Gravity Discriminator Matrix

The discriminator matrix

A gravity discriminator matrix is a comparison table. Each row names a rival approach to quantum gravity: loop quantum gravity, string theory, causal dynamical triangulations, and Bohmian approaches. Each column names a measurable sector: the leading-log coefficient of black hole entropy, an echo damping ratio, and a phase delay. Each cell records a numerical band that Recognition Science predicts and the rival does not. The whole table is a compact way to see where two theories disagree before any experiment is run.

The matrix comes from the Recognition Science framework, which starts from the idea that reality keeps a discrete record of recognition events, and that the cost of recognition is forced, not chosen. From that starting point the framework derives constants and scaling laws. The discriminator matrix applies those results to quantum gravity. The framework's machine-checked library of formal theorems builds the table and proves every filled cell as a theorem, with no unproved assumptions left in the code.

The strongest cells carry explicit numerical margins. Against loop quantum gravity, the leading-log coefficient differs by more than one quarter. Against string theory, the margin is larger than five quarters. In the echo damping sector, Recognition Science predicts a ratio above one half, while the rivals predict nothing at all. The phase delay sits between zero and one half. These are not vague qualitative claims; each is a formal inequality with a named observational channel attached.

What the framework establishes in plain language is this: the predictions occupy bands that four rival theories do not share. For two rivals the bands are separated by explicit numbers. For the other two, the rivals predict no signal in the sector, so any positive signal discriminates. The matrix does not require any experimental input to be built. It organizes theorem-grade results into the format a discovery plan asked for, and it passes the plan's binding success criterion: at least one unambiguous distinction per rival.

The practical consequence is a short list of measurements that could tell the theories apart. If a future experiment measures the leading-log coefficient of black hole entropy and finds it in the band between negative one quarter and zero, that single number rules out both loop quantum gravity and string theory as formulated here. The matrix turns a large theoretical disagreement into a small set of testable numbers.

/-- (LQG, LeadingLog): RS leading-log coefficient is at least `1/4`
above LQG's `-1/2`. -/
theorem cell_LQG_LeadingLog : c_RS - (-1 / 2) > 1 / 4 :=
  c_RS_LQG_margin

/-- (String, LeadingLog): RS leading-log coefficient is at least `5/4`
above string-theory's `-3/2`. -/
theorem cell_String_LeadingLog : c_RS - (-3 / 2) > 5 / 4 :=
  c_RS_string_margin

/-- (LQG, EchoDamping): RS per-echo damping ratio `1/φ` is strictly
above LQG's uniform-discreteness `1/2`. -/
theorem cell_LQG_EchoDamping : echoDampingRatio > 1 / 2 :=
  echoDampingRatio_above_half

/-- (LQG, RungPhase): RS per-rung phase delay `log φ` is strictly
below LQG's half-quantum `1/2`. -/
theorem cell_LQG_RungPhase : rungPhaseDelay < 1 / 2 :=
  rungPhaseDelay_below_half

theorem discriminatorMatrixFull_inhabited :
    Nonempty DiscriminatorMatrixCert :=
  ⟨discriminatorMatrixFull⟩

What this page does not claim

The matrix does not prove that any rival theory is false; it proves that the rival predictions differ from Recognition Science's predictions. The matrix does not assign probabilities to the rival theories. The matrix does not replace the dataset-tied falsifier register that requires specific experimental sensitivity numbers.

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)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: