Pith Number

pith:KBMPD2TW

pith:2004:KBMPD2TWBW7OKSWR5MQCJ3CQ5G

not attested not anchored not stored refs pending

The period-index problem in WC-groups I: elliptic curves

Pete L. Clark

arxiv:math/0406131 v1 · 2004-06-07 · 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{KBMPD2TWBW7OKSWR5MQCJ3CQ5G}

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	2026-07-04T14:38:41.567110Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5058f1ea760dbee54ad1eb2024ec50e9a0fa12495eafa4bf8dc761bfafd0bd34

Aliases

arxiv: math/0406131 · arxiv_version: math/0406131v1 · doi: 10.48550/arxiv.math/0406131 · pith_short_12: KBMPD2TWBW7O · pith_short_16: KBMPD2TWBW7OKSWR · pith_short_8: KBMPD2TW

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/KBMPD2TWBW7OKSWR5MQCJ3CQ5G \
  | 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: 5058f1ea760dbee54ad1eb2024ec50e9a0fa12495eafa4bf8dc761bfafd0bd34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba5005ca41ef1c54f2faa6c5d6a65d61763967ea25050aee7ac8c5c1efb0fb7c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2004-06-07T22:24:34Z",
    "title_canon_sha256": "554f0ac16398c778686ab5708bdb49cff7bbd76a418caca0f7ef9b196339e6ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0406131",
    "kind": "arxiv",
    "version": 1
  }
}