Pith Number

pith:UZM7T45R

pith:2004:UZM7T45RWZ5YI4F3PMDGU4P7A5

not attested not anchored not stored refs pending

Toric Degenerations and Batyrev-Borisov Duality

Mark Gross

arxiv:math/0406171 v2 · 2004-06-09 · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UZM7T45RWZ5YI4F3PMDGU4P7A5}

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	2026-07-04T14:38:41.960032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a659f9f3b1b67b8470bb7b066a71ff075ec4eb0b4610b7340001834cd27b3089

Aliases

arxiv: math/0406171 · arxiv_version: math/0406171v2 · doi: 10.48550/arxiv.math/0406171 · pith_short_12: UZM7T45RWZ5Y · pith_short_16: UZM7T45RWZ5YI4F3 · pith_short_8: UZM7T45R

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/UZM7T45RWZ5YI4F3PMDGU4P7A5 \
  | 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: a659f9f3b1b67b8470bb7b066a71ff075ec4eb0b4610b7340001834cd27b3089

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "233bbbe0c9c77a4de6e05820c28da046075bce6585f8ee12b8aab3368dd73436",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2004-06-09T11:17:53Z",
    "title_canon_sha256": "1d72042d82527c5162c4c815b0e76829557a51aef96d1b15cd4d78b184aaf017"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406171",
    "kind": "arxiv",
    "version": 2
  }
}