IndisputableMonolith.CrossDomain.DevelopmentReversal
The module defines a reversal map on Fin 8 together with its basic algebraic properties to model inverted sequences of eight developmental stages. Cross-domain researchers would cite it when embedding Erikson stages into the eight-tick octave of the forcing chain. All statements are established by direct enumeration on the finite set.
claimLet $r : {0,1,2,3,4,5,6,7} → {0,1,2,3,4,5,6,7}$ be given by $r(i) = 7-i$. Then $r∘r = id$, $r(0)=7$, $r(7)=0$, and the midpoint stage inverts the first stage.
background
The module sits inside the CrossDomain namespace and imports only Mathlib. It introduces EriksonStage as the type Fin 8, eriksonCount as the cardinality 8, and erikson_eq_2cube as the equality 8 = 2^3. These objects align the developmental sequence with the eight-tick period required by the forcing chain. The central object is the reversal map reverse : Fin 8 → Fin 8 together with its involution and endpoint-swapping lemmas.
proof idea
This is a definition module, no proofs. The listed properties (involution, endpoint swap, midpoint inversion) are obtained by exhaustive case analysis on the eight elements of Fin 8.
why it matters in Recognition Science
The module supplies the concrete reversal structure that realizes the eight-tick octave (T7) inside a developmental model. It feeds the certificate DevelopmentReversalCert and supplies the involution and swap facts needed for any later cross-domain theorem that invokes the reversal.
scope and limits
- Does not assert empirical validity of any psychological stage theory.
- Does not extend the reversal construction past cardinality 8.
- Does not derive physical constants or mass ladders from the reversal.
- Does not claim that the reversal is the unique involution on Fin 8.