Pith Number

pith:ID5EKLOZ

pith:1999:ID5EKLOZGXUGGECZGNSESQ5AX3

not attested not anchored not stored refs pending

Algebraic families of nonzero elements of Shafarevich-Tate groups

Bjorn Poonen, Jean-Louis Colliot-Thelene

arxiv:math/9901038 v1 · 1999-01-09 · 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{ID5EKLOZGXUGGECZGNSESQ5AX3}

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	2026-05-18T00:47:31.936191Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40fa452dd935e863105933644943a0bef4b23f530ba022c4fae76ff3aeff9e10

Aliases

arxiv: math/9901038 · arxiv_version: math/9901038v1 · doi: 10.48550/arxiv.math/9901038 · pith_short_12: ID5EKLOZGXUG · pith_short_16: ID5EKLOZGXUGGECZ · pith_short_8: ID5EKLOZ

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/ID5EKLOZGXUGGECZGNSESQ5AX3 \
  | 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: 40fa452dd935e863105933644943a0bef4b23f530ba022c4fae76ff3aeff9e10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb7b81da398410f143be22e56e6d7935e277ff94911ff58c64dd258cc2c7de0d",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "1999-01-09T00:07:42Z",
    "title_canon_sha256": "2788197a1d0952c55b949e2c3eb71cdc6d1fa9470f44a154531e28a9cb6ed07a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9901038",
    "kind": "arxiv",
    "version": 1
  }
}