Pith Number

pith:VFNBNGIJ

pith:2010:VFNBNGIJ4IUOCUZN3YJLSW7OH3

not attested not anchored not stored refs pending

Yoshida lifts and Selmer groups

Neil Dummigan, Rainer Schulze-Pillot, Siegfried B\"ocherer

arxiv:1012.5817 v3 · 2010-12-28 · 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{VFNBNGIJ4IUOCUZN3YJLSW7OH3}

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	2026-05-18T04:06:17.725278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a95a169909e228e1532dde12b95bee3ed40df0bfd7daaa329a30bebe6e849712

Aliases

arxiv: 1012.5817 · arxiv_version: 1012.5817v3 · doi: 10.48550/arxiv.1012.5817 · pith_short_12: VFNBNGIJ4IUO · pith_short_16: VFNBNGIJ4IUOCUZN · pith_short_8: VFNBNGIJ

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/VFNBNGIJ4IUOCUZN3YJLSW7OH3 \
  | 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: a95a169909e228e1532dde12b95bee3ed40df0bfd7daaa329a30bebe6e849712

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "446438b84d0c0dc5f8854e186410911930bc3f7bdf5498db7b65c92bfaab9949",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-28T18:59:09Z",
    "title_canon_sha256": "af5c7de60433ec83e2eb26eb747740f571fbd628950d41458c976a793e15b326"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5817",
    "kind": "arxiv",
    "version": 3
  }
}