Pith Number

pith:HPFNXBP4

pith:2018:HPFNXBP4GJNXXEDWS3HYWPRNFM

not attested not anchored not stored refs pending

Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials

Antoine Douai

arxiv:1811.07724 v2 · 2018-11-19 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HPFNXBP4GJNXXEDWS3HYWPRNFM}

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	2026-05-17T23:58:36.358259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3bcadb85fc325b7b907696cf8b3e2d2b2495ce3b292dfc72c13a0ad1aa716ee9

Aliases

arxiv: 1811.07724 · arxiv_version: 1811.07724v2 · doi: 10.48550/arxiv.1811.07724 · pith_short_12: HPFNXBP4GJNX · pith_short_16: HPFNXBP4GJNXXEDW · pith_short_8: HPFNXBP4

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/HPFNXBP4GJNXXEDWS3HYWPRNFM \
  | 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: 3bcadb85fc325b7b907696cf8b3e2d2b2495ce3b292dfc72c13a0ad1aa716ee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f61df2172747421fb9cfc858ead34e27b9ac8e5892cd0ee425d99bc6d05e17",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-11-19T14:30:15Z",
    "title_canon_sha256": "1b77c70b746e2c057b2b2e7ce5ffd4532c581331295644129f431ea3b2c3eccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07724",
    "kind": "arxiv",
    "version": 2
  }
}