Pith Number

pith:RTOK567P

pith:2010:RTOK567P2JRA7D3USNSFHGQFVC

not attested not anchored not stored refs pending

Renormalization, Thermodynamic Formalism and Quasi-Crystals in Subshifts

Henk Bruin, Renaud Leplaideur (LM)

arxiv:1010.4643 v3 · 2010-10-22 · 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{RTOK567P2JRA7D3USNSFHGQFVC}

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	2026-05-18T03:59:47.894547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8cdcaefbefd2620f8f749364539a05a8b7b10f620c21936bb8c16223a07e0ce3

Aliases

arxiv: 1010.4643 · arxiv_version: 1010.4643v3 · doi: 10.48550/arxiv.1010.4643 · pith_short_12: RTOK567P2JRA · pith_short_16: RTOK567P2JRA7D3U · pith_short_8: RTOK567P

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/RTOK567P2JRA7D3USNSFHGQFVC \
  | 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: 8cdcaefbefd2620f8f749364539a05a8b7b10f620c21936bb8c16223a07e0ce3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6481c07e0f0dbfada6da63cecfbb44d20bc902d8bbaac2e42f4b8a4c3f274dd0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-10-22T08:56:29Z",
    "title_canon_sha256": "d17e33db045086ab1d861ba9ce4ab8baed7711dde8cb59017c132f68beda9423"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4643",
    "kind": "arxiv",
    "version": 3
  }
}