Foundation Rs Wave Function Collapse Rswfcollapse Cert

The collapse certificate

In quantum mechanics, wave function collapse is the abrupt change of a system's state when it is measured. The Recognition Science framework models this as a ledger, a discrete record of events where measurement is a posting, a recognition event. The declaration RSWFCollapseCert in the framework's machine-checked library bundles three general facts about a cost function, not a proof about measurement.

The cost function is defined as J(m/e), where J(x) = (x + 1/x)/2 - 1. The three facts are: the cost is zero when the two inputs are equal, the cost is never negative for positive inputs, and a threshold constant phi - 3/2 is positive. These are elementary consequences of the cost's definition, proved for any positive real numbers m and e. The certificate is a structure that packages these three theorems together, and the library shows such a certificate exists.

The framework's own documentation is explicit about the limit. The paragraph describing wave function collapse as a ledger posting, with an eight-tick cycle determining the minimal time for a recognition event, is a research note recording where the idea was meant to go, not a result. The code proves nothing specific to wave function collapse, because the cost function is defined without reference to any quantum mechanical quantity. The same body of text is shared verbatim with 2383 sibling modules, each with a different subject name but the same three facts.

What would make this declaration a theorem about its subject is a definition of m and e in that subject's own terms, for example, a measured value and an expected value. Without that, the certificate is a template, not a physical claim. It establishes that if you have two positive numbers and define a cost by J(m/e), then the cost has three basic properties. It does not establish that wave function collapse happens, that it follows this cost, or that the eight-tick cycle is real.

In plain language, the certificate is a well-formed box with three correct facts inside, but the label on the box promises more than the contents deliver. The library proves the box is sound; the research note says what the box was intended for. The reader should see the distinction: a proof about a cost function is not a proof about quantum measurement.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

theorem cert_inhabited : Nonempty RSWFCollapseCert := ⟨cert⟩

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

What this page does not claim

This answer does not claim that wave function collapse is a real physical process. This answer does not claim that the cost function J(m/e) has been shown to govern any actual measurement. This answer does not claim that the eight-tick cycle is a proved result.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/RS_Wave_Function_Collapse.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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