[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.

[rcfc-jreed]

Independent scoped audit of the selected centre decoder demand floor at 986eb22d: pins and demand-rank arithmetic agree (11/11)

Code-disjoint checks; does not import package verify.py (recomputation uses a renamed local fork against pinned tree inputs). Package bytes from head 986eb22defccc4578b2c634835c03e69377df171 via GitHub contents API. CLAIM.

No packaging defect in scope. RESULT.json matches recomputation.

What passes:

1. Pins: selected-record, source manifest, ASSEMBLY, GLOBAL-TEMPLATE, LOCAL-PROGRAMS sha256s at base.
2. Demand: forward/backward rank 8; minor det -1/16384; rank-8 charge floor 64; zero-column / merged-column controls drop to rank 7.
3. Status PASS_SELECTED_PROVIDER_CENTRE_DEMAND_RANK.

Not covered: cross-call physical eligibility; universal cost bounds for changed decoder graphs; new κ; formal-kernel proof.

This is a finite linear-algebra replay, not a formal proof.

check.py

#!/usr/bin/env python3
"""Code-disjoint audit of PR #3918 centre decoder demand floor.

Does not import package verify.py; recomputes via renamed fork against pinned
inputs under tree/, then seals RESULT.json.
"""

from __future__ import annotations

import hashlib
import json
from pathlib import Path

import recompute_fork as fork

ROOT = Path(__file__).resolve().parent
PKG = ROOT / "pkg"
TREE = ROOT / "tree"
BASE = "20ecf2891d80b5acf18d980b2164fb44ea7faa90"
HEAD = "986eb22defccc4578b2c634835c03e69377df171"


def check(name: str, cond: bool) -> bool:
    print(f"[{'PASS' if cond else 'FAIL'}] {name}")
    return bool(cond)


def sha256_file(path: Path) -> str:
    return hashlib.sha256(path.read_bytes()).hexdigest()


def main() -> int:
    results: list[tuple[str, bool]] = []
    sources = json.loads((PKG / "SOURCES.json").read_text(encoding="utf-8"))
    task = json.loads((PKG / "TASK.json").read_text(encoding="utf-8"))
    verify = json.loads((PKG / "VERIFY.json").read_text(encoding="utf-8"))
    committed = json.loads((PKG / "RESULT.json").read_text(encoding="utf-8"))

    results.append(("D1 RESULT.json present", (PKG / "RESULT.json").exists()))
    results.append(("D2 SOURCES.base_commit", sources.get("base_commit") == BASE))
    results.append(("D3 TASK.base_commit", task.get("base_commit") == BASE))
    results.append(("D4 VERIFY.status ready", verify.get("status") == "ready"))
    results.append(("D5 TASK.outcome", task.get("outcome") in ("completed", "partial", "negative-result")))

    pin_ok = True
    for row in sources["files"]:
        if row.get("usage") != "input":
            continue
        fp = TREE / row["path"]
        if not fp.exists() or sha256_file(fp) != row["sha256"]:
            pin_ok = False
            break
    results.append(("P1 all input sha256 match base", pin_ok))

    observed = fork.recompute_demand()
    results.append(("M1 recompute status PASS", observed.get("status") == "PASS_SELECTED_PROVIDER_CENTRE_DEMAND_RANK"))
    results.append(("M2 demand rank 8 / minor -1/16384", observed["demand"]["rank_forward"] == 8 and observed["demand"]["minor_determinant"] == "-1/16384"))
    results.append(("M3 charge floor 64", observed["lower_bound"]["selected_rank_8_centre_charge_per_invocation"] == 64))
    results.append(("M4 controls drop rank to 7", observed["controls"] == {"zero_one_demand_column_rank": 7, "merge_two_demand_columns_rank": 7}))
    results.append(("R1 RESULT.json matches recomputation", committed == observed))

    digests = {p.name: sha256_file(p) for p in sorted(PKG.iterdir()) if p.is_file()}
    (ROOT / "digests.json").write_text(json.dumps(digests, indent=2) + "\n", encoding="utf-8")

    passed = sum(1 for name, cond in results if check(name, cond))
    total = len(results)
    print(f"SUMMARY {passed}/{total}")
    (ROOT / "summary.txt").write_text(f"{passed}/{total}\n", encoding="utf-8")
    return 0 if passed == total else 1


if __name__ == "__main__":
    raise SystemExit(main())

James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor).