Pith Number

pith:C3RWDZTD

pith:2017:C3RWDZTD4RZ2G7UPIGZW456YS7

not attested not anchored not stored refs pending

Pesin's Entropy Formula for $C^1$ non-uniformly expanding maps

Felipe Santos, Vitor Araujo

arxiv:1707.04311 v4 · 2017-07-13 · 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{C3RWDZTD4RZ2G7UPIGZW456YS7}

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	2026-05-17T23:49:18.028351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

16e361e663e473a37e8f41b36e77d897c3684ee11fd90cff056991e1a5124489

Aliases

arxiv: 1707.04311 · arxiv_version: 1707.04311v4 · doi: 10.48550/arxiv.1707.04311 · pith_short_12: C3RWDZTD4RZ2 · pith_short_16: C3RWDZTD4RZ2G7UP · pith_short_8: C3RWDZTD

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/C3RWDZTD4RZ2G7UPIGZW456YS7 \
  | 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: 16e361e663e473a37e8f41b36e77d897c3684ee11fd90cff056991e1a5124489

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49f2711842cce17c86b79061c8eec044cb10845a29a40490017f208b5175898d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-07-13T20:35:55Z",
    "title_canon_sha256": "31202566744d82d60f7ecbf378d6f91c14e6dc3b746c4758ddbc4d27ee9e5410"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.04311",
    "kind": "arxiv",
    "version": 4
  }
}