Pith Number

pith:L2FQLVZY

pith:2009:L2FQLVZY27B5OQLPBAY6U2C3RH

not attested not anchored not stored refs pending

Root numbers and parity of ranks of elliptic curves

Tim Dokchitser, Vladimir Dokchitser

arxiv:0906.1815 v1 · 2009-06-09 · 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{L2FQLVZY27B5OQLPBAY6U2C3RH}

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	2026-05-18T03:12:48.824171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e8b05d738d7c3d7416f0831ea685b89f25bab5baec149e5b197a95a83a37ffc

Aliases

arxiv: 0906.1815 · arxiv_version: 0906.1815v1 · doi: 10.48550/arxiv.0906.1815 · pith_short_12: L2FQLVZY27B5 · pith_short_16: L2FQLVZY27B5OQLP · pith_short_8: L2FQLVZY

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/L2FQLVZY27B5OQLPBAY6U2C3RH \
  | 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: 5e8b05d738d7c3d7416f0831ea685b89f25bab5baec149e5b197a95a83a37ffc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6060c9ea873787a77868f63f5941f72b3e821433e96f6835f967f7134aa7ccd2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-06-09T20:20:48Z",
    "title_canon_sha256": "3b9f6db8dfe1485e9dff8dbccc128079142a7a45bc520a09c07df2e84c4458fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.1815",
    "kind": "arxiv",
    "version": 1
  }
}