Object Invocation Protocol · protocol specification

Node C06: Information / Entropy / Compression

Posted Jul 4, 2026 · Updated Jul 17, 2026 · 2 min read

C06 — Information / Entropy / Compression { "id": "C06", "claim": "Order is compressibility; physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit; information is physical.", "domain": ["communications engineering", "statistical mechanics", "quantum computing", "machine_learning", "molecular_biology"], "pattern": ["entropy_as_information", "Landauer_bound", "MaxEnt", "compression"], "mechanism": "Shannon entropy H = -Σ p_i log p_i measures information content. Boltzmann entropy S = k ln W counts microstates. Landauer: erasing one bit of information requires dissipation of at least kT ln(2) of heat — information destruction is irreversible and physical. Kolmogorov complexity: the shortest program that produces a string is its information content.", "scale": "quantum → cosmic", "claim_tier": "T0/T1", "sources": [ "Shannon, C.E. (1948). 'A Mathematical Theory of Communication.' Bell System Tech. J., 27, 379-423, 623-656.", "Landauer, R. (1961). 'Irreversibility and Heat Generation in the Computing Process.' IBM J. Res. Dev., 5(3), 183-191.", "Jaynes, E.T. (1957). 'Information Theory and Statistical Mechanics.' Phys. Rev., 106(4), 620-630.", "Kolmogorov, A.N. (1965). 'Three Approaches to the Quantitative Definition of Information.' Probl. Peredachi Inf., 1(1), 3-11.", "Bennett, C.H. (1982). 'The Thermodynamics of Computation.' Int. J. Theor. Phys., 21(12), 905-940." ], "dual": "Noise / incompressibility — maximum entropy, no pattern to encode.", "falsifier": "Information erasure below the Landauer bound (dissipation < kT ln(2) per bit) in a physically realizable process; or information processing with no physical substrate.", "rival_frame": "Information is a human construct mapped onto physics. The Landauer bound is a calculation about a specific model of computation, not a fundamental physical limit. 'Information is physical' is a metaphorical extension of thermodynamic vocabulary to abstract domains.", "independence_check": "HIGH. Shannon (Bell Labs, 1948) derived entropy from communication engineering — minimizing transmission cost. Boltzmann/Gibbs (statistical mechanics, 1870s-1900s) derived entropy from counting gas microstates. Landauer (IBM, 1961) derived the bound from thermodynamics of computation. Kolmogorov (Soviet mathematics, 1965) derived complexity from algorithmic theory. Four fields, four nations, four decades, unified result: information and entropy are the same quantity.", "pattern_type": "mathematical", "maps_to_axiom": ["A2", "A11", "A7"] }

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Corpus map

Same node, other planes: Encyclopedia C06 · Inventory invariant
Edges touching C06: convergence edge 5
Catalogue hub: Public Article · Schema

Key evidence

7 claims · tier-ranked · API

mechanistic

Order is compressibility.

mechanistic

Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.

mechanistic

Information is physical.

mechanistic

Shannon entropy H = -Σ p_i log p_i measures information content.

mechanistic

Boltzmann entropy S = k ln W counts microstates.

mechanistic

Erasing one bit of information requires dissipation of at least kT ln(2) of heat.

mechanistic

Kolmogorov complexity is the length of the shortest program that produces a string.

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grok/grok-4.3atomizer

atomize2026-07-07 08:01

atomize · 7 claims

inspect — what it was prompted & output

prompted with

You are the claim atomizer for the miscsubjects.com philosophy and OIP corpus. You read an existing article body and extract its material assertions into the same claims+sources JSON schema the health content uses. The body is read-only input.

ALWAYS:
- Extract every material assertion as one atomic claim, tied to the ## section it came from.
- Tier honestly: human = empirically established; mechanistic = formally proven or mathematical; anecdotal = historical or textual attribution; speculative = metaphysical or interpretive.
- Attach real sources (primary works, papers, books) with exact quotes only where you can verify them; otherwise mark the claim unsourced.
- Prefer fewer, harder claims over many soft ones.

NEVER:
- Never rewrite, summarize, or output the body.
- Never invent a URL, quote, or publication.
- Never duplicate an existing claim text.

input: atomize oip-node-c06-information-entropy-compression

it output

{
  "claims": [
    {
      "id": "c1",
      "text": "Order is compressibility.",
      "section": "C06 — Information / Entropy / Compression",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core assertion equating order with a fundamental property of information."
    },
    {
      "id": "c2",
      "text": "Physical erasure of information has a minimum thermodynamic cost of kT ln(2) per bit.",
      "section": "C06 — Information / Entropy / Compression",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "States the Landauer bound as a physical limit on information destruction."
    },
    {
      "id": "c3",
      "text": "Information is physical.",
      "section": "C06 — Information / Entropy / Compression",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Unifies information theory with physical laws."
    },
    {
      "id": "c4",
      "text": "Shannon entropy H = -Σ p_i log p_i measures information content.",
      "section": "C06 — Information / Entropy / Compression",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Formal definition linking probability to information measure."
    },
    {
      "id": "c5",
      "te

db345b646db8e44d

Machine verification: /api/articles/oip-node-c06-information-entropy-compression/contributions

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