IndisputableMonolith.CrossDomain.DevelopmentReversal
The module defines a reversal map on Fin 8 that models inversion across Erikson's eight developmental stages. Researchers linking Recognition Science to psychology would cite it when applying the eight-tick structure to stage sequences. The module supplies the type alias, the count equality to 2 cubed, the reverse function, and lemmas establishing its involution and endpoint-swapping properties.
claimLet $E = $ Fin $8$ index the stages. The reversal $r: E → E$ obeys $r(r(n)) = n$ for all $n$, swaps the endpoints $r(0) = 7$ and $r(7) = 0$, and inverts the first stage at the midpoint.
background
The module sits in the CrossDomain section that connects Recognition Science to external domains. It introduces EriksonStage as the Fin 8 type, proves the count equals 8 which is $2^3$, and defines the reverse map together with its basic algebraic facts. This construction realizes the eight-tick octave (period $2^3$) inside a psychological model.
proof idea
This is a definition module, no proofs. It assembles the stage type, the count lemma, the reverse definition, and four short lemmas whose verifications are direct finite checks or algebraic identities.
why it matters in Recognition Science
The module supplies the reversal infrastructure that supports cross-domain applications of the eight-tick octave. It feeds the DevelopmentReversalCert and supplies the concrete realization of T7 inside an external stage sequence.
scope and limits
- Does not model empirical stage-transition data.
- Does not extend the map beyond Fin 8.
- Does not assert dynamical evolution of stages.
- Does not claim the reversal applies to non-Erikson sequences.