Pith Number

pith:GQ3H45YP

pith:2011:GQ3H45YP5KPXHRPZEFNWFER7JU

not attested not anchored not stored refs pending

A generalization of the Birthday problem and the chromatic polynomial

Sukhada Fadnavis

arxiv:1105.0698 v3 · 2011-05-03 · 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{GQ3H45YP5KPXHRPZEFNWFER7JU}

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.

Cited by

1 paper in Pith

Counting birthday collisions using partitions

Receipt and verification

First computed	2026-05-18T01:32:42.167112Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34367e770fea9f73c5f9215b62923f4d149b490167c4e9616e56e5ca1f8ab20a

Aliases

arxiv: 1105.0698 · arxiv_version: 1105.0698v3 · doi: 10.48550/arxiv.1105.0698 · pith_short_12: GQ3H45YP5KPX · pith_short_16: GQ3H45YP5KPXHRPZ · pith_short_8: GQ3H45YP

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/GQ3H45YP5KPXHRPZEFNWFER7JU \
  | 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: 34367e770fea9f73c5f9215b62923f4d149b490167c4e9616e56e5ca1f8ab20a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97d3f8231eafc1096bfd3aff307907fc3e834bfb6a545fefc377092ca150bfb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-05-03T21:56:33Z",
    "title_canon_sha256": "26b0e528af11ed1d140a624fdc59bf67ee2b766fcfb41467cea69a6086fcbef6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.0698",
    "kind": "arxiv",
    "version": 3
  }
}