Pith Number

pith:DFWWJ5EP

pith:2010:DFWWJ5EP3F77JDOGYSCCMDQIW7

not attested not anchored not stored refs pending

On Mordell-Weil groups of Jacobians over function fields

Douglas Ulmer

arxiv:1002.3310 v3 · 2010-02-17 · 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{DFWWJ5EP3F77JDOGYSCCMDQIW7}

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	2026-05-18T04:28:21.759172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

196d64f48fd97ff48dc6c484260e08b7cb736c37a79a125883cb87168f84cfbc

Aliases

arxiv: 1002.3310 · arxiv_version: 1002.3310v3 · doi: 10.48550/arxiv.1002.3310 · pith_short_12: DFWWJ5EP3F77 · pith_short_16: DFWWJ5EP3F77JDOG · pith_short_8: DFWWJ5EP

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/DFWWJ5EP3F77JDOGYSCCMDQIW7 \
  | 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: 196d64f48fd97ff48dc6c484260e08b7cb736c37a79a125883cb87168f84cfbc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79603817c642da1f2cbd60e1b9256478f26629e71b2dead9b2102c32c4409852",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-02-17T16:50:09Z",
    "title_canon_sha256": "fc2d19870331cd27ff7befd3d2b52c23cc4d6e18e2289e085aaa2d9dadd79600"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1002.3310",
    "kind": "arxiv",
    "version": 3
  }
}