Pith Number

pith:7QPPW5NO

pith:2022:7QPPW5NOAP272ENFPNOBH2CBHG

not attested not anchored not stored refs pending

Thermodynamic formalism for expanding measures

Paulo Varandas, Vilton Pinheiro

arxiv:2202.05019 v2 · 2022-02-10 · 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{7QPPW5NOAP272ENFPNOBH2CBHG}

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.

Cited by

1 paper in Pith

Density of spectral gap property for positively expansive dynamics and smooth potentials, with applications to the phase transition problem

Receipt and verification

First computed	2026-07-05T06:54:11.850696Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc1efb75ae03f5fd11a57b5c13e84139bc1a3cac800497112d865868037e68d4

Aliases

arxiv: 2202.05019 · arxiv_version: 2202.05019v2 · doi: 10.48550/arxiv.2202.05019 · pith_short_12: 7QPPW5NOAP27 · pith_short_16: 7QPPW5NOAP272ENF · pith_short_8: 7QPPW5NO

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/7QPPW5NOAP272ENFPNOBH2CBHG \
  | 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: fc1efb75ae03f5fd11a57b5c13e84139bc1a3cac800497112d865868037e68d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "15a9260339aeab48fc7ce7eb17dc1d7cdaebf3cbc574a748157368cb6338fc73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2022-02-10T13:24:37Z",
    "title_canon_sha256": "529cb61a9bba742363217c4102f49e23be79089c347d0f8391656e0355a64722"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2202.05019",
    "kind": "arxiv",
    "version": 2
  }
}