Constants Dimensions Dimensions Status

A status report for dimensions

In the Recognition Science framework's machine-checked library of formal statements, dimensions_status is a simple text string, a status report. It lists five completed items: a dimensional signature structure tracking length, time, and mass exponents; the dimensions of the physical constants c, ℏ, and G; the dimensions of the Planck units; the dimension of the fundamental tick τ₀; and the algebra for multiplying and dividing dimensioned quantities. The declaration itself is a definition, not a proven statement. It does not prove that these dimensions are correct or that the constants have those values. It merely records that the module has defined these objects.

What the declaration does establish is a consistent bookkeeping system. Each physical quantity carries a signature like [L²T⁻¹M¹] for the reduced Planck constant, meaning length squared over time times mass. The status string confirms that the Planck length, time, and mass formulas have been checked to have the right dimensions, and that τ₀ has dimension [T]. This is the framework's internal housekeeping: a way to track dimensions through calculations so that derived constants stay dimensionally consistent.

The status report does not claim that the framework has derived the values of c, ℏ, or G from first principles. Those derivations, where they exist, live elsewhere in the library. The declaration also does not claim that the dimensional analysis is complete or that every physical constant has been assigned a signature. It is a snapshot of what the module has defined, not a statement about the physical world. A reader should treat it as a checklist, not a result.

/-- Summary of dimensional analysis module. -/
def dimensions_status : String :=
  "✓ Dimension structure [L, T, M] defined\n" ++
  "✓ Physical constant dimensions (c, ℏ, G) specified\n" ++
  "✓ Planck unit dimensions documented\n" ++
  "✓ τ₀ dimension documented as [T]\n" ++
  "✓ DimensionedQuantity algebra defined"

/-- Summary of dimensional analysis module. -/
def dimensions_status : String :=
  "✓ Dimension structure [L, T, M] defined\n" ++
  "✓ Physical constant dimensions (c, ℏ, G) specified\n" ++
  "✓ Planck unit dimensions documented\n" ++
  "✓ τ₀ dimension documented as [T]\n" ++
  "✓ DimensionedQuantity algebra defined"

/-- Summary of dimensional analysis module. -/
def dimensions_status : String :=
  "✓ Dimension structure [L, T, M] defined\n" ++
  "✓ Physical constant dimensions (c, ℏ, G) specified\n" ++
  "✓ Planck unit dimensions documented\n" ++
  "✓ τ₀ dimension documented as [T]\n" ++
  "✓ DimensionedQuantity algebra defined"

What this page does not claim

The status report does not prove the values of c, ℏ, or G. The status report does not claim the dimensional analysis is complete. The status report does not itself derive any physical law.

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/Constants/Dimensions.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

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