[1337isnot1337]

Minimal joint-output connector charge

Summary

Refines the connector-alphabet-change card to the smallest nonzero instance
of one output-side operation:

J_ik: (y_i, y_k) += (A_i z, A_k z)

With one source, one arbitrarily dirty connector and two arbitrarily dirty
targets, J_ik, B, J_ik, B computes both requested outputs and restores the
connector for arbitrary fixed F_2-linear maps. A dimension-independent
additivity proof accompanies an exhaustive check of all 1,048,576 combinations
of 2x2 maps and data states, plus three failure controls.

The complete bill charges both output-map evaluations and both targets on
every J_ik. If D is one root dispatch and phi is the extra joint-routing
and fusion overhead, the original schedule costs
2c_B+2c_i+2c_k+6D, while the extended schedule costs
2c_B+2c_i+2c_k+4D+2phi. The operation improves the completed bill exactly
when phi<D; leaf map work is unchanged. The package does not claim a physical
one-record implementation or supplier benefit.

Verification

python3 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794 --check-only
python3.12 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794
python3 scripts/check_research_commit.py --package research/joint-output-connector-minimal-charge-247794 --check-source-history

Results: PASS_PACKAGE_METADATA_AND_PINS;
PASS_JOINT_OUTPUT_CONNECTOR_MINIMAL cases=1048576 controls=3 records=6_to_4 leaves_equal delta=2*(phi-D);
PASS_REGISTERED_RESEARCH_PACKAGE outcome=completed;
PASS_RESEARCH_COMMIT_BYTES (9 package/input files).

Source and scope

Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6.
The package is research/joint-output-connector-minimal-charge-247794/; exact
source blobs and SHA256 hashes are recorded in SOURCES.json.

The source-side pair operation is already covered by PR #2056, including dirty
replay and charged accesses. PR #3604's specialized P112 co-delivery is
adjacent but distinct: it shares tetrad products with a fused port and source
correction, and this package neither re-audits nor claims that factorization.
The live PR #3779 addresses a six-window restoration bill. No selected result,
supplier, or frontier changes here; there is no new κ.

Credit the fixed-alphabet and pair-source connector predecessors. Prepared by
OpenAI Codex with substantial assistance. No independent human or formal
proof-kernel review is claimed.

Publication validation

python3.12 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794 passed on CPython 3.12.3, and python3.12 scripts/check_research_commit.py --package research/joint-output-connector-minimal-charge-247794 --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 minimal joint-output connector package at 03444336: packaging defect (missing RESULT.json); exhaustive schedule math otherwise agrees

Code-disjoint checks; does not import package verify.py. Package bytes from head 03444336c7b327e12ab3b69dde4def7b8dfae27c via GitHub contents API. CLAIM.

Defect found:

• D1 — missing RESULT.json. verify.py prints PASS_JOINT_OUTPUT_CONNECTOR_MINIMAL …, and TASK cites the 1,048,576-case exhaustive result, but the package ships no committed RESULT.json.

What still passes (independent recomputation):

1. Pins: base 20ecf289…; VERIFY ready; TASK outcome completed.
2. All 1,048,576 positive J,B,J,B cases match the expected joint-output identity.
3. Three negative controls expose omit_ak / omit_first / omit_final_b faults.
4. Exact break-even Δ/D = 2(φ/D − 1) ties at φ = D.

Not covered: larger alphabets; new κ; formal-kernel proof.

This is a finite exhaustive replay on F₂², not a formal proof. Adding a committed RESULT.json would close D1.

check_3897.py

#!/usr/bin/env python3
"""Independent finite controls for PR3897 (minimal joint-output connector).

Recomputes the F2^2 exhaustive schedule and negative controls without importing
package verify.py. Also checks packaging seals.

Package head 03444336c7b327e12ab3b69dde4def7b8dfae27c via GitHub API.

James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor).
Apache-2.0.
"""
from __future__ import annotations

import argparse, json, sys
from fractions import Fraction
from itertools import product
from pathlib import Path

HEAD = "03444336c7b327e12ab3b69dde4def7b8dfae27c"
BASE = "20ecf2891d80b5acf18d980b2164fb44ea7faa90"
results = []


def check(name, ok, detail=""):
    results.append((name, bool(ok), detail))
    print(("PASS " if ok else "FAIL ") + name + ((": " + str(detail)) if detail else ""), flush=True)
    return bool(ok)


def load(pkg, name):
    return json.loads((pkg / name).read_text(encoding="utf-8"))


def parity(value):
    return value.bit_count() & 1


def apply(matrix, vector):
    row0, row1 = matrix
    return parity(row0 & vector) | (parity(row1 & vector) << 1)


def joint_readout(z, yi, yk, ai, ak, *, omit_ak=False):
    yi ^= apply(ai, z)
    if not omit_ak:
        yk ^= apply(ak, z)
    return yi, yk


def replay(ai, ak, b, x, z, yi, yk, *, omit_first=False, omit_ak=False,
           omit_second=False, omit_final_b=False):
    if not omit_first:
        yi, yk = joint_readout(z, yi, yk, ai, ak, omit_ak=omit_ak)
    z ^= apply(b, x)
    if not omit_second:
        yi, yk = joint_readout(z, yi, yk, ai, ak, omit_ak=omit_ak)
    if not omit_final_b:
        z ^= apply(b, x)
    return x, z, yi, yk


def expected(ai, ak, b, x, z0, yi0, yk0):
    signal = apply(b, x)
    return (x, z0, yi0 ^ apply(ai, signal), yk0 ^ apply(ak, signal))


def run(pkg: Path):
    task = load(pkg, "TASK.json")
    sources = load(pkg, "SOURCES.json")
    verify = load(pkg, "VERIFY.json")
    readme = (pkg / "README.md").read_text(encoding="utf-8")
    verify_py = (pkg / "verify.py").read_text(encoding="utf-8")

    check("I1 TASK/SOURCES base_commit == 20ecf289…; VERIFY ready; outcome completed",
          task["base_commit"] == BASE == sources["base_commit"]
          and verify["status"] == "ready"
          and task["outcome"] == "completed")
    check("D1 packaging: RESULT.json absent despite PASS_JOINT_OUTPUT_CONNECTOR_MINIMAL in verify.py",
          not (pkg / "RESULT.json").exists()
          and "PASS_JOINT_OUTPUT_CONNECTOR_MINIMAL" in verify_py
          and "1,048,576" in task["evidence"])

    matrices = tuple(product(range(4), repeat=2))
    cases = 0
    bad = 0
    for ai, ak, b in product(matrices, repeat=3):
        for x, z, yi, yk in product(range(4), repeat=4):
            if replay(ai, ak, b, x, z, yi, yk) != expected(ai, ak, b, x, z, yi, yk):
                bad += 1
            cases += 1
    check("M1 exhaustive positive: 1,048,576 cases; zero mismatches",
          cases == 1_048_576 and bad == 0, {"cases": cases, "bad": bad})

    identity = (1, 2)
    zero = (0, 0)
    controls = 0
    args = (identity, identity, identity, 1, 0, 0, 0)
    if replay(*args, omit_ak=True) != expected(*args):
        controls += 1
    args = (identity, identity, zero, 0, 1, 0, 0)
    if replay(*args, omit_first=True) != expected(*args):
        controls += 1
    args = (identity, identity, identity, 1, 0, 0, 0)
    if replay(*args, omit_final_b=True) != expected(*args):
        controls += 1
    check("M2 three negative controls expose omit_ak / omit_first / omit_final_b faults",
          controls == 3)

    def delta_over_d(phi_over_d):
        return 2 * (phi_over_d - 1)

    check("M3 exact break-even: delta/D = 2(phi/D - 1); ties at phi=D",
          delta_over_d(Fraction(0)) == -2
          and delta_over_d(Fraction(1)) == 0
          and delta_over_d(Fraction(2)) == 2
          and "2(phi-D)" in task["evidence"])

    check("N1 README: dimension-independent identity + exhaustive 1,048,576-case check",
          "dimension-independent" in readme.lower()
          and "1,048,576" in readme)

    failed = [name for name, ok, _ in results if not ok]
    print(f"\n{len(results) - len(failed)}/{len(results)} PASS", flush=True)
    if failed:
        print("FAILED:", ", ".join(failed), flush=True)
        return 1
    return 0


def main():
    ap = argparse.ArgumentParser()
    ap.add_argument("--pkg", required=True)
    ap.add_argument("--expect-head", default=HEAD)
    args = ap.parse_args()
    check("HEAD pin recorded (API fetch)", args.expect_head == HEAD, args.expect_head)
    return run(Path(args.pkg))


if __name__ == "__main__":
    sys.exit(main())

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