Pith Number

pith:XL2R2FUK

pith:2011:XL2R2FUKSBYOE7K5DZ3TDHUMQL

not attested not anchored not stored refs pending

The class group pairing and $p$-descent on elliptic curves

Christian Wuthrich, Jean Gillibert

arxiv:1110.4232 v1 · 2011-10-19 · 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{XL2R2FUKSBYOE7K5DZ3TDHUMQL}

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	2026-05-18T02:58:00.319981Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baf51d168a9070e27d5d1e77319e8c82ee2ceea3c38145d7b7e0552dc3695f2a

Aliases

arxiv: 1110.4232 · arxiv_version: 1110.4232v1 · doi: 10.48550/arxiv.1110.4232 · pith_short_12: XL2R2FUKSBYO · pith_short_16: XL2R2FUKSBYOE7K5 · pith_short_8: XL2R2FUK

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/XL2R2FUKSBYOE7K5DZ3TDHUMQL \
  | 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: baf51d168a9070e27d5d1e77319e8c82ee2ceea3c38145d7b7e0552dc3695f2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7867fbb69b14040ac47e490bf69a2fb9cc0e116246ea1af2d9a2107f278fdb22",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-10-19T10:08:00Z",
    "title_canon_sha256": "e80c199b28b38a3768dfe0e8d13df09b58f83691f05bfb52849e0fae4b8b341b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.4232",
    "kind": "arxiv",
    "version": 1
  }
}