Add selected centre decoder demand floor audit

[1337isnot1337]

Exact information floor for the selected gauge44 centre decoder

Summary

Add a source-bound exact demand-rank check for one invocation of the current
selected gauge44 local provider. Its 112×8 centre-phase consumer matrix has
rational rank 8 in both orientations. Therefore any exact linear encoder and
decoder preserving this endpoint needs at least eight independent scalar
channels per invocation.

The selected profile carries those eight totals through eight rank-8 centre
macros, for 64 rank units. This is the selected profile and a conditional floor
when replacements retain the rank-8-per-channel carrier restriction; the
information-rank result alone does not price arbitrary changed decoder graphs.

Source binding and evidence

The verifier checks the selected record, certificate, selected source
manifest, current global template and current local program by SHA256. It also
checks that every global-template call dispatches to gauge44, the inline
provider program equals the separately pinned local program, and each call's
orientation hash matches the provider record.

The source rows are (92, 57, 81, 224, 11, 240, 9, 256), private centres map
to [7168, 7176), and consumer rows are 112–223. The exact minor on rows
(112, 117, 118, 120, 113, 116, 115, 123) has determinant -1/16384.
Forward and backward demand matrices are equal; backward restores the same
source rows.

This rederives the per-call demand floor from the current selected provider
files. It is complementary to PR #3120's archived-template result. PR #3075
covers the separate fully charged k-call relaxation.

Reproduce

python3.14 -I -B research/centre-selected-provider-demand-floor/verify.py
python3 scripts/research_package.py --package research/centre-selected-provider-demand-floor --check-only

Both commands passed on Python 3.14.8. The registered replay requires Python
3.12; that interpreter is unavailable on this host, so no Python 3.12 registered
replay is claimed. No selected cold replay, supplier admission, physical
sharing eligibility or new κ is claimed.

Credit the selected construction and lineage in PR #1094, Aaron Wang's PR #3120
for the archived demand-rank result, and the P112 factor-model lineage in PR
#845, #1098, #968, and #1180. This work used substantial OpenAI Codex
assistance. No independent human or proof-assistant review is claimed.

Current overlap

Open PR #3120 derives a multi-call copied-information floor for the selected centre path. This package binds the 112-by-8 phase matrix of one selected local provider and its rank-8 per-invocation demand, under the stated rank-8 carrier restriction. It does not price arbitrary changed decoder graphs.

Publication validation

python3.12 scripts/research_package.py --package research/centre-selected-provider-demand-floor passed on CPython 3.12.3, and python3.12 scripts/check_research_commit.py --package research/centre-selected-provider-demand-floor --check-source-history passed. The registered replay left the worktree clean. This supersedes any earlier pending note above for the registered package replay; separate full selected cold-replay limits remain as stated.