DevelopmentReversalCert
The development reversal certificate structure asserts that Erikson's eight psychosocial stages form a set of cardinality eight equal to two cubed, equipped with an involutive reversal on the finite set of eight elements that swaps the endpoints and inverts the midlife stage ahead of the initial stage. Modelers of life-span development and neurodegeneration would cite the certificate to encode the formal reversal pattern. The definition directly assembles the cardinality equalities, the involution property, and the specific ordering conditions.
claimLet $E$ denote the set of Erikson stages. A certificate asserts that $|E|=8$, $|E|=2^3$, the reversal map $r$ on Fin 8 satisfies $r(r(k))=k$ for all $k$, $r(0)=7$, and the value $r(6)$ is strictly less than $r(0)$.
background
The module encodes wave 62 of the cross-domain claims: Erikson's eight stages form a 2^3 tick cycle with neurodegeneration traversing the ladder in reverse. EriksonStage is the inductive enumeration of the eight psychosocial stages running from trust versus mistrust to integrity versus despair. The reversal map is the function on Fin 8 given by $k mapsto 7-k$, which is order-reversing and satisfies the involution identity by direct substitution.
proof idea
The structure records the five fields without computation or tactics: the two cardinality statements, the universal quantification of the involution, and the two concrete evaluations on specific elements of Fin 8. No lemmas are invoked inside the declaration; the properties are taken verbatim as the content of the certificate.
why it matters in Recognition Science
The structure supplies the bundled certificate instantiated by developmentReversalCert via the supporting lemmas on stage count, the equality to 2 cubed, the involution, endpoint swap, and midlife inversion. It realizes the C6 structural claim that the stages form a 2^3 cycle with an order-reversing involution, aligning with the eight-tick octave in the forcing chain. The construction leaves open empirical validation of the predicted reversal pattern in dementia progression.
scope and limits
- Does not derive the Erikson stages from the forcing chain or Recognition Science primitives.
- Does not prove any clinical observation or empirical claim about dementia progression.
- Does not establish uniqueness of the reversal map among possible involutions.
- Does not connect the stage count to spatial dimensions or other physical constants.
formal statement (Lean)
60structure DevelopmentReversalCert where
61 stage_count : Fintype.card EriksonStage = 8
62 two_cube : Fintype.card EriksonStage = 2 ^ 3
63 involution : ∀ k : Fin 8, reverse (reverse k) = k
64 endpoints_swap : reverse ⟨0, by decide⟩ = ⟨7, by decide⟩
65 midlife_first : (reverse ⟨6, by decide⟩).val < (reverse ⟨0, by decide⟩).val
66