Pith Number

pith:ODJVBSMP

pith:2010:ODJVBSMPVB5S6VPV7MB6UP4TVJ

not attested not anchored not stored refs pending

Intrinsic ergodicity beyond specification: beta-shifts, S-gap shifts, and their factors

Daniel J. Thompson, Vaughn Climenhaga

arxiv:1011.2780 v3 · 2010-11-11 · 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{ODJVBSMPVB5S6VPV7MB6UP4TVJ}

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	2026-05-18T02:23:36.950704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

70d350c98fa87b2f55f5fb03ea3f93aa627458c8f1ad8836766fadacce664db8

Aliases

arxiv: 1011.2780 · arxiv_version: 1011.2780v3 · doi: 10.48550/arxiv.1011.2780 · pith_short_12: ODJVBSMPVB5S · pith_short_16: ODJVBSMPVB5S6VPV · pith_short_8: ODJVBSMP

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/ODJVBSMPVB5S6VPV7MB6UP4TVJ \
  | 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: 70d350c98fa87b2f55f5fb03ea3f93aa627458c8f1ad8836766fadacce664db8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2022a5b1ae75b58661d97c07299a41e2f3c343482756420906ef1e581473591e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-11-11T21:41:38Z",
    "title_canon_sha256": "9fc3dc3ffbb0a7d35592275b346c847bf855fd97b4875abf98f4e78a877feddb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2780",
    "kind": "arxiv",
    "version": 3
  }
}