Pith Number

pith:KOFQCDSL

pith:2014:KOFQCDSLWZAL7FVXMPTOEOGTKM

not attested not anchored not stored refs pending

Graph colouring and the total Betti number

Alexander Engstrom

arxiv:1412.8460 v2 · 2014-12-29 · math.CO · math.AT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KOFQCDSLWZAL7FVXMPTOEOGTKM}

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	2026-05-18T02:30:17.352814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

538b010e4bb640bf96b763e6e238d353100884aabbda79f1dac2dc8a29f16fd9

Aliases

arxiv: 1412.8460 · arxiv_version: 1412.8460v2 · doi: 10.48550/arxiv.1412.8460 · pith_short_12: KOFQCDSLWZAL · pith_short_16: KOFQCDSLWZAL7FVX · pith_short_8: KOFQCDSL

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/KOFQCDSLWZAL7FVXMPTOEOGTKM \
  | 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: 538b010e4bb640bf96b763e6e238d353100884aabbda79f1dac2dc8a29f16fd9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e77afb6c222db84fb488d4e1aab290e63906e7190d1b08ca2be65c1520f246ff",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-29T20:51:23Z",
    "title_canon_sha256": "363c7e4cc1b485eda9fcb1ddea301418f636afbe9eb3c158efa651d15beff25a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.8460",
    "kind": "arxiv",
    "version": 2
  }
}