Pith Number

pith:4ZQ2AUXS

pith:2011:4ZQ2AUXSHX4ULMIGUCCO6PZ3XP

not attested not anchored not stored refs pending

Explicit n-descent on elliptic curves. III. Algorithms

Cathy O'Neil, Denis Simon, John Cremona, Michael Stoll, Tom Fisher

arxiv:1107.3516 v2 · 2011-07-18 · 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{4ZQ2AUXSHX4ULMIGUCCO6PZ3XP}

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	2026-05-18T01:10:11.308770Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e661a052f23df945b106a084ef3f3bbbdbffde4b6ca1c1dd0f4e335bee46e863

Aliases

arxiv: 1107.3516 · arxiv_version: 1107.3516v2 · doi: 10.48550/arxiv.1107.3516 · pith_short_12: 4ZQ2AUXSHX4U · pith_short_16: 4ZQ2AUXSHX4ULMIG · pith_short_8: 4ZQ2AUXS

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/4ZQ2AUXSHX4ULMIGUCCO6PZ3XP \
  | 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: e661a052f23df945b106a084ef3f3bbbdbffde4b6ca1c1dd0f4e335bee46e863

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "814e656f819b72a3403dfd9f7bd211e100cfd4fb3ffc1f0b5b01cda1b7bfc71f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-07-18T17:49:21Z",
    "title_canon_sha256": "8731d6a0b88b0b67b60e5bacc363c36d0f6b943d496abf8bff7f938d023e5c7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3516",
    "kind": "arxiv",
    "version": 2
  }
}