Physics Supernova Classification From Rs

Supernova classes in the framework

Supernovae are the explosive deaths of stars, and astronomers sort them by the elements in their spectra and the shape of their brightening and fading over time. The standard scheme recognizes two broad families: thermonuclear explosions of white dwarfs, which are Type Ia, and core-collapse explosions of massive stars, which are divided into Types Ib, Ic, II-P, and II-L. The Roman numerals and letters encode real observational differences, such as whether hydrogen lines appear and whether the light curve, the graph of brightness against time, stays flat or declines steadily.

In Recognition Science, the framework models this classification as a finite set of exactly five types. The machine-checked library of formal theorems defines an inductive type with five constructors, one for each canonical class, and proves by computation that the number of types is five. The proof is a direct calculation, not an assumption: the theorem supernovaType_count evaluates the cardinality and finds it equal to five. The framework also records the light-curve decline timescales on a ladder built from the golden ratio φ, the number approximately 1.618 that arises throughout the framework as a self-similar scaling constant.

In Recognition Science, the framework treats the five-type scheme as a structural consequence of its cost function, the forced price of recognition events, rather than as an arbitrary observational taxonomy. The framework's library proves that the number of types is five and that the decline timescales sit on the φ-ladder. This is a formal statement about the framework's own model of the classification, not a claim that the framework discovered a new supernova type or that the mapping from observed spectra to the five classes is derived from first principles.

The practical consequence is that the framework offers a compact, machine-checked representation of the standard five-class scheme, with the count proved and the timescales linked to a single scaling ratio. For an astronomer, this is a formalization of what is already known observationally; for the framework, it is a test case showing that a recognized classification can be expressed as a finite structure with a proved cardinality. The framework's contribution is the formal scaffolding, not new astrophysics.

inductive SupernovaType where
  | typeIa
  | typeIb
  | typeIc
  | typeIIP
  | typeIIL
  deriving DecidableEq, Repr, BEq, Fintype

theorem supernovaType_count : Fintype.card SupernovaType = 5 := by decide

inductive SupernovaType where
  | typeIa
  | typeIb
  | typeIc
  | typeIIP
  | typeIIL
  deriving DecidableEq, Repr, BEq, Fintype

What this page does not claim

The framework does not derive the five-type classification from first principles; it models an observational scheme. The framework does not predict new supernova types beyond the five canonical classes. The φ-ladder timescales are recorded in the framework, not derived from a physical model of stellar explosions.

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

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