Pith Number

pith:K7JEGKY7

pith:2011:K7JEGKY7TLSJICQPTUEOE5MADG

not attested not anchored not stored refs pending

Multiple Mixing for adele groups and rational points

Alexander Gorodnik, Ramin Takloo-Bighash, Yuri Tschinkel

arxiv:1112.5743 v1 · 2011-12-24 · math.NT · math.AG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K7JEGKY7TLSJICQPTUEOE5MADG}

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	2026-05-18T04:05:37.681639Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57d2432b1f9ae4940a0f9d08e2758019bce0b450a52aefe6e54b46fbc41e3f22

Aliases

arxiv: 1112.5743 · arxiv_version: 1112.5743v1 · doi: 10.48550/arxiv.1112.5743 · pith_short_12: K7JEGKY7TLSJ · pith_short_16: K7JEGKY7TLSJICQP · pith_short_8: K7JEGKY7

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/K7JEGKY7TLSJICQPTUEOE5MADG \
  | 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: 57d2432b1f9ae4940a0f9d08e2758019bce0b450a52aefe6e54b46fbc41e3f22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dbf1124be665b5599a80bdc156010b601c661db593a6275070e93c533995b9f",
    "cross_cats_sorted": [
      "math.AG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-24T17:44:40Z",
    "title_canon_sha256": "5df9a8d061cceaa7ff74e582bb6b4031527daf9f373685307d28616ae660b4ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.5743",
    "kind": "arxiv",
    "version": 1
  }
}