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Independent verification: stdlib re-certification of PR1615's eight-transfer threshold, with all 2,502 eight-transfer schedules (only port splits r=1, r=5) (no new kappa) - #1767
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…er threshold with all 2,502 solutions (no new kappa) PR1615 (bbMisk) first proved that the PR1438/PR1498 free-port two-connector family needs exactly eight transfers. This concurrent, code-disjoint package agrees with every overlapping PR1615 number and adds: a standard-library certificate of the exclusion and exact count that runs in the generic package hook (gap-reduction lemma), cross-checked by full-placement C and per-occurrence numpy engines; the complete eight-transfer solution set (2,502 canonical schedules, only port splits r=1 with 2,376 and r=5 with 126, all replayed as 80-call programs); and the exact four-transfer split maxima (PR1498's r=2 bound of 25 is not attained; the maximum is 21). Seed 58, connector-alphabet-change (refined). Prepared with substantial Anthropic Claude assistance.
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Batch review at Merged to Reviewed scope: Independent standard-library census reproduces the credited eight-transfer threshold and enumerates2502 canonical schedules, all replayed as80-call programs. Gap-reduction proof and full registered controls/six/eight coverage checked. Separate author C/numpy histories are supporting provenance, not newly replayed here; incidence-minimal one-way-transfer model only. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
2 participants
Change and mathematical scope
Independent verification. No new κ, and no change to any construction,
certificate, selected record or pinned file. It adds one registered package,
research/two-connector-eight-transfer-census-seed58/.Priority belongs to #1615. The six-transfer exclusion and the sharp
eight-transfer threshold for the free-port two-connector family are
#1615 (Hanson Sun / bbMisk). That family is the one from #1438/#1498: five
sources, every B and A called exactly twice, and paid one-way transfers
C: z0 += z1. The eight-transfer word is Discussion #1412 (Cinna Davis).This package was built concurrently without reading #1615's code. It agrees
with every #1615 number it overlaps.
What it adds:
--witness-only, and its exclusion needs a native C++ workflow.exhaustive
t ≤ 7exclusion and the exactt = 8count. On 10 cores ittakes about 20 s and 50 s, inside the generic Python 3.12 package hook.
z1is fixed. So three transfers act like oneand four like two, with coverage and restoration parities preserved.
and a numpy census with per-occurrence ports.
source on
z1and 126 with all five onz1. The second class isDiscussion Read-only five-source connector: second dirty root and eight paid XORs (seed54) #1412's restricted alphabet, up to renaming.
The best coverages are 31, 31, 27 and 24 of 32.
arbitrary dirt.
are recorded here with replay evidence.
attained; the exact maximum is 21. The other bounds are exact, as Research: four transfers cannot realize universal two-connector masks #1498
itself allowed ("need not be sharp").
Scope. The incidence-minimal 72-call family only. It is a finite census
plus a short reduction lemma. There is no supplier claim. The cost condition is
#1498's
t·σtariff att = 8, as in #1615.Task and overlap
0b1cccf8; catalogue priority revision 3 leaves thecard unchanged. Seed 58 → recursive interfaces, card
connector-alphabet-change, scope refined to independent verificationand classification.
96916897): the threshold theorem. Its files contain noeight-transfer count, no split classification, no
t = 4split maxima andno stdlib exclusion; I checked every file.
b7baacc8): the four-transfer obstruction and the question.Validation
Registered parts (standard library, parallel):
controls:t = 2censuses for 1 to 5 sources: everyrestored count and histogram;
t = 0andt = 4, withno universal schedule;
t.six: an exhaustivet = 6census over all 945 words and 32 splits.None is universal, and the per-split maxima equal Research: sharp eight-transfer threshold with free source-port choice #1615's
(31, 31, 28, 22, 23, 31). The full histogram is pinned.
eight:ba04f277…and split counts;
Offline receipts.
independent/census.c(every placement, no reduction) agrees exactly:tThe
t = 6totals reproduce Research: sharp eight-transfer threshold with free source-port choice #1615.independent/census_numpy.py(per-occurrence ports) gives 74,692,800legal schedules and 0 universal at
t = 6.Pre-PR review. A three-lens review covered the mathematics, verifier
soundness and the claims.
t = 8, each withmaximum gap 2;
maxima alone miss;
t = 0all-split check;Tested on Python 3.12.15 and 3.14.8 (macOS, 10 cores). On a 4-core runner each
part fits well within the 600 s per-command limit.
Credit
priority.
tariff and question.
AI disclosure: prepared by Sagar Thakrar with substantial Anthropic Claude
assistance, including explorer, judge and reviewer subagents. Two of those
subagents wrote the independent engines. New work is Apache-2.0.
Open next questions
explains why only r = 1 and r = 5 reach eight?
engine.pyto 73 calls with full dirt vectors.