Pith Number

pith:N7QGXA2F

pith:2012:N7QGXA2FPALFH7ZQ5HKQ7AIOMT

not attested not anchored not stored refs pending

24 faces of the Borcherds modular form Phi_{12}

Valery Gritsenko

arxiv:1203.6503 v1 · 2012-03-29 · math.AG · hep-th · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N7QGXA2FPALFH7ZQ5HKQ7AIOMT}

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	2026-05-18T03:59:02.358639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fe06b8345781653ff30e9d50f810e64cde79f69aeff2ea347f0d6fb669e5124

Aliases

arxiv: 1203.6503 · arxiv_version: 1203.6503v1 · doi: 10.48550/arxiv.1203.6503 · pith_short_12: N7QGXA2FPALF · pith_short_16: N7QGXA2FPALFH7ZQ · pith_short_8: N7QGXA2F

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/N7QGXA2FPALFH7ZQ5HKQ7AIOMT \
  | 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: 6fe06b8345781653ff30e9d50f810e64cde79f69aeff2ea347f0d6fb669e5124

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de90f3d4c5f9bcfaf9baa6b24035fcd47da00059573c67543e852eb253e0e6a4",
    "cross_cats_sorted": [
      "hep-th",
      "math.NT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-03-29T12:18:59Z",
    "title_canon_sha256": "8f9755e38cb28ef5e9cf8e1bcd53c27551b2616e4c1a9bd28eb149c0f9e396c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.6503",
    "kind": "arxiv",
    "version": 1
  }
}