Pith Number

pith:C3OOHF7J

pith:2012:C3OOHF7JJ4KQEHPXOQWAQEKALF

not attested not anchored not stored refs pending

Ordinary Modular Forms and Companion Points on the Eigencurve

John Bergdall

arxiv:1210.0165 v2 · 2012-09-30 · 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{C3OOHF7JJ4KQEHPXOQWAQEKALF}

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	2026-05-18T01:11:55.555383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca

Aliases

arxiv: 1210.0165 · arxiv_version: 1210.0165v2 · doi: 10.48550/arxiv.1210.0165 · pith_short_12: C3OOHF7JJ4KQ · pith_short_16: C3OOHF7JJ4KQEHPX · pith_short_8: C3OOHF7J

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/C3OOHF7JJ4KQEHPXOQWAQEKALF \
  | 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: 16dce397e94f15021df7742c081140595339d3b8749019ba805f471a9264d5ca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d29e569221ae2e1b0f9192aa745ef41d4de421cbe5327bb2000e6d233a1b0557",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-30T03:02:40Z",
    "title_canon_sha256": "3c73001ca4a6c3f21c5f6d0bbf4a9b9389eadfa7c924d13cd80a492a6938a554"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.0165",
    "kind": "arxiv",
    "version": 2
  }
}