Pith Number

pith:UCMIN4C4

pith:2012:UCMIN4C4KBBSLDDALF5SWL3KZ6

not attested not anchored not stored refs pending

Moduli of elliptic curves via twisted stable maps

Andrew Niles

arxiv:1207.7280 v2 · 2012-07-31 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UCMIN4C4KBBSLDDALF5SWL3KZ6}

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	2026-05-18T02:38:19.802774Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a09886f05c5043258c60597b2b2f6acfa8ab09d49a94e4020f51219d99c1e5de

Aliases

arxiv: 1207.7280 · arxiv_version: 1207.7280v2 · doi: 10.48550/arxiv.1207.7280 · pith_short_12: UCMIN4C4KBBS · pith_short_16: UCMIN4C4KBBSLDDA · pith_short_8: UCMIN4C4

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/UCMIN4C4KBBSLDDALF5SWL3KZ6 \
  | 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: a09886f05c5043258c60597b2b2f6acfa8ab09d49a94e4020f51219d99c1e5de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32d690f6ac2b6a4e9167ebe1c70bc901e282db970f02cbbfb3b5ba94d79f7a93",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-31T15:10:46Z",
    "title_canon_sha256": "2803f3ffebef865d4b9d61e3cbc3e60b82376bf1a7ab01a8e455a48d06fd6012"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.7280",
    "kind": "arxiv",
    "version": 2
  }
}