Pith Number

pith:LAJ75RII

pith:2010:LAJ75RII64HZ64QGLAHW7YWNG7

not attested not anchored not stored refs pending

Coboundary expanders

Dominic Dotterrer, Matthew Kahle

arxiv:1012.5316 v2 · 2010-12-23 · math.CO · math.AT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LAJ75RII64HZ64QGLAHW7YWNG7}

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	2026-05-18T04:24:07.068657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5813fec508f70f9f7206580f6fe2cd37c1ee2219bbcf5689b388f80843c41bd3

Aliases

arxiv: 1012.5316 · arxiv_version: 1012.5316v2 · doi: 10.48550/arxiv.1012.5316 · pith_short_12: LAJ75RII64HZ · pith_short_16: LAJ75RII64HZ64QG · pith_short_8: LAJ75RII

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/LAJ75RII64HZ64QGLAHW7YWNG7 \
  | 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: 5813fec508f70f9f7206580f6fe2cd37c1ee2219bbcf5689b388f80843c41bd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73fb96e2150c9cf3d307b2e6ce6ad0666c968dcf8447adbcc1de25866adeff0c",
    "cross_cats_sorted": [
      "math.AT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-23T23:06:04Z",
    "title_canon_sha256": "5c120f960b71d21a26e9710884ab738f99704e16206c48b2ac2e7d876a87c6a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5316",
    "kind": "arxiv",
    "version": 2
  }
}