Pith Number

pith:BXCUS2ZS

pith:2010:BXCUS2ZSPJUEAZOIVH2IL3LKUU

not attested not anchored not stored refs pending

Betti numbers of the geometric spaces associated to nonrational simple convex polytopes

Fiammetta Battaglia

arxiv:1004.4763 v1 · 2010-04-27 · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BXCUS2ZSPJUEAZOIVH2IL3LKUU}

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	2026-05-18T02:24:15.961855Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0dc5496b327a684065c8a9f485ed6aa531f2f90a1af2650aa103759ac8172100

Aliases

arxiv: 1004.4763 · arxiv_version: 1004.4763v1 · doi: 10.48550/arxiv.1004.4763 · pith_short_12: BXCUS2ZSPJUE · pith_short_16: BXCUS2ZSPJUEAZOI · pith_short_8: BXCUS2ZS

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/BXCUS2ZSPJUEAZOIVH2IL3LKUU \
  | 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: 0dc5496b327a684065c8a9f485ed6aa531f2f90a1af2650aa103759ac8172100

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19c7107e526876106aa88d47d74f33456fa538be0bc9d8e4f823c2f397495c99",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-04-27T11:18:00Z",
    "title_canon_sha256": "015af1e8e8f492b38b60db076b734aca7ed10094784b019fd12b94f8433ea255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4763",
    "kind": "arxiv",
    "version": 1
  }
}