Pith Number

pith:52UJT6VQ

pith:2010:52UJT6VQXD52HTJ5Q743KDAU53

not attested not anchored not stored refs pending

Modular polynomials via isogeny volcanoes

Andrew V. Sutherland, Kristin Lauter, Reinier Broker

arxiv:1001.0402 v2 · 2010-01-03 · 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{52UJT6VQXD52HTJ5Q743KDAU53}

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	2026-05-18T03:34:46.657544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea899fab0b8fba3cd3d87f9b50c14eec67e74d091fb23e768b45a164ae2e4bd

Aliases

arxiv: 1001.0402 · arxiv_version: 1001.0402v2 · doi: 10.48550/arxiv.1001.0402 · pith_short_12: 52UJT6VQXD52 · pith_short_16: 52UJT6VQXD52HTJ5 · pith_short_8: 52UJT6VQ

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/52UJT6VQXD52HTJ5Q743KDAU53 \
  | 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: eea899fab0b8fba3cd3d87f9b50c14eec67e74d091fb23e768b45a164ae2e4bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5826033c9b788f562bfd49e22fb26131f28410c5f15f927fc82f6c6c1c74b44b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-01-03T19:46:54Z",
    "title_canon_sha256": "774c105af36ff66bfe5328f7d423ed13534e74dba69dd515e4a39534575407f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.0402",
    "kind": "arxiv",
    "version": 2
  }
}