Pith Number

pith:CCNFCPRM

pith:2012:CCNFCPRMEWNX5T2WKPIAWLJ23P

not attested not anchored not stored refs pending

Commutator methods for the spectral analysis of uniquely ergodic dynamical systems

Rafael Tiedra de Aldecoa

arxiv:1208.3784 v2 · 2012-08-18 · math.DS · math-ph · 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{CCNFCPRMEWNX5T2WKPIAWLJ23P}

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	2026-05-17T23:53:36.099462Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

109a513e2c259b7ecf5653d00b2d3adbdbc285c6d22fb0e7a09f1400a25f0379

Aliases

arxiv: 1208.3784 · arxiv_version: 1208.3784v2 · doi: 10.48550/arxiv.1208.3784 · pith_short_12: CCNFCPRMEWNX · pith_short_16: CCNFCPRMEWNX5T2W · pith_short_8: CCNFCPRM

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/CCNFCPRMEWNX5T2WKPIAWLJ23P \
  | 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: 109a513e2c259b7ecf5653d00b2d3adbdbc285c6d22fb0e7a09f1400a25f0379

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b79b1ff8921936095e8e98997846f56290c662675ee7f50ddd31102a18324b57",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-18T20:08:19Z",
    "title_canon_sha256": "aefe65be91c2b0411111e7571f2c565faaef8e0f448c1cbbe2219346c0366777"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3784",
    "kind": "arxiv",
    "version": 2
  }
}