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research: exact QQ16 consumer budget obstruction under centre-64 law - #3908
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FINDING / scoped DONE — independent consumer-budget audit completed; claim released. Published PR #3946, exact head Decision: pause expansion of the unchanged recipe toward the selected target. Under centre 64, decoder-only replacements need at most 121 rank-one calls per pair with rank-eight work waived, or 61 with it retained, versus the current 336. Hypothetical centre 63 with the existing decoder and rank-eight work leaves only about 0.0000126126 normalized allowance; this is an optimistic budget opening, not a coverage construction. Next bounded task: pin an actual downstream F17-native demand, compose it with the literal decoder and exhibit eliminated work under an explicitly changed native/endpoint contract. Derive its coverage identity and charge acquisition, frames, restoration and the complete consumer before extending tape implementation. Scalar/axis improvements alone do not delete recursive charges; a justified all-depth direct-tape tariff replacement is a separately priced changed premise. Distinguish adjacent #2391/#2461/#3120/#3873 scopes. Stop if no named consumer or real saving is supplied. Evidence: CPython 3.12.3 normal/optimized warning-strict verification, eleven behavioral groups, exact retained predecessor replay, registered package replay, read-only Git-free export, semantic/source/receipt controls and published-byte/source-history preflight (18 files) pass. The original PR3908 registered replay and its previously unrun source-history preflight also pass at its exact head (12 files). Hosted status is tracked separately in PR3946. Full native/bridge/decoder correctness, physical admission, complete supplier, human/formal review and a new kappa are not claimed. Credit 1337isnot1337/#3908, dcharb78/#3181, ywz65/#2707, Ali Romman and the conserved QQ16/native lineage, Douglas Colkitt and the coverage-ceiling authors, Sagar Thakrar, Nick Petalas and retained notices. Clear1nsight with substantial OpenAI assistance; Apache-2.0. Original scoped claim (released)CLAIM — independent audit of this exact draft, with caller applicability and a quantitative next-step budget. Pinned PR3908 head: 0d8880e. Canonical main: 20ecf28, priority revision 6 (refreshed 2026-10-19 05:35 UTC). Explicit assigned follow-up to PR3932. I will independently expand the literal F0/B_1_2 source and count the #2707 decoder word, check the moment with a separately implemented rational interval method, and delimit the connection to F0 event 9894 on L546. Then derive a decoder/centre-charge tradeoff identifying what a changed consumer must save. Physical caller admission and the selected frontier remain separate. Expected within one session; claim expires 2026-10-19 07:40 UTC. Credit 1337isnot1337/#3908, dcharb78/#3181, ywz65/#2707, the conserved QQ16/native lineage and coverage-ceiling authors. Clear1nsight with substantial OpenAI assistance; no human review claimed. |
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Independent scoped audit of the QQ16 consumer-cap obstruction under centre-64 at Code-disjoint checks; does not import package Defect found:
What still passes:
Not covered: new κ; formal-kernel proof; re-deriving producer/decoder invoices from scratch. This is a finite arithmetic replay, not a formal proof. Adding a committed check.py#!/usr/bin/env python3
"""Code-disjoint audit of PR #3908 QQ16 consumer budget obstruction."""
from __future__ import annotations
import gzip
import hashlib
import json
from fractions import Fraction as Q
from math import factorial
from pathlib import Path
ROOT = Path(__file__).resolve().parent
PKG = ROOT / "pkg"
UP = ROOT / "upstream"
BASE = "20ecf2891d80b5acf18d980b2164fb44ea7faa90"
HEAD = "0d8880e38ed7c88d70eec6a48e5aa829d0fb22f3"
SELECTED_A = Q(836330098538459, 499163669901461541)
KAPPA_STR = "836330098538459/500000000000000000"
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 git_blob(raw: bytes) -> str:
return hashlib.sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest()
def load_up(rel: str) -> bytes:
return (UP / rel.replace("/", "__")).read_bytes()
def ln_unit_lb(y: Q, terms: int = 32) -> Q:
assert Q(1) <= y <= Q(2)
z = (y - 1) / (y + 1)
return 2 * sum((z ** (2 * j + 1)) / (2 * j + 1) for j in range(terms))
def ln_ratio_lb(x: Q) -> Q:
assert x >= 1
k = 0
while x >= 2:
x /= 2
k += 1
return k * ln_unit_lb(Q(2)) + ln_unit_lb(x)
def exp_lb(x: Q, terms: int = 5) -> Q:
assert x >= 0
return sum(x**j / factorial(j) for j in range(terms))
def child_lb(rank: int, m: int, a: Q) -> Q:
assert 0 < rank < m
return Q(rank, m) * exp_lb(a * ln_ratio_lb(Q(m, rank)))
def merge_profiles(f_prof, b_prof, decoder_children, calls=2):
assert calls > 0 and decoder_children % calls == 0
out = {}
for key in set(f_prof) | set(b_prof):
rank = int(key)
out[rank] = (Q(f_prof.get(str(rank), 0)) + Q(b_prof.get(str(rank), 0))) / calls
out[1] = out.get(1, Q(0)) + Q(decoder_children, calls)
return {r: n for r, n in out.items() if n}
def moment_lb(profile, m, w, centre, idle_rank, unpaid=1):
assert 2 * idle_rank * idle_rank < m * m
total = (m - unpaid) * w + centre
local_mass = sum(Q(r) * Q(n) for r, n in profile.items())
idle_mass = total - local_mass
assert idle_mass >= 0
local = sum(Q(n) * child_lb(r, m, SELECTED_A) for r, n in profile.items())
idle = idle_mass / idle_rank * child_lb(idle_rank, m, SELECTED_A)
return (local + idle) / w, total, local_mass, idle_mass
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"))
target = json.loads((PKG / "TARGET.json").read_text(encoding="utf-8"))
readme = (PKG / "README.md").read_text(encoding="utf-8")
results.append(("D1 RESULT.json absent (packaging)", not (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 completed", task.get("outcome") == "completed"))
results.append(("D6 README mentions centre-64 / QQ16", "centre" in readme.lower() and "QQ16" in readme))
# Pin checks against fetched base blobs
pin_ok = True
for row in sources["files"]:
if row.get("usage") != "input":
continue
raw = load_up(row["path"])
if sha256_file(UP / row["path"].replace("/", "__")) != row["sha256"]:
pin_ok = False
if git_blob(raw) != row["git_blob"]:
pin_ok = False
results.append(("P1 input sha256+git_blob match base", pin_ok))
selected = json.loads(load_up("certificates/selected-result.json"))
ceiling = json.loads(load_up("research/complex-local-word-ceiling/RESULT.json"))
ceiling_code = load_up("research/complex-local-word-ceiling/ceiling.py").decode()
producer = json.loads(load_up("research/joint-query/evidence/CONSERVED-QQ16.json"))
decoder = json.loads(load_up("research/qq16-line-normalized-decoder/RESULT.json"))
results.append(("P2 selected kappa pin", selected.get("kappa") == KAPPA_STR))
model = ceiling["model"]
results.append(("P3 ceiling status + model (73,9,64,51)", ceiling.get("status") == "PASS_COMPLEX_LOCAL_WORD_CEILING" and (model["m"], model["stages"], model["centre_per_call"], model["idle_rank_cap"]) == (73, 9, 64, 51)))
results.append(("P4 live_families_per_call == 896/9", Q(model["live_families_per_call"]) == Q(896, 9)))
results.append(("P5 ceiling.py contains monotone + halving guards", "non-increasing in r" in ceiling_code and "2 * R * R < m * m" in ceiling_code))
claim = target["audited_claim"]
source = target["source"]
external = gzip.decompress((PKG / source["local_archive"]).read_bytes())
results.append(("E1 PR3181 archive blob/sha256", git_blob(external) == source["git_blob"] and hashlib.sha256(external).hexdigest() == source["sha256"]))
results.append(("E2 PR head/state premises", source["pr"] == 3181 and source["state_at_check"] == "OPEN" and source["head"] == "80fc72d14546088e9fce3c06dc12bc67270da0af"))
et = external.decode()
results.append(("E3 profile/cap text in archive", "`{1: 2596, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8}`" in et and "`0.001631159602`" in et and "`centre = 64`" in et))
child_count = decoder["invoice"]["rank_one_children"]
results.append(("D7 decoder events/children", decoder["events"] == 3823 and child_count == claim["decoder_rank_one_children_per_pair"] == 336))
results.append(("D8 producer B_1_2 added rank1", producer["native_cases"]["B_1_2"]["added_rank1_children"] == 24))
f_profile = producer["invoices"]["F"]["native_profile"]
b_profile = producer["invoices"]["B"]["native_profile"]
derived = merge_profiles(f_profile, b_profile, child_count, calls=2)
full = dict(derived)
full[8] = Q(claim["reported_profile_per_call"]["8"])
reported = {int(r): Q(n) for r, n in claim["reported_profile_per_call"].items()}
results.append(("M1 reconstructed profile matches claim", full == reported))
relaxed = {r: n for r, n in full.items() if r != 8}
moment, total, local_mass, idle = moment_lb(relaxed, 73, Q(896, 9), 64, 51)
results.append(("M2 coverage mass 7232/5706/1526", (total, local_mass, idle) == (Q(7232), Q(5706), Q(1526))))
results.append(("M3 relaxed moment > 100009/100000", moment > Q(100009, 100000)))
full_moment, _, _, _ = moment_lb(full, 73, Q(896, 9), 64, 51)
results.append(("M4 full profile moment > relaxed", full_moment > moment))
no_centre, _, _, _ = moment_lb(relaxed, 73, Q(896, 9), 0, 51)
results.append(("M5 centre-free moment < 1", no_centre < 1))
bad_idle = False
try:
moment_lb(relaxed, 73, Q(896, 9), 64, 52)
except AssertionError:
bad_idle = True
results.append(("N1 idle rank 52 rejected by halving guard", bad_idle))
bad_split = False
try:
merge_profiles(f_profile, b_profile, 335, calls=2)
except AssertionError:
bad_split = True
results.append(("N2 uneven decoder split rejected", bad_split))
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_n = len(results)
print(f"SUMMARY {passed}/{total_n}")
print(f"moment_decimal={float(moment):.15f} full={float(full_moment):.15f} no_centre={float(no_centre):.15f}")
(ROOT / "summary.txt").write_text(f"{passed}/{total_n}\n", encoding="utf-8")
return 0 if passed == total_n else 1
if __name__ == "__main__":
raise SystemExit(main())James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor). |
1 similar comment
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Independent scoped audit of the QQ16 consumer-cap obstruction under centre-64 at Code-disjoint checks; does not import package Defect found:
What still passes:
Not covered: new κ; formal-kernel proof; re-deriving producer/decoder invoices from scratch. This is a finite arithmetic replay, not a formal proof. Adding a committed check.py#!/usr/bin/env python3
"""Code-disjoint audit of PR #3908 QQ16 consumer budget obstruction."""
from __future__ import annotations
import gzip
import hashlib
import json
from fractions import Fraction as Q
from math import factorial
from pathlib import Path
ROOT = Path(__file__).resolve().parent
PKG = ROOT / "pkg"
UP = ROOT / "upstream"
BASE = "20ecf2891d80b5acf18d980b2164fb44ea7faa90"
HEAD = "0d8880e38ed7c88d70eec6a48e5aa829d0fb22f3"
SELECTED_A = Q(836330098538459, 499163669901461541)
KAPPA_STR = "836330098538459/500000000000000000"
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 git_blob(raw: bytes) -> str:
return hashlib.sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest()
def load_up(rel: str) -> bytes:
return (UP / rel.replace("/", "__")).read_bytes()
def ln_unit_lb(y: Q, terms: int = 32) -> Q:
assert Q(1) <= y <= Q(2)
z = (y - 1) / (y + 1)
return 2 * sum((z ** (2 * j + 1)) / (2 * j + 1) for j in range(terms))
def ln_ratio_lb(x: Q) -> Q:
assert x >= 1
k = 0
while x >= 2:
x /= 2
k += 1
return k * ln_unit_lb(Q(2)) + ln_unit_lb(x)
def exp_lb(x: Q, terms: int = 5) -> Q:
assert x >= 0
return sum(x**j / factorial(j) for j in range(terms))
def child_lb(rank: int, m: int, a: Q) -> Q:
assert 0 < rank < m
return Q(rank, m) * exp_lb(a * ln_ratio_lb(Q(m, rank)))
def merge_profiles(f_prof, b_prof, decoder_children, calls=2):
assert calls > 0 and decoder_children % calls == 0
out = {}
for key in set(f_prof) | set(b_prof):
rank = int(key)
out[rank] = (Q(f_prof.get(str(rank), 0)) + Q(b_prof.get(str(rank), 0))) / calls
out[1] = out.get(1, Q(0)) + Q(decoder_children, calls)
return {r: n for r, n in out.items() if n}
def moment_lb(profile, m, w, centre, idle_rank, unpaid=1):
assert 2 * idle_rank * idle_rank < m * m
total = (m - unpaid) * w + centre
local_mass = sum(Q(r) * Q(n) for r, n in profile.items())
idle_mass = total - local_mass
assert idle_mass >= 0
local = sum(Q(n) * child_lb(r, m, SELECTED_A) for r, n in profile.items())
idle = idle_mass / idle_rank * child_lb(idle_rank, m, SELECTED_A)
return (local + idle) / w, total, local_mass, idle_mass
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"))
target = json.loads((PKG / "TARGET.json").read_text(encoding="utf-8"))
readme = (PKG / "README.md").read_text(encoding="utf-8")
results.append(("D1 RESULT.json absent (packaging)", not (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 completed", task.get("outcome") == "completed"))
results.append(("D6 README mentions centre-64 / QQ16", "centre" in readme.lower() and "QQ16" in readme))
# Pin checks against fetched base blobs
pin_ok = True
for row in sources["files"]:
if row.get("usage") != "input":
continue
raw = load_up(row["path"])
if sha256_file(UP / row["path"].replace("/", "__")) != row["sha256"]:
pin_ok = False
if git_blob(raw) != row["git_blob"]:
pin_ok = False
results.append(("P1 input sha256+git_blob match base", pin_ok))
selected = json.loads(load_up("certificates/selected-result.json"))
ceiling = json.loads(load_up("research/complex-local-word-ceiling/RESULT.json"))
ceiling_code = load_up("research/complex-local-word-ceiling/ceiling.py").decode()
producer = json.loads(load_up("research/joint-query/evidence/CONSERVED-QQ16.json"))
decoder = json.loads(load_up("research/qq16-line-normalized-decoder/RESULT.json"))
results.append(("P2 selected kappa pin", selected.get("kappa") == KAPPA_STR))
model = ceiling["model"]
results.append(("P3 ceiling status + model (73,9,64,51)", ceiling.get("status") == "PASS_COMPLEX_LOCAL_WORD_CEILING" and (model["m"], model["stages"], model["centre_per_call"], model["idle_rank_cap"]) == (73, 9, 64, 51)))
results.append(("P4 live_families_per_call == 896/9", Q(model["live_families_per_call"]) == Q(896, 9)))
results.append(("P5 ceiling.py contains monotone + halving guards", "non-increasing in r" in ceiling_code and "2 * R * R < m * m" in ceiling_code))
claim = target["audited_claim"]
source = target["source"]
external = gzip.decompress((PKG / source["local_archive"]).read_bytes())
results.append(("E1 PR3181 archive blob/sha256", git_blob(external) == source["git_blob"] and hashlib.sha256(external).hexdigest() == source["sha256"]))
results.append(("E2 PR head/state premises", source["pr"] == 3181 and source["state_at_check"] == "OPEN" and source["head"] == "80fc72d14546088e9fce3c06dc12bc67270da0af"))
et = external.decode()
results.append(("E3 profile/cap text in archive", "`{1: 2596, 2: 418, 3: 432, 4: 142, 5: 82, 8: 8}`" in et and "`0.001631159602`" in et and "`centre = 64`" in et))
child_count = decoder["invoice"]["rank_one_children"]
results.append(("D7 decoder events/children", decoder["events"] == 3823 and child_count == claim["decoder_rank_one_children_per_pair"] == 336))
results.append(("D8 producer B_1_2 added rank1", producer["native_cases"]["B_1_2"]["added_rank1_children"] == 24))
f_profile = producer["invoices"]["F"]["native_profile"]
b_profile = producer["invoices"]["B"]["native_profile"]
derived = merge_profiles(f_profile, b_profile, child_count, calls=2)
full = dict(derived)
full[8] = Q(claim["reported_profile_per_call"]["8"])
reported = {int(r): Q(n) for r, n in claim["reported_profile_per_call"].items()}
results.append(("M1 reconstructed profile matches claim", full == reported))
relaxed = {r: n for r, n in full.items() if r != 8}
moment, total, local_mass, idle = moment_lb(relaxed, 73, Q(896, 9), 64, 51)
results.append(("M2 coverage mass 7232/5706/1526", (total, local_mass, idle) == (Q(7232), Q(5706), Q(1526))))
results.append(("M3 relaxed moment > 100009/100000", moment > Q(100009, 100000)))
full_moment, _, _, _ = moment_lb(full, 73, Q(896, 9), 64, 51)
results.append(("M4 full profile moment > relaxed", full_moment > moment))
no_centre, _, _, _ = moment_lb(relaxed, 73, Q(896, 9), 0, 51)
results.append(("M5 centre-free moment < 1", no_centre < 1))
bad_idle = False
try:
moment_lb(relaxed, 73, Q(896, 9), 64, 52)
except AssertionError:
bad_idle = True
results.append(("N1 idle rank 52 rejected by halving guard", bad_idle))
bad_split = False
try:
merge_profiles(f_profile, b_profile, 335, calls=2)
except AssertionError:
bad_split = True
results.append(("N2 uneven decoder split rejected", bad_split))
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_n = len(results)
print(f"SUMMARY {passed}/{total_n}")
print(f"moment_decimal={float(moment):.15f} full={float(full_moment):.15f} no_centre={float(no_centre):.15f}")
(ROOT / "summary.txt").write_text(f"{passed}/{total_n}\n", encoding="utf-8")
return 0 if passed == total_n else 1
if __name__ == "__main__":
raise SystemExit(main())James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor). |
3 participants
Summary
Adds
research/qq16-consumer-cap-audit/, an exact independent audit of the recursive-price budget for the pinnedCONSERVED-QQ16F0 + B_1_2pair and #2707 decoder under the unchanged centre-64 coverage law.The source-pinned F/B profiles average to 2,428 rank-one children per call. The decoder contributes 336 rank-one children across two calls, producing the #3181 profile
{1:2596,2:418,3:432,4:142,5:82,8:8}. At the selectedkappa = 836330098538459/500000000000000000, the verifier removes the eight rank-eight children and relaxes their 64 mass units into rank-51 idle children. Even this favorable relaxation has an exact rational moment lower bound above100009/100000at the selected exponent.This is a scoped necessary-budget obstruction for that fixed profile and coverage law. It does not establish a physical F17 consumer, an exact cap root, a global barrier, a changed-coverage result or a new selected kappa.
Verification
All three commands passed locally at base
20ecf2891d80b5acf18d980b2164fb44ea7faa90. The registered replay reportsPASS_REGISTERED_RESEARCH_PACKAGE research/qq16-consumer-cap-audit outcome=completed.Review focus and limits
Please check the profile reconstruction, the exact atanh/log and positive Taylor lower bounds, and the rank-51 favorable relaxation. The open physical caller, retention, routing, movement and F17-consumer obligations remain outside this package. No selected full historical replay or formal-kernel proof was run.
The exact #3181 README used for its profile premise is retained in compressed form and checked against its source blob/SHA256 at head
80fc72d14546088e9fce3c06dc12bc67270da0af.Credit the
CONSERVED-QQ16producer lineage, ywz65/#2707, dcharb78/#3181, and the selected coverage-ceiling authors. No independent human review is claimed.Publication validation
The registered package replay passed on CPython 3.12.3 with
python3.12 scripts/research_package.py --package research/qq16-consumer-cap-audit. The optional--check-source-historypreflight could not run because this MacBook checkout is shallow and the checker requires full Git history. This package's source manifest pins only files at its exact base commit20ecf2891d80b5acf18d980b2164fb44ea7faa90; it contains nohead:source pins. Any earlier pending note above refers to the state before this publication-time replay.