Conditional κ = 0.001734865178472710998233 (+0.00109%): pooled R438 slack across bit replicas on #3934, complex binds again

[rohanarun]

Conditional κ = 0.001734865178472710998233 − 10⁻⁴⁶ − 10⁻⁷⁰, which is +0.00109% over #3934 (0.001734846264120199151475). Draft: full verification is running.

	complex endpoint	bit endpoint	binds	κ
#3934	0.0017348651784727109982331	R438 0.001734846264120199151475	bit	0.001734846264120199151475 − …
this	0.0017348651784727109982331	pooled R438 0.001734900431583947157341	complex	0.001734865178472710998233 − …

Idea

#3934 made the bit side bind at R438's endpoint. R438 is #1043's word with #2423's re-hosting. It leaves 54 width-8 slack units per replica, and its proven replica-local optimum is 10 empty capacity-42 copies plus one capacity-42 copy holding one residual (idle 34).

Pooling across the 32 replicas gives 32·54 = 345·5 + 3. That makes the pooled32 optimum 345 empty 42-copies plus one empty 28-copy, with value 0.001734900431583947 (bit-partial-width7-optimum, k = 1 row). Both that package and seed72 leave open whether a cross-replica owner map can realize it. The complex T16 supplier already uses such maps (owner_replica ≠ replica).

This PR builds that map explicitly from R438's own placement. It makes 35 moves:

• the 32 single residuals (one per replica, child 6);
• the 3 residuals of one full capacity-28 copy of replica 0 (child 7, stages 5–8, inside child 6's window 3–8).

These go into 7 previously empty child-6 copies, five per copy. The idle bill changes by {2:+7, 4:−1, 28:+1, 34:−32, 42:+25}. Mass, child count and maxchild 42 are unchanged.

Verification

research/rank7-pooled-r438-bit/verify.py runs in about 7 s and is independent of build.py.

• Placement binding. ALLOC-R438.json.gz matches slot_list_sha256 in R438's rehost receipt on main.
• Role audit. All 126,144 roles are rebuilt and audited: windows, inactive host pairs, extents, cells, compact prefixes, and once-only hosting.
• Baseline check. The baseline equals the R438 certificate profile and endpoint.
• Pooled endpoint. It is accepted at c and rejected at c + 10⁻²⁴, with the fallback envelope.
• Composition. Conditional κ = 0.001734846264120199151475 (+0.00176%): hosted remainders as receivers on #3251, complex passes R438 again #3934's complex root is rechecked, and κ = min(floor₂₄(complex), floor₂₄(bit)) − ….
• Controls. 6 mutation controls are rejected.

scripts/research_package.py passes locally under Python 3.12. This PR stacks on #3934.

Scope

New hypothesis: the bit supplier may use a cross-replica owner map. The slot rules are audited, but #1043's native hosted emission (C++17/Boost) has not been run. This is conditional on R438 (#1043 is open) and on the whole #3934 stack.

Credits: Ali Romman (#1043), Sagar Thakrar (#2423), mightyOil (#1281 pooled32 optimum), seed72/seed14 (windows, placement), #1023 (slot model), and the #3934 stack's credits, including OpenCode (Space bunny free). Prepared by Rohan Arun with Anthropic Claude assistance.

🤖 Generated with Claude Code

https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy

[rohanarun]

Retracted, closing. This draft belongs to the #3934 → #3959 chain, which is built on #3251's idle-axis moves. Those were retracted on 2026-10-18 because #3190's donations change the exact eight-stream operator (see #3296/#3311/#3187). Native admission, the controller audit and the outer release never ran. #3995 and #4046 show the pooled move is rejected. The κ claimed here is not valid. Prepared by Rohan Arun with Anthropic Claude assistance.