Pith Number

pith:2TBAU24M

pith:1999:2TBAU24MHZPINIACUVU2R6RMPZ

not attested not anchored not stored refs pending

The Cassels-Tate pairing on polarized abelian varieties

Bjorn Poonen, Michael Stoll

arxiv:math/9911267 v1 · 1999-11-01 · 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{2TBAU24MHZPINIACUVU2R6RMPZ}

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	2026-05-18T00:47:31.922490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4c20a6b8c3e5e86a002a569a8fa2c7e61e8fda1c72ab17037389d0f6b39d6a5

Aliases

arxiv: math/9911267 · arxiv_version: math/9911267v1 · doi: 10.48550/arxiv.math/9911267 · pith_short_12: 2TBAU24MHZPI · pith_short_16: 2TBAU24MHZPINIAC · pith_short_8: 2TBAU24M

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/2TBAU24MHZPINIACUVU2R6RMPZ \
  | 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: d4c20a6b8c3e5e86a002a569a8fa2c7e61e8fda1c72ab17037389d0f6b39d6a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "284bfb0afd940c2bffb96a5fedd044d4db4b12eedcd35d9bb4ac7a0544589d17",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "1999-11-01T00:00:00Z",
    "title_canon_sha256": "6a9388ad2cfbb5c8873888c4f31036d8d13ba2a238b268aedfdc1c1a49c76071"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911267",
    "kind": "arxiv",
    "version": 1
  }
}