Pith Number

pith:Q3IOZNZN

pith:2010:Q3IOZNZNHZNXA42FITB6JT4F7B

not attested not anchored not stored refs pending

Few smooth d-polytopes with n lattice points

Andreas Paffenholz, Benjamin Lorenz, Benjamin Nill, Christian Haase, Francisco Santos, G\"unter Rote, Hal Schenck, Milena Hering, Tristram Bogart

arxiv:1010.3887 v2 · 2010-10-19 · math.AG · math.CO · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q3IOZNZNHZNXA42FITB6JT4F7B}

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	2026-05-18T01:32:42.195517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

86d0ecb72d3e5b70734544c3e4cf85f84ebf5bcce12c0364fa8515dc6e9a2722

Aliases

arxiv: 1010.3887 · arxiv_version: 1010.3887v2 · doi: 10.48550/arxiv.1010.3887 · pith_short_12: Q3IOZNZNHZNX · pith_short_16: Q3IOZNZNHZNXA42F · pith_short_8: Q3IOZNZN

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/Q3IOZNZNHZNXA42FITB6JT4F7B \
  | 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: 86d0ecb72d3e5b70734544c3e4cf85f84ebf5bcce12c0364fa8515dc6e9a2722

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0ee094119ed6fda2b51f4c13aeecb57932bc5f2efd31b045bc70b83e2615ab6",
    "cross_cats_sorted": [
      "math.CO",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-10-19T12:52:38Z",
    "title_canon_sha256": "e6cf38a2740d343c2fa783619244cc83b028a1a9d624af9141a7955f862f9a86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3887",
    "kind": "arxiv",
    "version": 2
  }
}