Pith Number

pith:QNGORMMF

pith:2026:QNGORMMF2D4AIV4K757ZAWVBCW

not attested not anchored not stored refs pending

On the structure of dense graphs with given odd girth

Shipeng Wang, Xingyan Lu

arxiv:2607.04323 v1 · 2026-07-05 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QNGORMMF2D4AIV4K757ZAWVBCW}

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	2026-07-07T02:19:08.770309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

834ce8b185d0f804578aff7f905aa115a79b33d0b595c5d0f07d866e7fe8cf0d

Aliases

arxiv: 2607.04323 · arxiv_version: 2607.04323v1 · doi: 10.48550/arxiv.2607.04323 · pith_short_12: QNGORMMF2D4A · pith_short_16: QNGORMMF2D4AIV4K · pith_short_8: QNGORMMF

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/QNGORMMF2D4AIV4K757ZAWVBCW \
  | 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: 834ce8b185d0f804578aff7f905aa115a79b33d0b595c5d0f07d866e7fe8cf0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fca80e27c5719267a1d8d41cb4cb707c571ea1d2798f2b4a2b8368c83072808f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-05T14:14:28Z",
    "title_canon_sha256": "888dededa2603272d6002caef0c80b51e9cef23bf8cf06551714a5269835e3f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.04323",
    "kind": "arxiv",
    "version": 1
  }
}