Pith Number

pith:Z2772VEX

pith:2002:Z2772VEXTBWU5SLEIVFP7B4AVU

not attested not anchored not stored refs pending

Extensions of abelian varieties defined over a number field

Matthew A. Papanikolas, Niranjan Ramachandran

arxiv:math/0212050 v3 · 2002-12-03 · 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{Z2772VEXTBWU5SLEIVFP7B4AVU}

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	2026-05-18T01:37:47.793552Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cebffd5497986d4ec964454aff8780ad25dd2fecce1d79d192513112f4f6f457

Aliases

arxiv: math/0212050 · arxiv_version: math/0212050v3 · doi: 10.48550/arxiv.math/0212050 · pith_short_12: Z2772VEXTBWU · pith_short_16: Z2772VEXTBWU5SLE · pith_short_8: Z2772VEX

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/Z2772VEXTBWU5SLEIVFP7B4AVU \
  | 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: cebffd5497986d4ec964454aff8780ad25dd2fecce1d79d192513112f4f6f457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79712326a1dc98b2eff8bfc9577f985595bdb90fd25fdc31bfb4b07ccdd7b870",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2002-12-03T22:21:19Z",
    "title_canon_sha256": "d734e4181a7b3b4a348620f8d4c6f817cba337282454219e2a6c85ec2ec1fefd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0212050",
    "kind": "arxiv",
    "version": 3
  }
}