Pith Number

pith:3GJRODEA

pith:2025:3GJRODEAZBG4CCVB32EAWVFUOG

not attested not anchored not stored refs pending

Cycles and paths through vertices whose degrees are at least the bipartite-hole-number

Chengli Li, Feng Liu, Yurui Tang

arxiv:2506.09750 v1 · 2025-06-11 · 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{3GJRODEAZBG4CCVB32EAWVFUOG}

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	2026-07-05T11:19:56.338688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d993170c80c84dc10aa1de880b54b471b8f963f8a8891f97c73cbf66537ab829

Aliases

arxiv: 2506.09750 · arxiv_version: 2506.09750v1 · doi: 10.48550/arxiv.2506.09750 · pith_short_12: 3GJRODEAZBG4 · pith_short_16: 3GJRODEAZBG4CCVB · pith_short_8: 3GJRODEA

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/3GJRODEAZBG4CCVB32EAWVFUOG \
  | 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: d993170c80c84dc10aa1de880b54b471b8f963f8a8891f97c73cbf66537ab829

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb6ca9ca960639e2e3c42a29b93173ed0c5c6c13917aabbd3c67cc8b53172ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-11T13:54:27Z",
    "title_canon_sha256": "7f475963a96d3f636dccdc8a4b2db038a9eec36415c9341aee23f43c32f0428b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.09750",
    "kind": "arxiv",
    "version": 1
  }
}