Pith Number

pith:AZEBZXIM

pith:2014:AZEBZXIMRMUKZWWYYC2JV2ZRZI

not attested not anchored not stored refs pending

The frequency of elliptic curve groups over prime finite fields

Chantal David, Dimitris Koukoulopoulos, Ethan Smith, Vorrapan Chandee

arxiv:1405.6923 v2 · 2014-05-27 · 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{AZEBZXIMRMUKZWWYYC2JV2ZRZI}

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	2026-07-04T23:56:26.764109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06481cdd0c8b28acdad8c0b49aeb31ca00703c15d130238c1f133b1e775038ff

Aliases

arxiv: 1405.6923 · arxiv_version: 1405.6923v2 · doi: 10.48550/arxiv.1405.6923 · pith_short_12: AZEBZXIMRMUK · pith_short_16: AZEBZXIMRMUKZWWY · pith_short_8: AZEBZXIM

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/AZEBZXIMRMUKZWWYYC2JV2ZRZI \
  | 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: 06481cdd0c8b28acdad8c0b49aeb31ca00703c15d130238c1f133b1e775038ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d71863ae8bc1f62c1f2f61c20e589c21b9c9b12d4d19b79a4977d4ecdb275b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-05-27T14:25:14Z",
    "title_canon_sha256": "0332413ef63618c39c6a8e5d65870bb2ca9ce9ffe77b61664c6498342f43344f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1405.6923",
    "kind": "arxiv",
    "version": 2
  }
}