Pith Number

pith:CVSHJKN2

pith:2012:CVSHJKN2SPAVZIYJTGDEEHPRR7

not attested not anchored not stored refs pending

Betti diagrams from graphs

Alexander Engstr\"om, Matthew T. Stamps

arxiv:1210.8069 v3 · 2012-10-30 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CVSHJKN2SPAVZIYJTGDEEHPRR7}

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	2026-05-18T01:22:26.074413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

156474a9ba93c15ca3099986421df18fe88119cd69b794d4cd00cc32dbfa394c

Aliases

arxiv: 1210.8069 · arxiv_version: 1210.8069v3 · doi: 10.48550/arxiv.1210.8069 · pith_short_12: CVSHJKN2SPAV · pith_short_16: CVSHJKN2SPAVZIYJ · pith_short_8: CVSHJKN2

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/CVSHJKN2SPAVZIYJTGDEEHPRR7 \
  | 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: 156474a9ba93c15ca3099986421df18fe88119cd69b794d4cd00cc32dbfa394c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b785d14fc4561b1f121116a9932a9f55f41d5ca3e3318fd57a0cff5ea72b5cf4",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-30T16:18:22Z",
    "title_canon_sha256": "0b20674ab56d58be1c94cd231afd753ae3bb6267565addf90248f5efc2bc1683"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.8069",
    "kind": "arxiv",
    "version": 3
  }
}