Pith Number

pith:ZKDOGUN4

pith:2015:ZKDOGUN4U45WP3SYMUQWZQ5RKB

not attested not anchored not stored refs pending

Commutator criteria for strong mixing II. More general and simpler

Rafael Tiedra de Aldecoa, Serge Richard

arxiv:1510.00201 v1 · 2015-10-01 · math.DS · math-ph · math.FA · math.MP · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZKDOGUN4U45WP3SYMUQWZQ5RKB}

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	2026-05-18T01:31:20.480029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca86e351bca73b67ee5865216cc3b15050a37e05afb8083661d46b1a582058b0

Aliases

arxiv: 1510.00201 · arxiv_version: 1510.00201v1 · doi: 10.48550/arxiv.1510.00201 · pith_short_12: ZKDOGUN4U45W · pith_short_16: ZKDOGUN4U45WP3SY · pith_short_8: ZKDOGUN4

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/ZKDOGUN4U45WP3SYMUQWZQ5RKB \
  | 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: ca86e351bca73b67ee5865216cc3b15050a37e05afb8083661d46b1a582058b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e7f06a4aaaf1696867a7bf34d8deb0e5197537255893791d4b2db9b6915cce1",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-01T12:37:15Z",
    "title_canon_sha256": "958b7e71bb0c6fab2a918fcf43ac14fa1507cf57f47f40956355afb1972ee1b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00201",
    "kind": "arxiv",
    "version": 1
  }
}