Pith Number

pith:BMRQLQS5

pith:2026:BMRQLQS5NDZI7OCLOSJXALOKTW

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The unique, universal entropy for complex systems

Kenric P. Nelson

Coupled entropy is the unique universal entropy for complex systems because it measures uncertainty at the maximizing distribution's scale and is extensive across all scaling classes.

arxiv:2605.04493 v4 · 2026-05-06 · cond-mat.stat-mech · cs.IT · math.IT

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\pithnumber{BMRQLQS5NDZI7OCLOSJXALOKTW}

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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 coupled entropy, maximized by the coupled stretched exponential distributions, is proven to be the unique, universal entropy that satisfies these requirements.

C2weakest assumption

The requirement that entropy must measure the uncertainty at the informational scale of the maximizing distribution where the log-log slope equals -1, plus the requirement of extensivity across the full Hanel-Thurner universality scaling classes; these are asserted as previously missing from decades of research.

C3one line summary

The coupled entropy maximized by coupled stretched exponential distributions is the unique universal entropy satisfying the requirements to measure uncertainty at the informational scale with log-log slope -1 and extensivity across Hanel-Thurner universality classes.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-29T02:05:45.836440Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b2305c25d68f28fb84b7493702dca9db5d785022ddd1497d5b0c589986f6380

Aliases

arxiv: 2605.04493 · arxiv_version: 2605.04493v4 · doi: 10.48550/arxiv.2605.04493 · pith_short_12: BMRQLQS5NDZI · pith_short_16: BMRQLQS5NDZI7OCL · pith_short_8: BMRQLQS5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BMRQLQS5NDZI7OCLOSJXALOKTW \
  | 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: 0b2305c25d68f28fb84b7493702dca9db5d785022ddd1497d5b0c589986f6380

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36cfe9330395e6d8809008fb614e89046d876459860cd1f6fb898392acf25aa6",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-06T04:47:03Z",
    "title_canon_sha256": "b021c353ac6c410eb6a39292ea667de2d3d50b7220a33223d15bbaadddf66000"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04493",
    "kind": "arxiv",
    "version": 4
  }
}