Pith Number

pith:ZNHO6BRS

pith:2007:ZNHO6BRS4XLY5KMRR4F7VLPAZV

not attested not anchored not stored refs pending

Distribution of periodic torus orbits and Duke's theorem for cubic fields

Akshay Venkatesh, Elon Lindenstrauss, Manfred Einsiedler, Philippe Michel

arxiv:0708.1113 v2 · 2007-08-08 · math.NT · 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{ZNHO6BRS4XLY5KMRR4F7VLPAZV}

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	2026-05-18T02:35:52.948400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb4eef0632e5d78ea9918f0bfaade0cd5a428c261942e9deccf5f316fd81b5fa

Aliases

arxiv: 0708.1113 · arxiv_version: 0708.1113v2 · doi: 10.48550/arxiv.0708.1113 · pith_short_12: ZNHO6BRS4XLY · pith_short_16: ZNHO6BRS4XLY5KMR · pith_short_8: ZNHO6BRS

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/ZNHO6BRS4XLY5KMRR4F7VLPAZV \
  | 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: cb4eef0632e5d78ea9918f0bfaade0cd5a428c261942e9deccf5f316fd81b5fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb70bc8d45097ed5fc23d1ac23f5a860639bde356b703826a0efded20c075582",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-08-08T19:03:57Z",
    "title_canon_sha256": "dfa2b9fe6d27e3e5129f4cde5f32ef4361d4f5a33a59f94b36d9ee0a0770e831"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.1113",
    "kind": "arxiv",
    "version": 2
  }
}