Pith Number

pith:GBTGNF3C

pith:2007:GBTGNF3CLGGAU3Y5LB2NH3MR3I

not attested not anchored not stored refs pending

A note on a degree sum condition for long cycles in graphs

Janusz Adamus

arxiv:0711.4394 v2 · 2007-11-28 · 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{GBTGNF3CLGGAU3Y5LB2NH3MR3I}

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	2026-05-18T04:09:04.471309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3066669762598c0a6f1d5874d3ed91da2e60398c1b56da4cbc8b6dde90aa4347

Aliases

arxiv: 0711.4394 · arxiv_version: 0711.4394v2 · doi: 10.48550/arxiv.0711.4394 · pith_short_12: GBTGNF3CLGGA · pith_short_16: GBTGNF3CLGGAU3Y5 · pith_short_8: GBTGNF3C

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/GBTGNF3CLGGAU3Y5LB2NH3MR3I \
  | 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: 3066669762598c0a6f1d5874d3ed91da2e60398c1b56da4cbc8b6dde90aa4347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15cdc71a5dfdd47fd270fd81d69d6dd405480e7129223e54031fae288f9869bc",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2007-11-28T01:00:01Z",
    "title_canon_sha256": "3c1b18b8d04c384972874d492a4f717dee717982cbf4ead8ab73523d034a5a6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.4394",
    "kind": "arxiv",
    "version": 2
  }
}