Pith Number

pith:QJ7SNPL4

pith:2012:QJ7SNPL4VVAZC5OHMNDV2XLGA4

not attested not anchored not stored refs pending

Diophantine properties of measures invariant with respect to the Gauss map

David Simmons, Lior Fishman, Mariusz Urbanski

arxiv:1208.2088 v2 · 2012-08-10 · 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{QJ7SNPL4VVAZC5OHMNDV2XLGA4}

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	2026-05-18T02:46:31.536584Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

827f26bd7cad419175c763475d5d66071a7e7c6ace7d2c25ce2e67f89bed7621

Aliases

arxiv: 1208.2088 · arxiv_version: 1208.2088v2 · doi: 10.48550/arxiv.1208.2088 · pith_short_12: QJ7SNPL4VVAZ · pith_short_16: QJ7SNPL4VVAZC5OH · pith_short_8: QJ7SNPL4

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/QJ7SNPL4VVAZC5OHMNDV2XLGA4 \
  | 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: 827f26bd7cad419175c763475d5d66071a7e7c6ace7d2c25ce2e67f89bed7621

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b74ea01b0d463f24474f9d249388c533f6f197728dc3721d47e52feead31205",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-10T05:29:39Z",
    "title_canon_sha256": "87323a985a6e1daebdd5e1abd0ff6a477976a844a78af46a2943d91ab0143604"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2088",
    "kind": "arxiv",
    "version": 2
  }
}