Pith Number

pith:M36FGJLR

pith:2009:M36FGJLR5ONGOXMWKNBMJKDBU7

not attested not anchored not stored refs pending

Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees

Erik Stokes, Sonja Petrovi\'c

arxiv:0910.1610 v4 · 2009-10-08 · math.AC · math.CO · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M36FGJLR5ONGOXMWKNBMJKDBU7}

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	2026-05-18T03:26:32.794342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66fc532571eb9a675d965342c4a861a7e609f7bf3c20150de5b2dc8fcb7d8eb0

Aliases

arxiv: 0910.1610 · arxiv_version: 0910.1610v4 · doi: 10.48550/arxiv.0910.1610 · pith_short_12: M36FGJLR5ONG · pith_short_16: M36FGJLR5ONGOXMW · pith_short_8: M36FGJLR

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/M36FGJLR5ONGOXMWKNBMJKDBU7 \
  | 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: 66fc532571eb9a675d965342c4a861a7e609f7bf3c20150de5b2dc8fcb7d8eb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a30fe8a159a01c73b80f71987d9420d939304615fd4394b3a546c5ff47f6334",
    "cross_cats_sorted": [
      "math.CO",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2009-10-08T20:46:09Z",
    "title_canon_sha256": "9fee71acda2d8ac623d90fd950c6691ff0e95e94ee1cd834e017d575234f5bfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.1610",
    "kind": "arxiv",
    "version": 4
  }
}