Pith Number

pith:4X2QGUN2

pith:2009:4X2QGUN2J6UXGGX2KFBDIZF6BP

not attested not anchored not stored refs pending

Effective Siegel's theorem for modular curves

Marco Illengo, Yuri Bilu

arxiv:0905.0418 v3 · 2009-05-04 · 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{4X2QGUN2J6UXGGX2KFBDIZF6BP}

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	2026-05-18T02:58:03.301278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5f50351ba4fa9731afa51423464be0bc77e9dd9de01992562d8ca9c7430c05c

Aliases

arxiv: 0905.0418 · arxiv_version: 0905.0418v3 · doi: 10.48550/arxiv.0905.0418 · pith_short_12: 4X2QGUN2J6UX · pith_short_16: 4X2QGUN2J6UXGGX2 · pith_short_8: 4X2QGUN2

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/4X2QGUN2J6UXGGX2KFBDIZF6BP \
  | 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: e5f50351ba4fa9731afa51423464be0bc77e9dd9de01992562d8ca9c7430c05c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7c569b1c8ccf46c793e4fae1c6fcc4f1350a96d4617beb0add6c665c6c2377b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-05-04T16:38:29Z",
    "title_canon_sha256": "6b50fc288d6fbd3aa2b95ef902c331f956f7325a382571f448713a7be6d72be0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.0418",
    "kind": "arxiv",
    "version": 3
  }
}