Pith Number

pith:DEXEFG5Y

pith:2017:DEXEFG5YQLRP7TYGQNFQHHUNLZ

not attested not anchored not stored refs pending

New direct proofs of variational principles for t-entropy, spectral radius of weighted shift operators, and entropy statistic theorem

A. V. Lebedev, V. I. Bakhtin

arxiv:1705.01270 v1 · 2017-05-03 · 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{DEXEFG5YQLRP7TYGQNFQHHUNLZ}

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	2026-05-18T00:45:05.511941Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

192e429bb882e2ffcf06834b039e8d5e441141c82bd81f668ee116071ad52226

Aliases

arxiv: 1705.01270 · arxiv_version: 1705.01270v1 · doi: 10.48550/arxiv.1705.01270 · pith_short_12: DEXEFG5YQLRP · pith_short_16: DEXEFG5YQLRP7TYG · pith_short_8: DEXEFG5Y

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/DEXEFG5YQLRP7TYGQNFQHHUNLZ \
  | 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: 192e429bb882e2ffcf06834b039e8d5e441141c82bd81f668ee116071ad52226

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "855fabe878a7ad652ec97ae436812390d6cdefd4e9326ce1003eace88ef44eda",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-05-03T07:03:42Z",
    "title_canon_sha256": "84a2bc523739b45cd13e3b803f5c3f47a2473f054ee300130470b4f969834ae2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.01270",
    "kind": "arxiv",
    "version": 1
  }
}