scripts/research_package.py --package research/p104-mixed-port-root prints PASS_REGISTERED_RESEARCH_PACKAGE.

Credit: as #6902.

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

🤖 Generated with Claude Code