Pith Number

pith:SB2BPIY2

pith:2012:SB2BPIY277PZJFCA3AXVWKX5EI

not attested not anchored not stored refs pending

Modularity of Calabi--Yau varieties: 2011 and beyond

Noriko Yui

arxiv:1212.4308 v1 · 2012-12-18 · math.NT · 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{SB2BPIY277PZJFCA3AXVWKX5EI}

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	2026-05-18T03:38:13.351328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

907417a31affdf949440d82f5b2afd2204b5d4091985f2b5db3e052ce6017698

Aliases

arxiv: 1212.4308 · arxiv_version: 1212.4308v1 · doi: 10.48550/arxiv.1212.4308 · pith_short_12: SB2BPIY277PZ · pith_short_16: SB2BPIY277PZJFCA · pith_short_8: SB2BPIY2

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/SB2BPIY277PZJFCA3AXVWKX5EI \
  | 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: 907417a31affdf949440d82f5b2afd2204b5d4091985f2b5db3e052ce6017698

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5708dc56735c7fc6fd7bcf602ef1586b11e9c4c05d9ca026e7ba7c5226b0716e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-18T11:14:56Z",
    "title_canon_sha256": "67694b5c7aaa3cd2d11d6934a584a96690a78500c40aeb79853829af1830303c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4308",
    "kind": "arxiv",
    "version": 1
  }
}