Pith Number

pith:A5ZBI4WF

pith:2013:A5ZBI4WFPQPG6FKVUV4Q6HPXHT

not attested not anchored not stored refs pending

Bilinear pairings on elliptic curves

Andreas Enge (INRIA Bordeaux - Sud-Ouest)

arxiv:1301.5520 v2 · 2013-01-23 · 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{A5ZBI4WFPQPG6FKVUV4Q6HPXHT}

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	2026-05-18T02:58:57.452155Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07721472c57c1e6f1555a5790f1df73cc5a56b31657c499f836b213ac091c724

Aliases

arxiv: 1301.5520 · arxiv_version: 1301.5520v2 · doi: 10.48550/arxiv.1301.5520 · pith_short_12: A5ZBI4WFPQPG · pith_short_16: A5ZBI4WFPQPG6FKV · pith_short_8: A5ZBI4WF

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/A5ZBI4WFPQPG6FKVUV4Q6HPXHT \
  | 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: 07721472c57c1e6f1555a5790f1df73cc5a56b31657c499f836b213ac091c724

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e868242ee7db63e532aa3ec1acb714af1b4e9a2e85ce01c67aa7caed6d6d311",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-01-23T14:53:43Z",
    "title_canon_sha256": "4e542b493d437fabda07a7edc36a7f26eee7b722c0bd32a96093af7e0db5f9d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.5520",
    "kind": "arxiv",
    "version": 2
  }
}