IndisputableMonolith.Physics.PMNS.Construction
The PMNS.Construction module states an open conjecture that a unitary 3x3 matrix exists whose entry magnitudes equal the Recognition Science weights W_ij = phi^(-Delta tau_ij). Neutrino physicists exploring the framework's mixing sector would cite it as an unresolved question. The module imports only the Types definitions and contains no completed proofs or derivations.
claimThere exists a unitary matrix $U$ such that $|U_{ij}| = W_{ij}$ where the weights satisfy $W_{ij} = exp(-Delta tau_{ij} * J_bit) = phi^{-Delta tau_{ij}}$ following the Born rule on ladder steps.
background
The module resides in the Physics domain and imports IndisputableMonolith.Physics.PMNS.Types. That upstream module defines the PMNS mixing weights via the Born rule over the ladder steps: Weight W_ij = exp(-Delta tau_ij * J_bit) = phi^{-Delta tau_ij}. The local theoretical setting is the attempt to realize these magnitudes inside a unitary matrix inside the Recognition Science phi-ladder construction of mixing.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module states an open conjecture on PMNS unitarity but feeds no parent theorems (zero used_by edges). The supplied doc-comment explicitly isolates it from the hard-falsifiable angle and mass-splitting claims in IndisputableMonolith.Physics.MixingDerivation, marking it as exploratory rather than part of the T0-T8 forcing chain or RCL derivations.
scope and limits
- Does not prove existence of the unitary matrix.
- Does not derive numerical mixing angles or mass splittings.
- Does not supply any theorem used by MixingDerivation.
- Does not connect the weights to the eight-tick octave or D=3.