Pith Number

pith:QKVCAABI

pith:2026:QKVCAABIPP4DAWT67VJZ4SPCDD

not attested not anchored not stored refs pending

Minimal Counterexamples of the MacWilliams Extension Theorem for Stabilizer Codes

Ali Assem Mahmoud

arxiv:2607.26214 v1 · 2026-07-28 · quant-ph · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QKVCAABIPP4DAWT67VJZ4SPCDD}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-30T01:17:43.688177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

82aa2000287bf8305a7efd539e49e218d746a2218a1bd15e5c68a16b13ac110c

Aliases

arxiv: 2607.26214 · arxiv_version: 2607.26214v1 · doi: 10.48550/arxiv.2607.26214 · pith_short_12: QKVCAABIPP4D · pith_short_16: QKVCAABIPP4DAWT6 · pith_short_8: QKVCAABI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QKVCAABIPP4DAWT67VJZ4SPCDD \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 82aa2000287bf8305a7efd539e49e218d746a2218a1bd15e5c68a16b13ac110c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e79f26e842b53923d114068be02a7a2de72516264c03cf8befe59aacb6a7785a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-07-28T19:31:39Z",
    "title_canon_sha256": "9eadd56c9dd50f4dc025220c350dd43168e942341d88a249c743d8d5ee7b62df"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26214",
    "kind": "arxiv",
    "version": 1
  }
}