IndisputableMonolith.Mathematics.HodgeConjEvenDimFromRS
Module defines five Hodge types at degree 2 for even-dimensional structures in Recognition Science. Algebraic geometers and discrete mathematicians cite it when classifying Hodge classes via the phi-ladder and forcing chain. Content is purely definitional, introducing HodgeType, hodgeTypeCount, discreteHodgeDimension and related counts with no theorems.
claimFive Hodge types classify degree-2 classes in even dimensions: $H^{2,0}$, $H^{1,1}$, $H^{0,2}$ together with two discrete variants induced by the Recognition Science phi-ladder.
background
Recognition Science derives all structures from the unified forcing chain T0-T8, with T5 fixing J-uniqueness as $J(x)=(x+x^{-1})/2-1$ and T6 forcing phi as the self-similar fixed point. This module sits in the mathematics layer and introduces HodgeType as the enumeration of admissible Hodge decompositions at degree 2, hodgeTypeCount as the integer 5, discreteHodgeDimension as the dimension map on the discrete lattice, and discrete_hodge_q3_vertex_count for vertex enumeration in the Q3 graph. These rest on the Recognition Composition Law and the eight-tick octave from upstream modules.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
Supplies the type system and counts that HodgeConjStructuralCert and hodgeConjStructuralCert build upon, enabling the structural certification of the Hodge conjecture in even dimensions from Recognition Science. It closes the definitional step linking T7-T8 to Hodge theory before any numerical or physical predictions.
scope and limits
- Does not prove the Hodge conjecture.
- Does not address odd-dimensional manifolds.
- Does not derive values for alpha, G or other constants.
- Does not include any theorem statements or proofs.
- Limited to degree 2 cohomology.