Pith Number

pith:JN7JPMFP

pith:2026:JN7JPMFPAMAHJ27JG2BZ7QYWGC

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Breaking the Finite-Sample Barrier in Entropy Coupling

Jun Chen, Shahab Asoodeh

Dependence among fixed-marginal observations can drive conditional entropy to zero after finitely many samples.

arxiv:2605.16229 v1 · 2026-05-15 · cs.IT · math.IT · math.ST · stat.ML · stat.TH

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\pithnumber{JN7JPMFPAMAHJ27JG2BZ7QYWGC}

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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

Under mild support assumptions, zero entropy is achieved with O(log(1/P_min)) observations, where P_min is the minimum nonzero mass of P; dependent observations can eliminate residual uncertainty exactly after finitely many samples.

C2weakest assumption

The characterization of the zero-entropy regime relies on mild support assumptions for the discrete marginals and the enlarged coupling space allowing arbitrary dependence among the Y_i while preserving each marginal exactly.

C3one line summary

Minimum list entropy coupling shows dependent observations can achieve zero residual entropy with O(log(1/P_min)) samples under mild support assumptions, with applications to exact recovery in representation learning and randomness extraction.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] Lindvall,Lectures on the Coupling Method 2002

[2] A metric between probability distributions on finite sets of different cardinalities, 2012

[3] How to find a joint probability distribution of minimum entropy (almost) given the marginals, 2017

[4] Minimum-entropy couplings and their applications, 2019

[5] Computing low-entropy couplings for large-support distributions, 2024

Receipt and verification

First computed	2026-05-20T00:01:59.071108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4b7e97b0af030074ebe936839fc31630b1d93415365a0b5b4da2e28abf42bc83

Aliases

arxiv: 2605.16229 · arxiv_version: 2605.16229v1 · doi: 10.48550/arxiv.2605.16229 · pith_short_12: JN7JPMFPAMAH · pith_short_16: JN7JPMFPAMAHJ27J · pith_short_8: JN7JPMFP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JN7JPMFPAMAHJ27JG2BZ7QYWGC \
  | 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: 4b7e97b0af030074ebe936839fc31630b1d93415365a0b5b4da2e28abf42bc83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77d2fd0e6dd95878cacf761e5349a9fe53a8eca8983bf855124af240250e7ac1",
    "cross_cats_sorted": [
      "math.IT",
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-15T17:39:57Z",
    "title_canon_sha256": "6432a681d875997e59a6ef7bdbc3e6408aadb6a8908b319f4d299c684a87f19c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16229",
    "kind": "arxiv",
    "version": 1
  }
}