Pith Number

pith:DRHDSMQA

pith:2018:DRHDSMQARTG3KERFJWILVEE6ZJ

not attested not anchored not stored refs pending

Strong Birkhoff Ergodic Theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles

Kai Tao

arxiv:1805.00431 v2 · 2018-05-01 · math.DS · math-ph · math.MP · math.SP

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DRHDSMQARTG3KERFJWILVEE6ZJ}

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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.

Cited by

1 paper in Pith

Large Deviation theorems for Dirichlet determinants of analytic quasi-periodic Jacobi operators with Brjuno-R\"ussmann frequency

Receipt and verification

First computed	2026-05-18T00:10:21.789677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c4e3932008ccdb512254d90ba909eca6e1fcdbdfd8e270d6a75ac0858f7da6e

Aliases

arxiv: 1805.00431 · arxiv_version: 1805.00431v2 · doi: 10.48550/arxiv.1805.00431 · pith_short_12: DRHDSMQARTG3 · pith_short_16: DRHDSMQARTG3KERF · pith_short_8: DRHDSMQA

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/DRHDSMQARTG3KERFJWILVEE6ZJ \
  | 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: 1c4e3932008ccdb512254d90ba909eca6e1fcdbdfd8e270d6a75ac0858f7da6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dbf3e8f4a4c1a76c18cbd0cc264cd381210fc53cbf14dfd0e16a9a03860f6145",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-05-01T17:02:52Z",
    "title_canon_sha256": "9ccff1e4c9ad7e4f873dd4d02580d075904b4fde4bd5cb2fabb42875faac9279"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.00431",
    "kind": "arxiv",
    "version": 2
  }
}