Pith Number

pith:IGN6TSR5

pith:2005:IGN6TSR5JANHWDQO42Z6AH5MDV

not attested not anchored not stored refs pending

A Mordell-Weil theorem for abelian varieties over fields generated by torsion points

Michael Larsen

arxiv:math/0503378 v1 · 2005-03-18 · 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{IGN6TSR5JANHWDQO42Z6AH5MDV}

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	2026-07-04T14:39:48.282482Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

419be9ca3d481a7b0e0ee6b3e01fac1d562de7d15ca0c986fcb6376fa73d8164

Aliases

arxiv: math/0503378 · arxiv_version: math/0503378v1 · doi: 10.48550/arxiv.math/0503378 · pith_short_12: IGN6TSR5JANH · pith_short_16: IGN6TSR5JANHWDQO · pith_short_8: IGN6TSR5

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/IGN6TSR5JANHWDQO42Z6AH5MDV \
  | 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: 419be9ca3d481a7b0e0ee6b3e01fac1d562de7d15ca0c986fcb6376fa73d8164

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cbf477c8dd55452b474eb09cb015b082a886f1413bc07f74f3ce2ee5923d86e2",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-03-18T12:35:16Z",
    "title_canon_sha256": "e5a72b118f7a6e02d61b153af12dcfeccc2578f77591d6b9744ecbb94b9e2def"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0503378",
    "kind": "arxiv",
    "version": 1
  }
}