Pith Number

pith:O7AUU75I

pith:2011:O7AUU75ISV5GQUXP5NOT6HFD64

not attested not anchored not stored refs pending

Variational equalities of entropy in nonuniformly hyperbolic systems

Chao Liang, Gang Liao, Wenxiang Sun, Xueting Tian

arxiv:1110.6091 v2 · 2011-10-27 · 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{O7AUU75ISV5GQUXP5NOT6HFD64}

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	2026-05-18T00:50:52.750100Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77c14a7fa8957a6852efeb5d3f1ca3f71a290fe98573729d9db52e91a45d24f4

Aliases

arxiv: 1110.6091 · arxiv_version: 1110.6091v2 · doi: 10.48550/arxiv.1110.6091 · pith_short_12: O7AUU75ISV5G · pith_short_16: O7AUU75ISV5GQUXP · pith_short_8: O7AUU75I

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/O7AUU75ISV5GQUXP5NOT6HFD64 \
  | 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: 77c14a7fa8957a6852efeb5d3f1ca3f71a290fe98573729d9db52e91a45d24f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73a1e5541319b9bfc5012e70892356ed1027cb3892003ae42983c1174cc7c508",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-10-27T14:31:02Z",
    "title_canon_sha256": "73da8adbac281aab601d0433a3c814808e58319cb43619ece5516f376bbc21fd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6091",
    "kind": "arxiv",
    "version": 2
  }
}