PhysicsLogic / Hughes 1960 Reference Controls

What a Frequency Ratio Can Establish

Separate a null comparison, an independently known reference, and a finite physical bound.

Definitions and assumptions

Scope and physical limitations

The ratio diagnostics normalize frequencies to their respective baselines, so the recorded comparison is f/r. Reference access means independently calibrated information, not the instrument's nominal label. The separate spin model uses energies divided by Planck's constant and a first-order diagonal rank-two response in the field-defined basis. It is not a complete nuclear Hamiltonian, a cesium calculation, or a conversion from line width to mass anisotropy. Its physical identification with the proton response remains an explicit premise; insensitivity is now a zero frequency response, not an arbitrary predicate.

Other arguments
Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

∀ (referenceError ratioError : ℝ),
  0 ≤ ratioError →
    ∀ (actual : ℝ × ℝ),
      (boundedReferenceRecords referenceError).admissible actual →
        |actual.1 / actual.2 - 1| ≤ ratioError →
          (boundedReferenceRecords referenceError).RecordConstrainsValueAt false
            ((boundedReferenceRecords referenceError).recordAt false actual) fun frequency =>
            |frequency - 1| ≤ ratioError + referenceError + ratioError * referenceError
Compare two arguments

Compare their definitions and hypotheses. Shared declarations may be instantiated differently; differences do not establish equivalence or implication.

No comparison argument selected.

Compare an earlier extraction

Compare the displayed specifications with an earlier JSON export. This compares text, not mathematical equivalence. Files stay in this browser.

No earlier extraction selected.

Notes and questions

Note for

Unsubmitted text stays in this tab when navigating declarations, but is not saved across reloads.

Import merges local entries without overwriting them.

All declarations in the selected argument

Definitions, structures, and assumptions

Structures, classes, and inductive alternatives

  • structure
  • structure
  • structure
  • structure
  • structure

Definitions and domain choices

  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition
  • definition

Checked statements: parameters, hypotheses, and interpretation

  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement
  • checked statement

Constructors, projections, and other meaning dependencies

  • constructor
  • constructor
  • constructor
  • constructor
  • constructor

External mathematical declarations

  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary
  • external type boundary