Pith Number

pith:4KDH4ZX6

pith:2012:4KDH4ZX6NT75JAG2GBNF63IG4T

not attested not anchored not stored refs pending

Heuristics on pairing-friendly abelian varieties

David Gruenewald, John Boxall

arxiv:1202.1177 v4 · 2012-02-06 · 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{4KDH4ZX6NT75JAG2GBNF63IG4T}

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	2026-05-17T23:53:18.964102Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2867e66fe6cffd480da305a5f6d06e4dc4de4d28c26c74b2cb906551f8fb1ba

Aliases

arxiv: 1202.1177 · arxiv_version: 1202.1177v4 · doi: 10.48550/arxiv.1202.1177 · pith_short_12: 4KDH4ZX6NT75 · pith_short_16: 4KDH4ZX6NT75JAG2 · pith_short_8: 4KDH4ZX6

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/4KDH4ZX6NT75JAG2GBNF63IG4T \
  | 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: e2867e66fe6cffd480da305a5f6d06e4dc4de4d28c26c74b2cb906551f8fb1ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52a7a17d80009c09bcf9e42ea354dd8f0269be50a0947c58ded04a597d71a88e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-02-06T15:42:48Z",
    "title_canon_sha256": "7dd4155d3e08ba7d7c87c76f89270394a68fa80a0e5b1074d9573cd3121d17bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1177",
    "kind": "arxiv",
    "version": 4
  }
}