Pith Number

pith:YCIZLTSR

pith:2013:YCIZLTSRU33FVNBKKYQH4SM6JY

not attested not anchored not stored refs pending

On the non-idealness of cyclotomic families of pairing-friendly elliptic curves

Min Sha

arxiv:1304.7169 v4 · 2013-04-26 · 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{YCIZLTSRU33FVNBKKYQH4SM6JY}

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	2026-05-18T02:54:05.219904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c09195ce51a6f65ab42a56207e499e4e3f461d77e8a58d9c9f9598de0abd15db

Aliases

arxiv: 1304.7169 · arxiv_version: 1304.7169v4 · doi: 10.48550/arxiv.1304.7169 · pith_short_12: YCIZLTSRU33F · pith_short_16: YCIZLTSRU33FVNBK · pith_short_8: YCIZLTSR

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/YCIZLTSRU33FVNBKKYQH4SM6JY \
  | 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: c09195ce51a6f65ab42a56207e499e4e3f461d77e8a58d9c9f9598de0abd15db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26d249fafa50dfdc6efa51a4f245df5367f6295c547317f2fa2a1ae088bb1009",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-04-26T13:55:13Z",
    "title_canon_sha256": "e66a27e92b71d4e49fcae41b3607eb8b4408f395abfb6111f20cdce3594121c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7169",
    "kind": "arxiv",
    "version": 4
  }
}