developmentReversalCert
The definition constructs a certificate verifying that Erikson's eight life stages form a 2^3 cycle equipped with an involutive reversal map on Fin 8. Cognitive scientists modeling age-related cognitive decline would reference this certificate when formalizing the predicted reverse-order progression of dementia symptoms. It is constructed by directly assigning the fields of the DevelopmentReversalCert structure to the corresponding pre-established lemmas on stage cardinality, involution, and endpoint swapping.
claimThe structure asserts that the set of Erikson stages has cardinality 8 (equivalently $2^3$), that the reversal map $r$ on Fin 8 satisfies $r(r(k))=k$ for all $k$, that $r$ maps the initial stage to the final stage, and that the reversal of the generativity stage precedes the reversal of the trust stage in the ordering.
background
In the CrossDomain.DevelopmentReversal module the reversal map is defined by $r(k)=7-k$ on Fin 8. The DevelopmentReversalCert structure packages five properties: stage cardinality equals 8, equals $2^3$, the map is an involution, it swaps the endpoints 0 and 7, and the midlife inversion occurs before the initial-stage inversion. This formalizes the claim that neurodegeneration traverses the Erikson ladder in reverse order, with mid-life stages inverting before early ones, as part of the eight-tick octave structure.
proof idea
The definition is a one-line wrapper that populates the DevelopmentReversalCert structure by assigning stage_count to eriksonCount, two_cube to erikson_eq_2cube, involution to reverse_involution, endpoints_swap to the first component of reverse_swaps_endpoints, and midlife_first to midlife_inverts_first.
why it matters in Recognition Science
This definition supplies the concrete certificate for the C6 development reversal claim, which posits that the eight Erikson stages form a 2^3 tick cycle with an order-reversing involution modeling the reverse progression in neurodegeneration. It draws on the eight-tick octave landmark from the forcing chain. Although no downstream uses are recorded, the certificate closes the structural part of the wave-62 claim in the cross-domain development section.
scope and limits
- Does not derive the reversal map from the J-cost or Recognition Composition Law.
- Does not establish empirical validity of the dementia progression predictions.
- Does not connect to the phi-ladder or mass formulas in the core framework.
- Does not address clinical data or falsification criteria for the model.
formal statement (Lean)
67def developmentReversalCert : DevelopmentReversalCert where
68 stage_count := eriksonCount
proof body
Definition body.
69 two_cube := erikson_eq_2cube
70 involution := reverse_involution
71 endpoints_swap := reverse_swaps_endpoints.1
72 midlife_first := midlife_inverts_first
73
74end IndisputableMonolith.CrossDomain.DevelopmentReversal