PhysicsLogic / Penzias-Wilson 1965

Residual Detection and Interpretation

Follow component-error bounds through record compatibility, then distinguish spectral exclusion of a whole explanation from conditional origin inference.

Definitions and assumptions

Scope and physical limitations

This slice uses a bounded-error interpretation of the scalar residual, not a sampling distribution or a confidence level. Treating component errors as simultaneous hard bounds is a conditional model; its constructed backlobe value and recentered radius are not new observations or revised historical error bars. The spectral contradiction is checked, but calibration, the source-reported two-frequency bound, and known-source classification and spectra remain inputs. It does not establish actual-sky compatibility or a cosmological origin. The additional bound on other contributions is a diagnostic assumption, not a result of the paper.

Other arguments
Examples and distinctions

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

Exact root statement

∀ (center uncertaintyKelvin : ℝ),
  0 ≤ uncertaintyKelvin →
    uncertaintyKelvin < center →
      (recordAccess uncertaintyKelvin).RecordConstrainsValueAt () center fun residual => 0 < residual
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
  • 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

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

Constructors, projections, and other meaning dependencies

  • constructor
  • constructor
  • 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