Pith Number

pith:PBAVEAC3

pith:2013:PBAVEAC3CPFLRFGMXDTC3IGDBO

not attested not anchored not stored refs pending

Elliptic Curves over Real Quadratic Fields are Modular

Bao V. Le Hung, Nuno Freitas, Samir Siksek

arxiv:1310.7088 v4 · 2013-10-26 · 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{PBAVEAC3CPFLRFGMXDTC3IGDBO}

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	2026-05-18T02:47:23.138841Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

784152005b13cab894ccb8e62da0c30ba8d438b69b846c7f4706ea0b3b2ad8e3

Aliases

arxiv: 1310.7088 · arxiv_version: 1310.7088v4 · doi: 10.48550/arxiv.1310.7088 · pith_short_12: PBAVEAC3CPFL · pith_short_16: PBAVEAC3CPFLRFGM · pith_short_8: PBAVEAC3

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/PBAVEAC3CPFLRFGMXDTC3IGDBO \
  | 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: 784152005b13cab894ccb8e62da0c30ba8d438b69b846c7f4706ea0b3b2ad8e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f239b21b44e51fc841f0c0034ead80a5eace4b7755fd2b43c11c9c29f180cedf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-26T09:22:34Z",
    "title_canon_sha256": "b93cb3f5259c52b7eda21d2b848ad5f75a87fa6fe50d1ea8a676fdf28cbfa5c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.7088",
    "kind": "arxiv",
    "version": 4
  }
}