Pith Number

pith:LPPJEPZX

pith:2025:LPPJEPZXNNM22DHR2RJRJKKJDX

not attested not anchored not stored refs pending

Longest odd cycles in non-bipartite $C_{2k+1}$-free graphs

Rui Wang, Shipeng Wang

arxiv:2508.16199 v1 · 2025-08-22 · 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{LPPJEPZXNNM22DHR2RJRJKKJDX}

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	2026-07-05T11:57:43.871733Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bde923f376b59ad0cf1d45314a9491df7947cdcfd3833705edd02ccc4adfebf

Aliases

arxiv: 2508.16199 · arxiv_version: 2508.16199v1 · doi: 10.48550/arxiv.2508.16199 · pith_short_12: LPPJEPZXNNM2 · pith_short_16: LPPJEPZXNNM22DHR · pith_short_8: LPPJEPZX

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/LPPJEPZXNNM22DHR2RJRJKKJDX \
  | 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: 5bde923f376b59ad0cf1d45314a9491df7947cdcfd3833705edd02ccc4adfebf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "252dec873eb48bc92fb345a435c130d40c5a60cef4c8f0d0b33ac81a4bcfaa3e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-08-22T08:18:58Z",
    "title_canon_sha256": "22f1692db3eccdcf9eb7577b6fb98aa126c464c33c364f25ca04c5ac813fb1c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.16199",
    "kind": "arxiv",
    "version": 1
  }
}