Gravity Discriminator Matrix Cell Bohmian Leading Log Distinct

The Bohmian cell

The declaration is a small piece of a larger table. The table compares four rival approaches to quantum gravity, including string theory, loop quantum gravity, causal dynamical triangulations, and Bohmian approaches, across three measurable sectors. Each cell records whether the Recognition Science framework's prediction differs from the rival's. The declaration in question fills the cell for the Bohmian rival in the leading-log sector, the sector that measures the first correction term in black hole entropy.

What the declaration establishes is a single inequality: the framework's leading-log coefficient, written c_RS, is negative. The proof is a theorem in the framework's machine-checked library of formal theorems, meaning the statement is derived from the framework's axioms with no unproved assumptions. The rival, Bohmian approaches, predict no quantum-gravity signal in this sector at all. So the framework's negative value is a distinction: the framework predicts a signal where the rival predicts none.

This cell is one of several in the table. Against loop quantum gravity and string theory, the framework gives explicit numerical margins, for example c_RS minus the rival's value is greater than one quarter. Against Bohmian approaches and causal dynamical triangulations, the distinction is qualitative: the framework's value is positive or negative where the rival has nothing. The declaration does not say how large the negative value is, only that it is negative.

The declaration also does not claim that the framework's leading-log coefficient matches any measured black hole entropy value. It is a structural result about the framework's internal predictions, not an empirical measurement. The table organizes these theorem-grade inequalities, but it does not replace the separate register of falsifier predictions that name specific experimental sensitivities from observatories like LIGO, Virgo, LISA, or NANOGrav.

/-- (Bohmian, LeadingLog): Bohmian / Diosi-Penrose substrates do not
produce quantum-gravity signatures (continuous trajectories violate T2;
stochastic collapse violates T1). RS predicts `c_RS < 0`. -/
theorem cell_Bohmian_LeadingLog_distinct : c_RS < 0 :=
  c_RS_neg

What this page does not claim

The declaration does not state the magnitude of c_RS, only that it is negative. The declaration does not match the coefficient to any measured black hole entropy value. The declaration does not specify an experimental observation channel for the Bohmian rival.

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/Gravity/DiscriminatorMatrix.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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Derived articles

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