Pith Number

pith:35UU777M

pith:2018:35UU777MTQ7P7I2VIOHSYBT4E2

not attested not anchored not stored refs pending

Average Betti numbers of induced subcomplexes in triangulations of manifolds

Francisco Santos, Giulia Codenotti, Jonathan Spreer

arxiv:1808.04220 v2 · 2018-08-13 · math.CO · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{35UU777MTQ7P7I2VIOHSYBT4E2}

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	2026-07-05T01:28:58.245774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df694fffec9c3effa355438f2c067c269ec907b38aebece4c37ce9408d8bc646

Aliases

arxiv: 1808.04220 · arxiv_version: 1808.04220v2 · doi: 10.48550/arxiv.1808.04220 · pith_short_12: 35UU777MTQ7P · pith_short_16: 35UU777MTQ7P7I2V · pith_short_8: 35UU777M

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/35UU777MTQ7P7I2VIOHSYBT4E2 \
  | 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: df694fffec9c3effa355438f2c067c269ec907b38aebece4c37ce9408d8bc646

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7293b14e7607194b25bfaaf7dcff8019685300bdd7836a610a3fc573ce17395a",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-13T13:58:45Z",
    "title_canon_sha256": "60ba3a4fd36bf71716387b6e44a77628dccee49704fab75b60c1f12caa262e49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.04220",
    "kind": "arxiv",
    "version": 2
  }
}