Object Invocation Protocol · protocol specification

Node C18: Waves / Oscillatory Transmission

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

C18 — Waves / Oscillatory Transmission { "id": "C18", "claim": "Change propagates through media as oscillatory disturbances governed by the wave equation; this mathematical form recurs across all physical scales and media types.", "domain": ["fluid dynamics", "acoustics", "electromagnetism", "seismology", "neuroscience", "cardiology", "population biology", "quantum field theory"], "pattern": ["wave", "oscillation", "propagation", "interference", "resonance"], "mechanism": "The wave equation ∂²u/∂t² = c²∇²u describes propagation of a disturbance u at speed c. Solutions include plane waves, spherical waves, and standing waves. Fourier's theorem: any waveform is a superposition of sinusoids. Maxwell's equations yield electromagnetic waves; Schrodinger's equation yields matter waves; neural membrane potentials propagate as action potentials.", "scale": "all scales", "claim_tier": "T0", "sources": [ "d'Alembert, J. (1746). 'Recherches sur la courbe que forme une corde tendue mise en vibration.' Mem. Acad. Sci. Berlin, 2, 214-219.", "Fourier, J. (1822). Theorie Analytique de la Chaleur.", "Maxwell, J.C. (1865). 'A Dynamical Theory of the Electromagnetic Field.' Phil. Trans. R. Soc. Lond., 155, 459-512.", "Schrodinger, E. (1926). 'Quantisierung als Eigenwertproblem.' Ann. Phys., 384, 361-376.", "Hodgkin, A.L. & Huxley, A.F. (1952). 'A Quantitative Description of Membrane Current...' J. Physiol., 117, 500-544." ], "dual": "Static field / non-propagating change — a system where perturbation does not travel but remains localized.", "falsifier": "A propagating disturbance not governed by the wave equation or a straightforward generalization (e.g., nonlinear Schrodinger, Burgers' equation) — i.e., change that travels without wave characteristics.", "rival_frame": "Wave behavior is a mathematical description of energy propagation, not a physical 'pattern.' The equation predicts; the pattern does not explain. The ubiquity of the wave equation reflects its mathematical simplicity (second-order linear PDE), not a deep structural property of reality.", "independence_check": "EXTREMELY HIGH. d'Alembert (mathematics, Paris, 1746) derived the wave equation from vibrating strings. Fourier (mathematical physics, Paris, 1822) developed harmonic analysis from heat conduction. Maxwell (physics, Cambridge, 1865) unified electricity and magnetism, predicting EM waves. Schrodinger (physics, Zurich, 1926) developed wave mechanics from Hamiltonian analogies. Hodgkin-Huxley (physiology, Cambridge, 1952) modeled nerve impulse propagation from ion channel biophysics. Five fields, five centuries, five questions, same equation form.", "pattern_type": "mathematical", "maps_to_axiom": ["A7"] }

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Same node, other planes: Encyclopedia C18
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Key evidence

8 claims · tier-ranked · API

mechanistic

Change propagates through media as oscillatory disturbances governed by the wave equation; this mathematical form recurs across all physical scales and media types.

mechanistic

The wave equation ∂²u/∂t² = c²∇²u describes propagation of a disturbance u at speed c.

mechanistic

Solutions to the wave equation include plane waves, spherical waves, and standing waves.

mechanistic

Fourier's theorem states that any waveform is a superposition of sinusoids.

mechanistic

Maxwell's equations yield electromagnetic waves.

mechanistic

Schrodinger's equation yields matter waves.

mechanistic

Neural membrane potentials propagate as action potentials, modeled from ion channel biophysics.

anecdotal

The wave equation was independently derived across five fields spanning five centuries by d'Alembert (1746, vibrating strings), Fourier (1822, heat conduction), Maxwell (1865, electromagnetism), Schrodinger (1926, quantum mechanics), and Hodgkin-Huxley (1952, nerve impulses).

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grok/grok-4.3atomizer

atomize2026-07-07 07:54

atomize · 8 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-c18-waves-oscillatory-transmission

it output

{
  "claims": [
    {
      "id": "c1",
      "text": "Change propagates through media as oscillatory disturbances governed by the wave equation; this mathematical form recurs across all physical scales and media types.",
      "section": "# Node C18: Waves / Oscillatory Transmission",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Core assertion defining the node's central claim on wave propagation."
    },
    {
      "id": "c2",
      "text": "The wave equation ∂²u/∂t² = c²∇²u describes propagation of a disturbance u at speed c.",
      "section": "# Node C18: Waves / Oscillatory Transmission",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Specifies the governing mathematical equation for the pattern."
    },
    {
      "id": "c3",
      "text": "Solutions to the wave equation include plane waves, spherical waves, and standing waves.",
      "section": "# Node C18: Waves / Oscillatory Transmission",
      "tier": "mechanistic",
      "source_ids": [],
      "source_status": "unsourced",
      "why_material": "Enumerates key solution forms of the wave equation."
    },
    {
      "id": "c4",
      "text": "Fourier's theorem states that any waveform is a superposition of sinusoids.",
      "section": "# Node C18: Waves / Oscillatory Transmission"

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Machine verification: /api/articles/oip-node-c18-waves-oscillatory-transmission/contributions

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