Pith Number

pith:BC4JFWBZ

pith:2018:BC4JFWBZDNX3ZWXKJGN35J7FEO

not attested not anchored not stored refs pending

Entropy formula and continuity of entropy for piecewise expanding maps

Antonio Pumarino, Jose F. Alves

arxiv:1806.01095 v1 · 2018-06-04 · 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{BC4JFWBZDNX3ZWXKJGN35J7FEO}

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	2026-05-18T00:14:17.523896Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08b892d8391b6fbcdaea499bbea7e5239917f864d65758cf01a14d70981e0fec

Aliases

arxiv: 1806.01095 · arxiv_version: 1806.01095v1 · doi: 10.48550/arxiv.1806.01095 · pith_short_12: BC4JFWBZDNX3 · pith_short_16: BC4JFWBZDNX3ZWXK · pith_short_8: BC4JFWBZ

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/BC4JFWBZDNX3ZWXKJGN35J7FEO \
  | 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: 08b892d8391b6fbcdaea499bbea7e5239917f864d65758cf01a14d70981e0fec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95fc3fe5b3a2788bb79dc28628281e527d2ed9729ba083755191f3646e71fdc3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-06-04T13:19:02Z",
    "title_canon_sha256": "e62ed49749e441f5b2a9e53b4a748f0eb09592461593d9dad8f432f5ba85f78a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.01095",
    "kind": "arxiv",
    "version": 1
  }
}