Pith Number

pith:MNCWRAN7

pith:2009:MNCWRAN7ZLOLWLHZW5X7ZLQHHY

not attested not anchored not stored refs pending

Quaternion algebras, Heegner points and the arithmetic of Hida families

M. Longo, S. Vigni

arxiv:0903.2797 v2 · 2009-03-16 · 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{MNCWRAN7ZLOLWLHZW5X7ZLQHHY}

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	2026-05-18T04:39:16.973783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63456881bfcadcbb2cf9b76ffcae073e3232d09948f411d0cf0400dcc79bb6d0

Aliases

arxiv: 0903.2797 · arxiv_version: 0903.2797v2 · doi: 10.48550/arxiv.0903.2797 · pith_short_12: MNCWRAN7ZLOL · pith_short_16: MNCWRAN7ZLOLWLHZ · pith_short_8: MNCWRAN7

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/MNCWRAN7ZLOLWLHZW5X7ZLQHHY \
  | 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: 63456881bfcadcbb2cf9b76ffcae073e3232d09948f411d0cf0400dcc79bb6d0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ac4125b121b30c2622be332a4f20433fe07fe1b07142946eb94c7d27ae50074",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-03-16T16:41:36Z",
    "title_canon_sha256": "ae3f9ab1367d7839c081897ccebe5bc988062d1fb892ed9d9c86b8df8ea5012e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.2797",
    "kind": "arxiv",
    "version": 2
  }
}