Pith Number

pith:7F3JUDE5

pith:2011:7F3JUDE5F7WQ33TGO5HA2TZQAK

not attested not anchored not stored refs pending

On some special classes of complex elliptic curves

Bogdan Canepa, Radu Gaba

arxiv:1111.1073 v1 · 2011-11-04 · 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{7F3JUDE5F7WQ33TGO5HA2TZQAK}

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	2026-05-18T04:09:35.819301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9769a0c9d2fed0dee66774e0d4f300280e328d968a6e90c5a63f4096cad904d

Aliases

arxiv: 1111.1073 · arxiv_version: 1111.1073v1 · doi: 10.48550/arxiv.1111.1073 · pith_short_12: 7F3JUDE5F7WQ · pith_short_16: 7F3JUDE5F7WQ33TG · pith_short_8: 7F3JUDE5

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/7F3JUDE5F7WQ33TGO5HA2TZQAK \
  | 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: f9769a0c9d2fed0dee66774e0d4f300280e328d968a6e90c5a63f4096cad904d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83ea5a44dc355bb29b1ebcc490f3210a65a4aaa193622be1f29e5e1806978e0e",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-11-04T09:11:07Z",
    "title_canon_sha256": "428e4d585e5bd495a619ccb693c910018d5a4640e6ce462e2997a3fe09fb4f32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.1073",
    "kind": "arxiv",
    "version": 1
  }
}