Pith Number

pith:D7ALW7FL

pith:2017:D7ALW7FLT5G7CNVNSNIBOLLFUQ

not attested not anchored not stored refs pending

Rate distortion theory, metric mean dimension and measure theoretic entropy

Anibal Velozo, Renato Velozo

arxiv:1707.05762 v1 · 2017-07-18 · 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{D7ALW7FLT5G7CNVNSNIBOLLFUQ}

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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

3 papers in Pith

On quantization and the classical variational principle for the metric mean dimension

Metric mean dimension of factor maps

Dynamical metric order

Receipt and verification

First computed	2026-05-18T00:40:01.526149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc0bb7cab9f4df136ad9350172d65a42e8d0b83253580cb63e50990af70f830

Aliases

arxiv: 1707.05762 · arxiv_version: 1707.05762v1 · doi: 10.48550/arxiv.1707.05762 · pith_short_12: D7ALW7FLT5G7 · pith_short_16: D7ALW7FLT5G7CNVN · pith_short_8: D7ALW7FL

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/D7ALW7FLT5G7CNVNSNIBOLLFUQ \
  | 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: 1fc0bb7cab9f4df136ad9350172d65a42e8d0b83253580cb63e50990af70f830

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "75fd5a3984efaaecbdfcafb34904baeab4f0feb7cf4b4e22ef56abb62b18b437",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2017-07-18T17:45:09Z",
    "title_canon_sha256": "169fc0636a7f91f090e5e76af5c635a5c1133cdca2ccd539922cbab8966826aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1707.05762",
    "kind": "arxiv",
    "version": 1
  }
}