Pith Number

pith:FG2SIP2F

pith:2009:FG2SIP2FK5VFOYQ5SS4SFF6III

not attested not anchored not stored refs pending

On Neron-Raynaud class groups of tori and the Capitulation Problem

Cristian D. Gonzalez-Aviles

arxiv:0903.3221 v1 · 2009-03-18 · 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{FG2SIP2FK5VFOYQ5SS4SFF6III}

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	2026-07-04T15:39:39.014086Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29b5243f45576a57621d94b92297c8422622fe480b99aeda74d2c616999b4f7f

Aliases

arxiv: 0903.3221 · arxiv_version: 0903.3221v1 · doi: 10.48550/arxiv.0903.3221 · pith_short_12: FG2SIP2FK5VF · pith_short_16: FG2SIP2FK5VFOYQ5 · pith_short_8: FG2SIP2F

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/FG2SIP2FK5VFOYQ5SS4SFF6III \
  | 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: 29b5243f45576a57621d94b92297c8422622fe480b99aeda74d2c616999b4f7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e8b9a24cdc927827ace2e5e07a46087471cc6e410abfb733f903e4ffd6852ea1",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-03-18T18:44:56Z",
    "title_canon_sha256": "0ab4ab40e5e53a76bf2a8506eaaaf9ceb0031e1042e3cb01951fd607e809c14f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.3221",
    "kind": "arxiv",
    "version": 1
  }
}