Pith Number

pith:E5BWTLUN

pith:2025:E5BWTLUNZL5WGYV4JWRNDSHTWP

not attested not anchored not stored refs pending

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties

Zhuang He

arxiv:2507.15406 v2 · 2025-07-21 · 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{E5BWTLUNZL5WGYV4JWRNDSHTWP}

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	2026-07-05T12:05:19.078438Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

274369ae8dcafb6362bc4da2d1c8f3b3c7b5beecc5b73dc9e686530f661d7240

Aliases

arxiv: 2507.15406 · arxiv_version: 2507.15406v2 · doi: 10.48550/arxiv.2507.15406 · pith_short_12: E5BWTLUNZL5W · pith_short_16: E5BWTLUNZL5WGYV4 · pith_short_8: E5BWTLUN

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/E5BWTLUNZL5WGYV4JWRNDSHTWP \
  | 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: 274369ae8dcafb6362bc4da2d1c8f3b3c7b5beecc5b73dc9e686530f661d7240

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d28eb07ff9dd141da1f3e52693051d92cd5c89076ce02b9a85ee67b33b10e66",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-07-21T09:08:03Z",
    "title_canon_sha256": "aabf89561ad6494052e6a92b8cd76d28630e5b1ed735b1111707dfbba34f9e10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15406",
    "kind": "arxiv",
    "version": 2
  }
}