Pith Number

pith:COB27DMP

pith:2006:COB27DMPC3KFU3USZMNECPN627

not attested not anchored not stored refs pending

Explicit n-descent on elliptic curves, II. Geometry

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

arxiv:math/0611606 v1 · 2006-11-20 · 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{COB27DMPC3KFU3USZMNECPN627}

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	2026-05-18T01:10:00.361507Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1383af8d8f16d45a6e92cb1a413dbed7faf0ed3edabdbba882a4f45ce9c7d296

Aliases

arxiv: math/0611606 · arxiv_version: math/0611606v1 · doi: 10.48550/arxiv.math/0611606 · pith_short_12: COB27DMPC3KF · pith_short_16: COB27DMPC3KFU3US · pith_short_8: COB27DMP

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/COB27DMPC3KFU3USZMNECPN627 \
  | 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: 1383af8d8f16d45a6e92cb1a413dbed7faf0ed3edabdbba882a4f45ce9c7d296

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "700988cb836a9c1130534cc70e51a1a2a655a52299556fa7ee3fc7016d7023ed",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-11-20T13:39:01Z",
    "title_canon_sha256": "3d33e7c56eacb7fe900e3acbf19f2b6b0b34e9bdc98506de2cdce44c7bd9fdff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611606",
    "kind": "arxiv",
    "version": 1
  }
}