[Matarener]

Requested by Mark

Change and mathematical scope

Scoped proof + pricing screen (negative result); no new κ, selected record unchanged.

Package: research/centre-nonlinear-fresh-floor/.

• Theorem 1. Under the premises of research/centre-history-innovation, any fresh observation that is continuous, or semialgebraic (finitely many branches built from + - ×, division by nonzero values including the dyadic /2, /4, comparisons and adaptive reads that may depend on the history or on earlier fresh reads), still needs at least 8d complex coordinates per future owner, the same as the linear floor. Proof: on a subspace V ⊂ ker H the history vanishes and Q|_V is bijective, so the fresh observation must be injective on a real 16d-dimensional set; invariance of domain (continuous case) or semialgebraic dimension preservation (branching case) gives n ≥ 16d.
• Theorem 2. On a finite b-bit grid the only escape is Kronecker packing, which conserves bits (widths sum to ≥ 16db, attained exactly; one bit less collides). In the rank-mass model this keeps the coverage mass 72w + 64 and the deficit w − 64.
• Screen. Regrouping the 64 centre mass into larger children (bounding every packing) raises the complex-local-word ceiling by at most +0.67% (x1.006721, fractional rank-72), before guard bits, carries, unpacking or hosting are charged. The card's two-call sharing budget (x1.90) needs the fresh information halved, which Theorems 1–2 exclude.

Remaining obligations / not covered: all premises of centre-history-innovation are inherited (native common-frame, full-space cover view, one future owner, call 10); the step from 8d coordinates to 64 rank-mass units is #3918's rank-8 carrier premise, unchanged by nonlinearity; a terminal-only consumer that never forms the internal call-10 query is a changed contract and stays open.

Task and overlap

Card centre-path-sharing, priority revision 7, base 12fa8c5c844be21bfefb38a19503fbd867a11244. Scope refined: answers method 2 (copied-information lower bound) for the nonlinear/adaptive fresh-data interfaces.

Closes the case listed as not established in #3873 ("a lower bound against nonlinear or adaptive algorithms") and the fresh nonlinear-observation case left open by centre-history-innovation (including its "mutable eight-slot cache with fresh reads"). Nearest work inspected: #3075, #3120, #3147, #3151, #3291, #3548, #3873, #3918, #3948, #1888, and the nonlinear copy floors #785/#888 (which price nonlinear messages under an explicit additive-width premise on E8 lines, not the centre path). I found no nonlinear fresh-observation centre bound; no novelty guarantee.

Validation

python3.12 -I -B research/centre-nonlinear-fresh-floor/verify.py
python3.12 scripts/research_package.py --package research/centre-nonlinear-fresh-floor

CPython 3.12 on Windows: PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=negative-result (normal and -O replays), PASS_PACKAGE_METADATA_AND_PINS, PASS_RESEARCH_COMMIT_BYTES with --check-source-history. About 35 s, mostly the unchanged predecessor replay (PASS_CENTRE_HISTORY_INNOVATION sha256=8edf9aec…, bound to its RESULT.json).

Finite checks: Kronecker packing sharpness on six small grids; exact rational ceiling brackets via research/complex-local-word-ceiling/ceiling.py with mass conservation asserted. Controls: halved centre information reproduces x1.901107; a rank-73 child, a mass-losing pack and a corrupted predecessor digest are rejected. Theorems 1–2 are proof arguments in the README, not finite checks. No selected cold replay or formal-kernel review.

Credit

Builds on Jose Manuel (jmbarrancoml)'s centre-history-innovation and its lineage, Clear1nsight's centre-causal-tangent (#3873), Douglas Colkitt's complex-local-word ceiling, the nonlinear copy-floor line (#703, #785, #814, #888) and the centre-sharing budgets (#1791, #1888, #3075, #3548, #3948). Substantial Claude (Anthropic) assistance in proof, code and prose; no independent human review.

Open next questions

In the package README and TASK.json: (1) can a terminal-only consumer avoid forming the internal call-10 query (first step: test the 112 kernel witnesses against a stated terminal map); (2) does 8d fresh coordinates force 64 rank-mass units for carriers other than rank-8 channels (ideal gain capped here at +0.67%).

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