Pith Number

pith:XOZ3NFBP

pith:2012:XOZ3NFBPWZBJ6LAVRVIM5RM7B4

not attested not anchored not stored refs pending

Isogeny volcanoes

Andrew V. Sutherland

arxiv:1208.5370 v3 · 2012-08-27 · math.NT · cs.CR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XOZ3NFBPWZBJ6LAVRVIM5RM7B4}

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	2026-05-18T02:49:30.062470Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbb3b6942fb6429f2c158d50cec59f0f3a7e8cea01f2c1b1483b6abb31d0c1ff

Aliases

arxiv: 1208.5370 · arxiv_version: 1208.5370v3 · doi: 10.48550/arxiv.1208.5370 · pith_short_12: XOZ3NFBPWZBJ · pith_short_16: XOZ3NFBPWZBJ6LAV · pith_short_8: XOZ3NFBP

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/XOZ3NFBPWZBJ6LAVRVIM5RM7B4 \
  | 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: bbb3b6942fb6429f2c158d50cec59f0f3a7e8cea01f2c1b1483b6abb31d0c1ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03400d0daf1a5942287107923c4d66da15260f4dbf50550d923b03618c920447",
    "cross_cats_sorted": [
      "cs.CR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-27T11:50:27Z",
    "title_canon_sha256": "75d9cef1460db9338c854863265ea010048731ee022cdaf513a267484f7a164f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.5370",
    "kind": "arxiv",
    "version": 3
  }
}