Pith Number

pith:2WU64PDS

pith:2013:2WU64PDS5WJXAFHFPKV3NDOJCZ

not attested not anchored not stored refs pending

Explicit points on the Legendre curve II

Chris Hall, Douglas Ulmer, Ricardo Concei\c{c}\~ao

arxiv:1307.4251 v2 · 2013-07-16 · 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{2WU64PDS5WJXAFHFPKV3NDOJCZ}

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	2026-05-18T03:05:01.324018Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5a9ee3c72ed937014e57aabb68dc9165fbe155f101d7471644d32aeaf7c5b25

Aliases

arxiv: 1307.4251 · arxiv_version: 1307.4251v2 · doi: 10.48550/arxiv.1307.4251 · pith_short_12: 2WU64PDS5WJX · pith_short_16: 2WU64PDS5WJXAFHF · pith_short_8: 2WU64PDS

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/2WU64PDS5WJXAFHFPKV3NDOJCZ \
  | 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: d5a9ee3c72ed937014e57aabb68dc9165fbe155f101d7471644d32aeaf7c5b25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df25c2a36ab40d9a41574bc2261acc2b1fa35da3a15c4c52fd2c28b2532b5c85",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-07-16T11:52:44Z",
    "title_canon_sha256": "a0700d03f6357bfbd3531f8d41e4b1ad8fd4cb621e057d8f8740f9bbf5371d2e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.4251",
    "kind": "arxiv",
    "version": 2
  }
}