Pith Number

pith:KCN4ZDMJ

pith:2012:KCN4ZDMJYQ2PRRH2HJPU7ZHEYJ

not attested not anchored not stored refs pending

Tori in the Cremona groups

Vladimir L. Popov

arxiv:1207.5205 v3 · 2012-07-22 · 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{KCN4ZDMJYQ2PRRH2HJPU7ZHEYJ}

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	2026-05-18T01:56:15.317730Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

509bcc8d89c434f8c4fa3a5f4fe4e4c25b07157afd1a9cf1c4ca255b5b8f0a21

Aliases

arxiv: 1207.5205 · arxiv_version: 1207.5205v3 · doi: 10.48550/arxiv.1207.5205 · pith_short_12: KCN4ZDMJYQ2P · pith_short_16: KCN4ZDMJYQ2PRRH2 · pith_short_8: KCN4ZDMJ

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/KCN4ZDMJYQ2PRRH2HJPU7ZHEYJ \
  | 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: 509bcc8d89c434f8c4fa3a5f4fe4e4c25b07157afd1a9cf1c4ca255b5b8f0a21

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f00ec547caf9f7c66956244bf11916679d4fc72605d46fe0033aae3d3f7afb3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-07-22T08:40:43Z",
    "title_canon_sha256": "eba7c7e37bf37b34b6ec9274ecea63082d4aa2d3e25e5cc45393c59494d69af1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.5205",
    "kind": "arxiv",
    "version": 3
  }
}