Pith Number

pith:3P7OWL5P

pith:2026:3P7OWL5P6QCJTB355JKGYMAOY7

not attested not anchored not stored refs pending

Elliptic curve counting in toric threefolds: virtual, enumerative, and tropical

Sae Koyama

arxiv:2608.05486 v1 · 2026-08-06 · 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{3P7OWL5P6QCJTB355JKGYMAOY7}

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	2026-08-07T00:47:57.535753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbfeeb2faff40499877dea546c300ec7c1e2f138775b798ba0846b5740195761

Aliases

arxiv: 2608.05486 · arxiv_version: 2608.05486v1 · doi: 10.48550/arxiv.2608.05486 · pith_short_12: 3P7OWL5P6QCJ · pith_short_16: 3P7OWL5P6QCJTB35 · pith_short_8: 3P7OWL5P

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/3P7OWL5P6QCJTB355JKGYMAOY7 \
  | 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: dbfeeb2faff40499877dea546c300ec7c1e2f138775b798ba0846b5740195761

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a62ce3a44ca46a00644ca0f4e8510b92a90524c35e42d7bf5b29f275a41cbab",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-08-06T00:32:39Z",
    "title_canon_sha256": "1da403b4bd1d9afcd59ba506be6df449bf36c7f8de2793cbc5c111fda94028e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.05486",
    "kind": "arxiv",
    "version": 1
  }
}