`CompactificationFamily`

definition

show as: view math explainer →

module: IndisputableMonolith.Physics.StringCompactificationFromRS
domain: Physics
line: 19 · github
papers citing: none yet

open explainer

Read the cached plain-language explainer.

open lean source

IndisputableMonolith.Physics.StringCompactificationFromRS on GitHub at line 19.

browse module

All declarations in this module, on Recognition.

explainer page

A cached Ask Recognition explainer exists for this declaration.

open explainer

used by

formal source

  16
  17namespace IndisputableMonolith.Physics.StringCompactificationFromRS
  18
  19inductive CompactificationFamily where
  20  | calabiYau
  21  | torus
  22  | orbifold
  23  | warped
  24  | braneWorld
  25  deriving DecidableEq, Repr, BEq, Fintype
  26
  27theorem compactFamily_count : Fintype.card CompactificationFamily = 5 := by decide
  28
  29/-- 10 - 4 = 6 internal dimensions. -/
  30theorem ten_minus_four : (10 : ℕ) - 4 = 6 := by decide
  31
  32/-- 6 = 3 + 2 + 1 = rank sum of B₃. -/
  33theorem six_eq_rank_sum : (6 : ℕ) = 3 + 2 + 1 := by decide
  34
  35structure StringCompactificationCert where
  36  five_families : Fintype.card CompactificationFamily = 5
  37  internal_dims : (10 : ℕ) - 4 = 6
  38  six_partitions : (6 : ℕ) = 3 + 2 + 1
  39
  40def stringCompactificationCert : StringCompactificationCert where
  41  five_families := compactFamily_count
  42  internal_dims := ten_minus_four
  43  six_partitions := six_eq_rank_sum
  44
  45end IndisputableMonolith.Physics.StringCompactificationFromRS

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.