Pith Number

pith:NCEVVT7Q

pith:2012:NCEVVT7QSJVWWT6AF5CRS4OADZ

not attested not anchored not stored refs pending

Arithmetic mirror symmetry for the 2-torus

Timothy Perutz, Yanki Lekili

arxiv:1211.4632 v1 · 2012-11-20 · math.SG · math.AG · math.KT · 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{NCEVVT7QSJVWWT6AF5CRS4OADZ}

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	2026-05-18T03:40:26.131296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68895acff0926b6b4fc02f451971c01e466ba6eb31af4a15cfe58421f1c2d64b

Aliases

arxiv: 1211.4632 · arxiv_version: 1211.4632v1 · doi: 10.48550/arxiv.1211.4632 · pith_short_12: NCEVVT7QSJVW · pith_short_16: NCEVVT7QSJVWWT6A · pith_short_8: NCEVVT7Q

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/NCEVVT7QSJVWWT6AF5CRS4OADZ \
  | 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: 68895acff0926b6b4fc02f451971c01e466ba6eb31af4a15cfe58421f1c2d64b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d8c2297e9381b4faed984e06afe662f7b3a82f64354395ed173c2b1034ca14c",
    "cross_cats_sorted": [
      "math.AG",
      "math.KT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-11-20T00:04:15Z",
    "title_canon_sha256": "1e7ecbb0c5fc2daaaf45d900278e66a8759f9dc524b6569971ebf6967a88a9ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.4632",
    "kind": "arxiv",
    "version": 1
  }
}