Pith Number

pith:SSDVJOVF

pith:2015:SSDVJOVFO2SD2ETWZZZNQ4H3UN

not attested not anchored not stored refs pending

Entropy and Its Variational Principle for Locally Compact Metrizable Systems

Andr\'e Caldas, Mauro Patr\~ao

arxiv:1511.02057 v2 · 2015-11-06 · 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{SSDVJOVFO2SD2ETWZZZNQ4H3UN}

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	2026-05-18T01:17:25.105993Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

948754baa576a43d1276ce72d870fba365887e8188e0c35fb4b79f1b7054f9be

Aliases

arxiv: 1511.02057 · arxiv_version: 1511.02057v2 · doi: 10.48550/arxiv.1511.02057 · pith_short_12: SSDVJOVFO2SD · pith_short_16: SSDVJOVFO2SD2ETW · pith_short_8: SSDVJOVF

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/SSDVJOVFO2SD2ETWZZZNQ4H3UN \
  | 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: 948754baa576a43d1276ce72d870fba365887e8188e0c35fb4b79f1b7054f9be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42b39ba55b72e51d2802037b1079cb71dd7f09930980cac373f5470a0243c08b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-11-06T12:52:54Z",
    "title_canon_sha256": "0a71a3cfc64e8f3cceb950a2b453a69decc8e961445e6ab5dde36ac26820c2ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.02057",
    "kind": "arxiv",
    "version": 2
  }
}