Pith Number

pith:Y2YIITCL

pith:2012:Y2YIITCLJTX47QESHJNGRLDUGK

not attested not anchored not stored refs pending

A generalization of Opsut's lower bounds for the competition number of a graph

Yoshio Sano

arxiv:1205.4322 v1 · 2012-05-19 · 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{Y2YIITCLJTX47QESHJNGRLDUGK}

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	2026-05-18T03:09:22.902270Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6b0844c4b4cefcfc0923a5a68ac743286abb228d868a8b65000f4c1eb1f62af

Aliases

arxiv: 1205.4322 · arxiv_version: 1205.4322v1 · doi: 10.48550/arxiv.1205.4322 · pith_short_12: Y2YIITCLJTX4 · pith_short_16: Y2YIITCLJTX47QES · pith_short_8: Y2YIITCL

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/Y2YIITCLJTX47QESHJNGRLDUGK \
  | 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: c6b0844c4b4cefcfc0923a5a68ac743286abb228d868a8b65000f4c1eb1f62af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46f63ddf475a1bf8d6d073022270199db46cb426811d9a7f3acb1551efcdb06f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-19T12:22:27Z",
    "title_canon_sha256": "f0b02577bdd2244bd4df93c632d7af4d5a7e781b2f7f66aa71fcec07f4e0a08b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4322",
    "kind": "arxiv",
    "version": 1
  }
}