Certify exact distances for six previously unresolved PBB codes

[Jphilbrick10]

Certify exact distances for six previously unresolved PBB codes

This PR updates six entries currently marked d_is_exact: false. For each entry,
exhaustive qubit-paired Zimmermann searches found no nontrivial logical operator
below the stated distance and produced an explicit logical witness at the stated
distance. Each closure was executed twice using deterministically reconstructible,
provably distinct information sets.

One entry, 9_6_0172, was additionally reproduced by a separately implemented
runner that does not invoke the production search or certification code. It
rebuilt the information sets from recorded pivots, recomputed the deficiencies,
and exhaustively checked all 49,256,436,180 candidates across 582 shards.

IBM's published d is unchanged on all six. This confirms the existing
values; it revises none of them. 362 rows are untouched.

The six rows

code_id	bliss_hash	[[n,k]]	exact d	candidates/replica	depth p	measured deficiencies	evidence
9_6_0172	426b9d530929e62e	[[108,2]]	10	49,256,436,180	6	[0, 4]	2 replicas + independent reproduction
0571f76786029653	0571f76786029653	[[108,2]]	10	49,256,436,180	6	[0, 4]	2 replicas
phase2_64	d8f7c04aec559961	[[108,6]]	8	688,229,434,659	7	[0, 8]	2 replicas
phase2_65	d9457e4965aaa672	[[108,6]]	8	688,229,434,659	7	[0, 8]	2 replicas
12_6_0199	7989eece4ce9c3cd	[[144,4]]	12	8,149,473,282,198	7	[0, 4]	2 replicas
12_6_0201	a8879ca668587ffa	[[144,8]]	8	4,945,164,656,133	7	[0, 9]	2 replicas

Method

The two symplectic columns of each physical qubit are kept adjacent through row
reduction, so every pivot qubit owns the three non-identity options {X, Z, Y}
directly. Two consequences: the bound applies to qubit weight without the
factor-2 slack column enumeration incurs (a Y is one qubit, two columns); and
Zimmermann's rank-deficient refinement admits a second information set whose
deficiency is measured from the reduction rather than assumed:

d >= SUM_i max(0, p + 1 - deficiency_i)

d_method is set to a new value, qubit_paired_zimmermann. Reusing deep_milp
or milp_exact would attribute the result to a solver that did not produce it --
happy to rename if you prefer a different convention.

Evidence, and what each part costs to check

claim	how	cost	needs trust in us
the code is the one you published	rebuild from the row; stabilizers commute, k matches	ms	no
d <= d*	the witness: commutes with every stabilizer, not in S, weighs exactly d*	ms	no
candidate accounting	SUM_i SUM_q C(Kq_i, q) * 3^q from three integers per set	us	no
replicas searched differently	information-set hashes differ; each rebuilds from its recorded seed	min	no
no light operator at low depth	levels enumerated entirely by index, by code sharing nothing with the search	s-min	no
d >= d* in full	re-execution	hours, shardable	no

Disclosure on the lower bound

The lower bound has no succinct machine-checkable proof object. The upper
bound ships a witness anyone verifies in milliseconds; the lower bound is an
absence claim over up to 8.15e12 candidates, and independently verifying it from
first principles requires re-executing the declared search.

We looked for a short certificate and did not find one, for a reason worth
recording: any Delsarte/LP-style bound bounds the minimum weight of N(S) as a
linear code, and N(S) contains the stabilizers -- several of these codes carry
stabilizers lighter than their distance (weight 6 against d=10). No such bound
can exceed the lightest stabilizer. Applying the LP per logical coset instead
needs the weight distribution of S, which is 2^106 here.

Every certificate records lower_bound_is_machine_checkable: false internally,
so the caveat travels with the artifact rather than living only in this text.

The six are not equally independent

All six have two completed replicas on provably distinct information sets.
9_6_0172 additionally has a full lower-bound reproduction by an independently
implemented runner. independence_level is a field on each closure so the
distinction cannot be lost in summary.

Reproduction

Evidence release v1.0.1 is an immutable, self-contained bundle (57 files):
pristine catalogue inputs, per-closure certificates with witnesses and pivot
lists, the independent-reproduction manifests, verifier code, forgery
regressions, mutation report, environment records, Apache-2.0 licence.

sha256sum -c SHA256SUMS                                    # 57 OK, 0 failed
PYTHONPATH=. python verifiers/verify_closures.py           # seconds
PYTHONPATH=. python verifiers/challenge_lower_bound.py     # minutes

Every certificate is Ed25519-signed over the fields a forgery must touch
(bounds, witness, per-set deficiency/contribution/levels_swept/pivot_list),
against a key pinned in ISSUERS.json.

v1.0.0 should not be used. An external audit found its first documented
command crashed on any machine without the author's directory layout, and that
its certificates were unsigned -- so a doctored claim with self-consistent
bookkeeping was accepted. Both are fixed in v1.0.1; the audit findings and the
fixes ship inside the bundle rather than being summarised here.

The bundle is currently held privately. We would rather hand it to reviewers
than publish it unprompted: tell us where to send it, or give us a GitHub handle
and we will grant read access immediately. Nothing in this PR should be taken on
trust meanwhile -- the witnesses below are checkable from the catalogue row
alone.

Certificate schema 2.0.0; verifier floor 2.0.0.

Code-input hashes:

code_id	code_input_hash (first 16)
9_6_0172	95a416506e3ac009
0571f76786029653	ca31654d55e7fe9f
phase2_64	f54c5128f3082445
phase2_65	5acaeac02707c9a5
12_6_0199	658d23d8d1748589
12_6_0201	e61a9e67e0309d65

Fields we deliberately did not touch

logicals_optimal, logicals_incumbent and logicals_failed record the MILP
campaign's per-operator progress. This method bounds the minimum weight over all
of N(S)\S in one sweep and never resolves logicals individually, so it cannot
honestly report k-of-k optimal. Those fields are left exactly as the MILP
left them.

That leaves rows reading trust_level: EXACT beside logicals_incumbent: 1,
which is inconsistent inside a schema that assumes per-logical resolution. We
would rather surface that than paper over it. Three questions:

1. Is a non-per-logical exactness proof admissible for d_is_exact, or does the
   field specifically mean "every logical was individually resolved"?
2. Should logicals_* be normalised, left alone, or given a separate marker?
3. Is d_exactness_source the right shape for external provenance, or would you
   prefer flat fields or a sidecar file?

We are asking for technical review of the mathematics and the evidence -- not
endorsement of anything beyond these six rows.

[CLAassistant]

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[Jphilbrick10]

Superseded by #2 — the identical six-row diff, re-authored under our organization identity (Coherence Energy Labs). All review discussion welcome there.