Pith Number

pith:FXIH7E5X

pith:2015:FXIH7E5XEXLQMHTBCO3Z4XI2DN

not attested not anchored not stored refs pending

More bounds for the Grundy number of graphs

Baoyindureng Wu, Lin Hu, Manoucheher Zaker, Zixing Tang

arxiv:1507.01080 v2 · 2015-07-04 · 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{FXIH7E5XEXLQMHTBCO3Z4XI2DN}

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	2026-05-18T01:24:43.670516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dd07f93b725d7061e6113b79e5d1a1b77e5effbd627a9cd523b0f08b2ea4e09

Aliases

arxiv: 1507.01080 · arxiv_version: 1507.01080v2 · doi: 10.48550/arxiv.1507.01080 · pith_short_12: FXIH7E5XEXLQ · pith_short_16: FXIH7E5XEXLQMHTB · pith_short_8: FXIH7E5X

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/FXIH7E5XEXLQMHTBCO3Z4XI2DN \
  | 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: 2dd07f93b725d7061e6113b79e5d1a1b77e5effbd627a9cd523b0f08b2ea4e09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa2f782b6222587dedddfecb10d33e4349bb8b7e44fff67ac4795ca128e0ed69",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-04T08:25:02Z",
    "title_canon_sha256": "f8bc12c0574f610805e4c0a09976889bf0d848380cb0277b03a5e061593877bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01080",
    "kind": "arxiv",
    "version": 2
  }
}