Pith Number

pith:F5BTJ5VK

pith:2006:F5BTJ5VKS4N2EKG7MCMQZMR3MA

not attested not anchored not stored refs pending

An "Anti-Hasse Principle" for Prime Twists

Pete L. Clark

arxiv:math/0609465 v1 · 2006-09-16 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F5BTJ5VKS4N2EKG7MCMQZMR3MA}

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	2026-07-04T14:56:34.422511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172

Aliases

arxiv: math/0609465 · arxiv_version: math/0609465v1 · doi: 10.48550/arxiv.math/0609465 · pith_short_12: F5BTJ5VKS4N2 · pith_short_16: F5BTJ5VKS4N2EKG7 · pith_short_8: F5BTJ5VK

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/F5BTJ5VKS4N2EKG7MCMQZMR3MA \
  | 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: 2f4334f6aa971ba228df60990cb23b6019c5290d51d7e5549207c427db044172

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bfce09c5248276c2f035d7394a93c1879445801afd793747c1aed388cb43109",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2006-09-16T17:55:39Z",
    "title_canon_sha256": "ca783410a15f8d8d8a128d60593139579e62c35edaf0c153c8291f298b882106"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0609465",
    "kind": "arxiv",
    "version": 1
  }
}