[1337isnot1337]

With Cao Yifan's frozen #4610 round-three local profile, further binary stage thinning cannot improve the retained paired-path raw moment. This adds a written infinite-family reduction covering every pair count, prefix/suffix split, and full/query-only stage subset under the explicit retained endpoint contract. The existing p16 pattern attains the best raw crossing in (0.0030217758, 0.0030217759). No new kappa is claimed.

A new optimistic corollary deletes all eight owned-centre jobs and globally reoptimizes the same family. Its best raw crossing is (0.0080596238, 0.0080596239), at p5. Thus even free centres cannot reach C=0.01 by thinning or retuning this path. Free centres are hypothetical; this is not a construction at that larger value.

Three concavity moves reduce arbitrary masks to eight canonical families. Exact adjacent differences certify their maxima over all integer sizes; a derivative bound and a small-exponent estimate exclude every larger saving C<1. The infinite statement is the written proof, not an inference from the finite census. Changed scalar words, other idle masks, query alphabets, local profiles and supplier interfaces remain open.

Package: research/controller-thinning-global-ceiling/. Start with README.md and PROOF.md. The literal source binding independently checks rational projector identities and all 12,744 stage subsets through p5, over every split. It does not infer new universal native or absolute-phase identities from finite checks.

Validation completed on Python 3.12:

• Registered replay passes, including outward rational intervals, source/invoice binding, charge controls and four actual mutation rejections.
• Committed-byte/source-history preflight passes for all 15 checked package/input files.
• The frozen Conditional κ = 0.0030217758: joint helper interfaces and Lean compiler tightening #4610 arithmetic has its exact original Git blob c89e009ca4a5ad316c69f0371d885d72045ba415, with CRLF preserved.
• git diff --check passes. Main refreshed at b58ad9ef4d4e861b0eaa5dba41742bdc072dca51; relevant instructions, inputs and selected record are unchanged. No hosted CI pass is claimed at opening.

Reproduce:

python3.12 -B scripts/research_package.py --package research/controller-thinning-global-ceiling

The user assigned aggressive higher-K research; TASK.json records the changed card scope. Fresh overlap covered 425 open PRs and 3,588 Discussion records with reported complete pagination; sparse local note coverage is incomplete. This differs from #4602's lever budget, #4603's fixed query-fusion floor, #4623's border/recovery model and #4610's native-profile improvement.

No selected frontier, BIT construction, compiler, shared verifier or canonical source is modified. No complete multiplier, formal proof-assistant theorem or independent human acceptance is claimed. The useful next step is a profitable changed word, idle topology or query interface with a fully charged endpoint contract.

Credit Cao Yifan (#4610), Cinna Davis and #4470's cumulative native/controller lineage, zxv, Jacob Alan Sussman and all retained predecessors. Prepared for Cinna Davis with substantial OpenAI Codex assistance; no subagents. Apache-2.0.

Final overlap refresh: concurrent #4658 certifies C<0.003022 for three profiles through p64. This proof instead handles unbounded p, tightens the round-three bracket, and adds the free-centre corollary. README.md credits that work and records #4654/#4660 as a changed typed-interface target outside this theorem; their descriptions were inspected without claiming independent source replay.