Pith Number

pith:FC5PW5VY

pith:2013:FC5PW5VYBGKTLR3SLZUHXDPYYX

not attested not anchored not stored refs pending

Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve

Rachel Newton, Tom Fisher

arxiv:1306.1410 v1 · 2013-06-06 · 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{FC5PW5VYBGKTLR3SLZUHXDPYYX}

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	2026-05-18T03:21:34.291652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

28bafb76b8099535c7725e687b8df8c5ee493ea5fa906a59949800221ef415ed

Aliases

arxiv: 1306.1410 · arxiv_version: 1306.1410v1 · doi: 10.48550/arxiv.1306.1410 · pith_short_12: FC5PW5VYBGKT · pith_short_16: FC5PW5VYBGKTLR3S · pith_short_8: FC5PW5VY

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/FC5PW5VYBGKTLR3SLZUHXDPYYX \
  | 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: 28bafb76b8099535c7725e687b8df8c5ee493ea5fa906a59949800221ef415ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "24e5272491e530a08663b4f7de6e3a1d3041b1f44f8d090da7a5302e7e8a893a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-06-06T13:58:42Z",
    "title_canon_sha256": "d476a29ca4f18080c368b1da2ef37fc62a0c0a9c86223f652d383987bcc94389"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1410",
    "kind": "arxiv",
    "version": 1
  }
}