Pith Number

pith:E4SF7K3Q

pith:2026:E4SF7K3QXA7YX2IOA3AHYPUM2P

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Watts-per-Intelligence Part II: Algorithmic Catalysis

Elija Perrier

Reusable computational structures bound any class-specific speed-up by the algorithmic mutual information between substrate and task descriptor, at a minimum energy cost from Landauer erasure.

arxiv:2604.20897 v2 · 2026-04-21 · cs.IT · cs.AI · math.IT · physics.comp-ph

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\pithnumber{E4SF7K3QXA7YX2IOA3AHYPUM2P}

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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

We prove that any class-specific speed-up is upper-bounded by the algorithmic mutual information between the substrate and the class descriptor, and that installing this information incurs a minimum thermodynamic cost via Landauer erasure. Combining these results yields a coupling theorem that lower-bounds the deployment horizon required for a catalyst to be energetically favourable.

C2weakest assumption

That reusable computational structures exist which satisfy bounded restoration and structural selectivity constraints for the task class while allowing the mutual information bound to be achieved in practice.

C3one line summary

Reusable algorithmic structures (catalysts) for task classes yield speed-ups upper-bounded by mutual information, with minimum thermodynamic installation costs via Landauer erasure and a lower bound on favorable deployment time.

Receipt and verification

First computed	2026-06-09T01:05:17.666310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27245fab70b83f8be90e06c07c3e8cd3e7e49a47619c0a09d0c3ce5448977274

Aliases

arxiv: 2604.20897 · arxiv_version: 2604.20897v2 · doi: 10.48550/arxiv.2604.20897 · pith_short_12: E4SF7K3QXA7Y · pith_short_16: E4SF7K3QXA7YX2IO · pith_short_8: E4SF7K3Q

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/E4SF7K3QXA7YX2IOA3AHYPUM2P \
  | 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: 27245fab70b83f8be90e06c07c3e8cd3e7e49a47619c0a09d0c3ce5448977274

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d33992d56dc440fd8795c34f847073c3dc55eadd5d488b6234c43ccfcff30091",
    "cross_cats_sorted": [
      "cs.AI",
      "math.IT",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-04-21T13:36:33Z",
    "title_canon_sha256": "54620ad6508e8e8b7ec1c73d34e6ace4cb536fae8ad8f5cfae6388b887a30f13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20897",
    "kind": "arxiv",
    "version": 2
  }
}