Pith Number

pith:K63WXDJX

pith:2007:K63WXDJXXNOMIDMWFTDVNPEQTD

not attested not anchored not stored refs pending

Linearizing torsion classes in the Picard group of algebraic curves over finite fields

Jean-Marc Couveignes

arxiv:0706.0272 v2 · 2007-06-02 · 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{K63WXDJXXNOMIDMWFTDVNPEQTD}

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	2026-05-18T03:56:24.715298Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57b76b8d37bb5cc40d962cc756bc9098f677c2c4c30564e4c1276261ff1f998e

Aliases

arxiv: 0706.0272 · arxiv_version: 0706.0272v2 · doi: 10.48550/arxiv.0706.0272 · pith_short_12: K63WXDJXXNOM · pith_short_16: K63WXDJXXNOMIDMW · pith_short_8: K63WXDJX

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/K63WXDJXXNOMIDMWFTDVNPEQTD \
  | 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: 57b76b8d37bb5cc40d962cc756bc9098f677c2c4c30564e4c1276261ff1f998e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d16e4f2c4a2536daf46a759b1e704495b935a49ea1b0736bdfb539d6338523b7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-06-02T14:20:14Z",
    "title_canon_sha256": "c8ba24a6e9cbb5d49c514bf70bc4631d185ed0006eb41b366babed4b9e1253cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0706.0272",
    "kind": "arxiv",
    "version": 2
  }
}