Pith Number

pith:4UJ7UZKE

pith:2026:4UJ7UZKEL7MWTL4PAFOQL7R4WN

not attested not anchored not stored refs pending

Rate-Distortion Theory for Deductive Sources under Closure Fidelity

Jianfeng Xu

The minimum zero-distortion rate equals the source mass of the core times the entropy of the source conditioned on that core.

arxiv:2604.15698 v4 · 2026-04-17 · cs.IT · cs.LO · math.IT

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\usepackage{pith}
\pithnumber{4UJ7UZKEL7MWTL4PAFOQL7R4WN}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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.

Claims

C1strongest claim

the minimum zero-distortion rate equals the source mass of the core times the entropy of the source conditioned on that core. For reconstruction alphabets contained in the deductive closure of the source knowledge base, the full rate-distortion function depends only on the core.

C2weakest assumption

natural disjointness condition on zero-distortion reconstruction sets; order-robustness assumption identifying the chosen core with the order-free essential set.

C3one line summary

The rate-distortion function for deductive sources depends only on their irredundant core, with zero-distortion rate equal to core mass times conditional entropy under closure fidelity.

Receipt and verification

First computed	2026-05-29T01:05:09.951849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e513fa65445fd969af8f015d05fe3cb36987ea2dcb6372ca20eb5b7f14464f2b

Aliases

arxiv: 2604.15698 · arxiv_version: 2604.15698v4 · doi: 10.48550/arxiv.2604.15698 · pith_short_12: 4UJ7UZKEL7MW · pith_short_16: 4UJ7UZKEL7MWTL4P · pith_short_8: 4UJ7UZKE

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/4UJ7UZKEL7MWTL4PAFOQL7R4WN \
  | 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: e513fa65445fd969af8f015d05fe3cb36987ea2dcb6372ca20eb5b7f14464f2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06446932f44eadab39b370f9719d0701b7853284aa3b53347496832e192dc1d3",
    "cross_cats_sorted": [
      "cs.LO",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-04-17T04:53:04Z",
    "title_canon_sha256": "6775e3babd19c57650fc882b8f5499d91cc3905b2697440ad7040d0510e8806d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15698",
    "kind": "arxiv",
    "version": 4
  }
}