Pith Number

pith:3Y3M4EC7

pith:2007:3Y3M4EC7QKQ4P6CAX3KODSOIYF

not attested not anchored not stored refs pending

The yoga of the Cassels-Tate pairing

Edward F. Schaefer, Michael Stoll, Tom Fisher

arxiv:0710.2079 v1 · 2007-10-10 · 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{3Y3M4EC7QKQ4P6CAX3KODSOIYF}

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	2026-05-17T23:53:20.258535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de36ce105f82a1c7f840bed4e1c9c8c1539c8156bdee837340cc154e7e690be8

Aliases

arxiv: 0710.2079 · arxiv_version: 0710.2079v1 · doi: 10.48550/arxiv.0710.2079 · pith_short_12: 3Y3M4EC7QKQ4 · pith_short_16: 3Y3M4EC7QKQ4P6CA · pith_short_8: 3Y3M4EC7

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/3Y3M4EC7QKQ4P6CAX3KODSOIYF \
  | 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: de36ce105f82a1c7f840bed4e1c9c8c1539c8156bdee837340cc154e7e690be8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d994b234f15cda86777687e3091aee824421fa346999a299d302f65cdd5c2781",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2007-10-10T17:52:01Z",
    "title_canon_sha256": "7f9c95ecd3190a7debff4a52c9435ad3a84d03cbdd1d7d56af30316d8f4be2b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0710.2079",
    "kind": "arxiv",
    "version": 1
  }
}