Pith Number

pith:SL5FICBF

pith:2006:SL5FICBFXZDF62ALUEFOMY7KGQ

not attested not anchored not stored refs pending

Modular Curves, Modular Surfaces, and Modular Fourfolds

Dinakar Ramakrishnan

arxiv:math/0609459 v1 · 2006-09-16 · 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{SL5FICBFXZDF62ALUEFOMY7KGQ}

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	2026-07-04T14:56:34.363271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92fa540825be465f680ba10ae663ea34141c1a1893d81261aa15a92565be027a

Aliases

arxiv: math/0609459 · arxiv_version: math/0609459v1 · doi: 10.48550/arxiv.math/0609459 · pith_short_12: SL5FICBFXZDF · pith_short_16: SL5FICBFXZDF62AL · pith_short_8: SL5FICBF

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/SL5FICBFXZDF62ALUEFOMY7KGQ \
  | 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: 92fa540825be465f680ba10ae663ea34141c1a1893d81261aa15a92565be027a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9f4a9e7339a3147d7b3e4953facac944d0dcbdc7deca83b6c9c01d68ad5dd95",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-09-16T05:55:32Z",
    "title_canon_sha256": "8dfc1501ddf06cfc1469eb3021ca258df8ad0add673b83eb76676592323442e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609459",
    "kind": "arxiv",
    "version": 1
  }
}