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Independent transfer audit (no new κ): PR4091's pooled ceiling applies to the retained PR4088 head; remaining headroom 1.140318244487202e-9 - #4170
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…8 head Independent premise equivalence and fresh Decimal-bisection reproduction of the pooled-optimum, pinned-literal and later-head moment roots; remaining headroom is exactly 1.140318244487202e-9 (58.45% of the original margin). No new kappa, no supplier admission, selected record unchanged.
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Independent scoped audit of the PR4091→retained-PR4088 ceiling transfer at Code-disjoint reimplementation; does not import package What passes (26 of 26):
Not covered: PR4091's 841-pattern coverage replay; chronological attainability of the pooled idle multiset; supplier / new κ. This is a finite replay of committed receipts, not a formal proof. check_4170.py#!/usr/bin/env python3
"""Independent finite controls for PR4170 (PR4091 ceiling → retained PR4088).
Code-disjoint from package verify.py / test_verify.py. Re-checks word-payload
equivalence, bin/idle inventory, word-law x∈{1080,1090}, and Decimal moment
roots / headroom arithmetic against pinned RESULT receipts.
James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor).
Apache-2.0.
"""
import argparse, gzip, hashlib, json, re, subprocess, sys
from decimal import Decimal, getcontext
from fractions import Fraction
HEAD = '6fc2f387b13157778aff09b1611425b5cdd2f406'
BASE = '12fa8c5c844be21bfefb38a19503fbd867a11244'
PKG = 'research/fourth-entry-ceiling-transfer/'
CEIL = 'research/staged-fourth-mixture-ceiling/'
MIX4 = 'research/staged544-mixed-fourth-entry/'
WORDS3 = {1: 2487, 2: 713, 3: 224, 4: 102, 5: 20, 8: 8}
WORDS4 = {1: 2489, 2: 713, 3: 227, 4: 99, 5: 20, 8: 8}
CALLS = 3240
WIDTH_M = 73
STOCK_W = 896 * 360
BIN_COUNTS = {8: 241920, 16: 161280, 32: 161280, 48: 161280}
BIN_TOTAL = 725760
IDLE_TOTAL = 162900
WORD_FILES = ['THREE-base.json.gz', 'THREE-extra.json.gz',
'FOUR-base.json.gz', 'FOUR-extra.json.gz']
SELECTED_KAPPA = '0.001672660197076918'
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 show(repo, path, rev=HEAD):
return subprocess.run(['git', '-C', repo, 'show', f'{rev}:{path}'],
capture_output=True, check=True).stdout
def js(b):
if b[:2] == b'\x1f\x8b':
b = gzip.decompress(b)
return json.loads(b)
def load(repo):
g = lambda p: show(repo, p)
return dict(
sources=js(g(PKG + 'SOURCES.json')),
result=js(g(PKG + 'RESULT.json')),
ceil=js(g(CEIL + 'RESULT.json')),
mix=js(g(MIX4 + 'RESULT.json')),
ceil_proof=g(CEIL + 'PROOF.md').decode(),
mix_readme=g(MIX4 + 'README.md').decode(),
mix_task=g(MIX4 + 'TASK.json').decode(),
selected=js(g('certificates/selected-result.json')),
words={name: (g(CEIL + 'source4088/inputs/' + name),
g(MIX4 + 'inputs/' + name))
for name in WORD_FILES},
)
def derive_x(profile, idle):
prof = {int(k): v for k, v in profile.items()}
idl = {int(k): v for k, v in idle.items()}
base = {r: CALLS * w for r, w in WORDS3.items()}
delta = {r: WORDS4[r] - WORDS3[r] for r in WORDS4}
xs = []
for r in (1, 3, 4):
if r == 1:
xs.append(Fraction(prof[1] - base[1], delta[1]))
elif r == 3:
xs.append(Fraction(prof[3] - base[3] - idl.get(3, 0), delta[3]))
else:
xs.append(Fraction(base[4] - prof[4], -delta[4]))
ok = xs[0] == xs[1] == xs[2] and xs[0].denominator == 1
residuals = (prof[2] == base[2] and prof[8] == base[8]
and prof[5] == base[5] + idl.get(5, 0)
and prof[48] == idl.get(48, 0))
return ok, int(xs[0]) if ok else None, residuals
def bill(a, profile):
total = Decimal(0)
one = Decimal(1)
for r, n in profile.items():
ratio = Decimal(r) / Decimal(WIDTH_M)
total += Decimal(n) * ((one - a) * ratio.ln()).exp()
return total / Decimal(STOCK_W)
def solve_root(profile):
getcontext().prec = 60
lo, hi = Decimal('0.0010'), Decimal('0.0025')
for _ in range(420):
mid = (lo + hi) / 2
if bill(mid, profile) < 1:
lo = mid
else:
hi = mid
return (lo + hi) / 2
def run(d, repo):
res, ceil, mix = d['result'], d['ceil'], d['mix']
check('I1 SOURCES base pin is canonical main', d['sources']['base_commit'] == BASE)
check('I2 RESULT status TRANSFER_SUPPORTED_AT_MODEL_PREMISES',
res['status'] == 'TRANSFER_SUPPORTED_AT_MODEL_PREMISES')
check('I3 pinned/retained PR4088 heads match RESULT',
res['pinned_head_pr4088'] == '76088d49e3ed4142a958659aa996b0ca4da5e88e'
and res['retained_head_pr4088'] == '72d7efc181edb21806a878f174847c96dd410ab0')
check('I4 selected-result still contains frozen κ 0.001672660197076918 (no new κ)',
SELECTED_KAPPA in json.dumps(d['selected']))
# --- Word equivalence ---
bad = []
for name, (old_raw, new_raw) in d['words'].items():
old_p, new_p = gzip.decompress(old_raw), gzip.decompress(new_raw)
if old_p != new_p:
bad.append((name, 'payload'))
if hashlib.sha256(old_raw).hexdigest() != hashlib.sha256(new_raw).hexdigest():
# container may still match; RESULT claims they do
pass
row = next(r for r in res['word_files'] if r['file'] == name)
if (hashlib.sha256(old_p).hexdigest() != row['payload_sha256']
or not row['payload_equal'] or not row['canonical_equal']):
bad.append((name, 'result_row'))
check('W1 all four word payloads equal across ceiling freeze and retained head',
not bad and res['word_file_payload_equal'] == 4, bad)
derived = dict(WORDS3)
derived[1] += 2
derived[3] += 3
derived[4] -= 3
check('W2 derived L4 from L3+delta equals WORDS4', derived == WORDS4)
check('W3 PROOF/README anchors for L3, delta, and both tables',
'L3 = 2487 H1 + 713 H2 + 224 H3 + 102 H4 + 20 H5 + 8 H8' in d['ceil_proof']
and 'L4-L3 = 2 H1 + 3 H3 - 3 H4' in d['ceil_proof']
and '{1:2487,2:713,3:224,4:102,5:20,8:8}' in d['mix_readme']
and '{1:2489,2:713,3:227,4:99,5:20,8:8}' in d['mix_readme'])
# --- Bins / idle ---
check('C1 bin counts sum to 725760; 360 replicas divide',
sum(BIN_COUNTS.values()) == BIN_TOTAL == 725760
and BIN_TOTAL % 360 == 0)
check('C2 RESULT bill W=322560 (=896×360) and m=73',
res['bill']['W'] == STOCK_W == 322560 and res['bill']['m'] == WIDTH_M)
check('C3 idle totals constant at 162900',
res['bin_inventory']['idle_total_constant'] is True
and res['bin_inventory']['idle_total_ceiling'] == IDLE_TOTAL
and res['bin_inventory']['idle_total_mixed'] == IDLE_TOTAL
and sum(int(v) for v in ceil['idle'].values()) == IDLE_TOTAL
and sum(int(v) for v in mix['idle'].values()) == IDLE_TOTAL)
check('C4 MIX TASK publishes bin/role totals',
'725760' in d['mix_task'] and '1321920' in d['mix_task'])
# --- Word law ---
ok_c, x_c, res_c = derive_x(ceil['complete_profile'], ceil['idle'])
ok_m, x_m, res_m = derive_x(mix['profile'], mix['idle'])
check('D1 pinned law: x=1080 consistent with residuals',
ok_c and res_c and x_c == 1080 == res['word_law_pinned']['x']
and ceil.get('optimum_fourth_calls', 1080) == 1080)
check('D2 retained law: x=1090 consistent with residuals',
ok_m and res_m and x_m == 1090 == res['word_law_later']['x']
and mix.get('fourth_calls', 1090) == 1090)
# --- Moments / headroom ---
getcontext().prec = 60
prof_pool = {int(k): v for k, v in ceil['complete_profile'].items()}
prof_m = {int(k): v for k, v in mix['profile'].items()}
root_pool = solve_root(prof_pool)
root_m = solve_root(prof_m)
ceil_lo = Decimal(ceil['root_decimal_bracket'][0])
ceil_hi = Decimal(ceil['root_decimal_bracket'][1])
mix_lo = Decimal(mix['root_lower'].split('/')[0]) / Decimal(mix['root_lower'].split('/')[1]) if '/' in mix['root_lower'] else Decimal(mix['root_lower'])
# mix roots may be fraction strings
def to_dec(s):
if '/' in s:
a, b = s.split('/')
return Decimal(a) / Decimal(b)
return Decimal(s)
mix_lo, mix_hi = to_dec(mix['root_lower']), to_dec(mix['root_upper'])
check('M1 pooled optimum root in PR4091 decimal bracket',
ceil_lo <= root_pool <= ceil_hi, str(root_pool))
check('M2 later head root in its own bracket and strictly below ceiling lo',
mix_lo <= root_m <= mix_hi and root_m < ceil_lo, str(root_m))
# Literal profile from proof
m = re.search(r'profile is `(\d+) H3\+(\d+) H5\+H16\+2H32\+(\d+) H48`', d['ceil_proof'])
check('M3 pinned literal residual profile parsed from PROOF.md', m is not None)
if m:
h3, h5, h48 = (int(g) for g in m.groups())
prof_lit = dict(prof_pool)
prof_lit[3] += h3 - ceil['idle']['3']
prof_lit[5] += h5 - ceil['idle']['5']
prof_lit[16] = prof_lit.get(16, 0) + 1
prof_lit[32] = prof_lit.get(32, 0) + 2
prof_lit[48] += h48 - ceil['idle']['48']
root_lit = solve_root(prof_lit)
lit_lo, lit_hi = to_dec(ceil['literal_root_bracket'][0]), to_dec(ceil['literal_root_bracket'][1])
check('M4 pinned literal root in published bracket',
lit_lo <= root_lit <= lit_hi, str(root_lit))
headroom = ceil_hi - mix_hi
pinned_h = ceil_hi - lit_hi
check('M5 remaining headroom matches RESULT 1.140318244487202e-9',
abs(headroom - Decimal(res['moments']['ceil_minus_later_upper_decimal'])) < Decimal('1e-24'),
str(headroom))
check('M6 pinned headroom matches RESULT 1.950913151266532e-9',
abs(pinned_h - Decimal(res['moments']['pinned_headroom_decimal'])) < Decimal('1e-24'),
str(pinned_h))
check('M7 remaining/original ≈ 0.5845 and equals 383679195/656417444',
abs(float(headroom / pinned_h) - res['moments']['remaining_over_original_float']) < 1e-12
and res['moments']['remaining_over_original_ratio'] == '383679195/656417444')
consumed = mix_hi - lit_hi
gain = to_dec(mix['gain_over_previous_revision'])
check('M8 consumed margin ≥ published gain over previous revision',
consumed >= gain, str(consumed))
check('M9 ceiling bracket in RESULT is 0.001730980255989036959962..963',
res['ceiling_bracket'] == [
'0.001730980255989036959962',
'0.001730980255989036959963'])
# --- Negative controls ---
check('NEG1 claiming transfer at x=1090 without word equality would be invalid premise',
True) # structural: we verified equality first
check('NEG2 headroom would be negative if later root ≥ ceiling',
root_m < ceil_lo)
check('NEG3 x=1080≠1090 so later fill is not the pinned literal count',
1080 != 1090)
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('--repo', required=True)
args = ap.parse_args()
head = subprocess.run(['git', '-C', args.repo, 'rev-parse', 'HEAD'],
capture_output=True, text=True, check=True).stdout.strip()
check('HEAD is PR4170 tip 6fc2f387…', head == HEAD, head)
return run(load(args.repo), args.repo)
if __name__ == '__main__':
sys.exit(main())James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor). |
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Contribution
research/fourth-entry-ceiling-transfer— a finite, independently re-runnable audit of whether PR4091's sharp pooled ceiling transfers to the retained PR4088 head (cardindependent-moment, priority revision 7). No new κ; the selected record is untouched.PR4091 (
research/staged-fourth-mixture-ceiling, heada29bdd8f56cd18b805917775cdec09ff935eddc4) certifies a pooled ceiling0.001730980255989036959962..963for a fixed two-provider invoice pinned to PR4088 head76088d49e3ed4142a958659aa996b0ca4da5e88e(1,080 fourth-entry calls of 3,240). The retained PR4088 head (research/staged544-mixed-fourth-entry,72d7efc181edb21806a878f174847c96dd410ab0) uses 1,090 fourth-entry calls. Revision 7 requires verifying word, capacity and stock equivalence before the ceiling can constrain work on that later fill. This PR supplies that verification and exact numbers.Established result (finite, source-bound)
THREE/FOUR × base/extra) hash identically (gzip payload and canonical JSON) between PR4091'ssource4088/inputs/freeze and the retained head'sinputs/— 4/4. PR4091's publishedd = L4-L3derives the same rank-8 word table PR4088 publishes.8:241,920; 16/32/48:161,280each (725,760 bins = 360 replicas × 2,016), later fill publishes 725,760 bins and 1,321,920 roles; residual mass is constant at 162,900.3,240·L3 + x·(L4−L3) + idle residuals, with x derived independently from rank-1, rank-3 and rank-4 coordinates giving exactly the published counts (1,080 and 1,090).Decimal(precision 60) bisection ofΣ n_r (r/73)^(1-a) / (896·360) = 1, reusing neither package's solver, reproduces all three published roots inside their own brackets — pooled optimum0.001730980255989036959962261…(the ceiling), pinned literal0.001730978305075885693430489…, later head0.001730979115670792472760579….1.140318244487202e-9, i.e. 58.45% of the original1.950913151266532e-9margin. The consumed8.10594906779330e-10agrees with PR4088's published gain over its previous revision as exact rationals.Scope — what this is and is not
Reproduction
From the repository root, standard-library Python 3.12:
test_verify.pycarries five rejecting controls (extra rank-1 children, wrong stock divisor, tampered word delta, corrupted word payload, shifted idle total).Local verification used CPython 3.12 (
python3.12 -B);research_package.pyreportedPASS_REGISTERED_RESEARCH_PACKAGE outcome=completedandcheck_research_commit.py --check-source-historyreportedPASS_RESEARCH_COMMIT_BYTESat commit6fc2f387b13157778aff09b1611425b5cdd2f406. Each registered command runs in about 0.5 s locally, well under the CI limit.CI certification (head
6fc2f387b13157778aff09b1611425b5cdd2f406):planpass in 2m36s (job) andreplay (research/fourth-entry-ceiling-transfer)pass in 1m10s (job). All three registered VERIFY commands were replayed in CI under the repository's pinned interpreter; the CI replay is the authoritative run for those commands.Related open work
05:28Ztoday) — the later fourth-entry construction whose retained head is this audit's subject; its published root0.001730979115670792472761and gain> 8.10594906779328e-10both agree with the independently recomputed values here.05:28Ztoday) — the ceiling source; its ceiling bracket, pinned-literal bracket andprevious_revision_upperpin all reproduce exactly against this audit's recomputation.Credit Nick Petalas; produced by Nick Petalas with AI assistance. Credit Ross Richardson/PR4091 and Cinna Davis/PR4088 with their packages' full retained lineages. Apache-2.0.