Pith Number

pith:3XEIS45Z

pith:2012:3XEIS45ZJYKUJ7RBMBW7RJNMJ4

not attested not anchored not stored refs pending

Differentiability of thermodynamical quantities in non-uniformly expanding dynamics

Armando Castro, Paulo Varandas, Thiago Bomfim

arxiv:1205.5361 v4 · 2012-05-24 · math.DS · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3XEIS45ZJYKUJ7RBMBW7RJNMJ4}

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	2026-05-18T01:18:57.793360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddc88973b94e1544fe21606df8a5ac4f310282b9b5405b795264e2f73c8ab8f0

Aliases

arxiv: 1205.5361 · arxiv_version: 1205.5361v4 · doi: 10.48550/arxiv.1205.5361 · pith_short_12: 3XEIS45ZJYKU · pith_short_16: 3XEIS45ZJYKUJ7RB · pith_short_8: 3XEIS45Z

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/3XEIS45ZJYKUJ7RBMBW7RJNMJ4 \
  | 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: ddc88973b94e1544fe21606df8a5ac4f310282b9b5405b795264e2f73c8ab8f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcb9b2d31b028af3b512716d77afe87f5506090278853c59e3e6e88d19261583",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-24T08:09:30Z",
    "title_canon_sha256": "8b0a6ff69ad974c5e054b27d7d36b312229c54fbb0869eed4bceb553bb765f03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.5361",
    "kind": "arxiv",
    "version": 4
  }
}