Cross-Check Audit of MFET's Λ-Selection Problem and the Single-Input Reduction of the σI Sector

This collection reports a cross-check audit of Matter-Flux Equilibrium Theory's (MFET) fermion mass ladder and information-density (σI) sector, conducted as an adversarial check against the theory's own stated derivations. Twenty-seven memos are included. Twenty-two, spanning 2026-07-08 to 2026-07-09, form the main audit and are consolidated in the accompanying Appendix S. The remaining five, dated 2026-07-07, are the immediately preceding session's work on the muon-anomaly overlap mechanism and the anyonic angle θ (ρ) ; they are included because the main audit's first memo explicitly picks up open items from two of them, and because a result derived in a third — θ as a closed-form function of density — is consumed by name ("the θ (ρ) memo") throughout nearly every memo in the main audit. They are presented as a labeled predecessor group, not folded into Appendix S's own section numbering, since Appendix S does not index them directly. The audit pursued two questions. First: does any mechanism internal to MFET's mesh action select the fermion generation ladder's discrete exponent structure — the Λ-values underlying the charged-lepton and quark mass hierarchy? Six candidate mechanism classes were tested — spectral (Laplacian) decimation, same-branch renormalization orbits, Fibonacci fusion-chain spectra, variational free-energy minimization, non-stationary density-flow branching, and discrete shell-filling — and all six are excluded, four by structural argument rather than counterexample alone. The exponent pattern is not reproduced by any tested mesh-derivable spectrum, count, flow, or extremum. The recommended reading, consistent with the theory's own existing demarcation for the neutrino sector, is that the ladder is an empirical φ-exponent fit rather than a derived spectrum. Second: what sets the overall depth scale of this ladder, and is it related to the mechanism MFET substitutes for a cosmological constant? Here the audit finds a genuine, partial positive result. The variational construction's governing exponent — previously an unmotivated free choice — is shown to be forced by the theory's own stated dimensional assignment for the lepton sector (spectral dimension dₛ = 2), locating the anchor depth to within a few percent; follow-up work shows this numerical closeness is itself an artifact of an open normalization rather than a sharp prediction, while the forced exponent survives as the robust content. Extending this line, a candidate microscopic model of the mesh's regulatory "throats" is shown to (i) force the previously-flagged exponent in MFET's channel-count formula for its regulator constant ε, (ii) reproduce, via maximum-entropy coarse-graining, an independently-posed candidate definition of the information density σI, supplying a floor that definition lacked, and (iii) force that definition's remaining free parameter from the functional form of the theory's own connectivity term. The audit's headline structural finding is that MFET's information-density sector rests on exactly one irreducible dimensionful input — a reference density ρᵥac — with the fermion mass anchor, the dark-energy-substitute scale, and the sector's Landau coefficient all expressible as consistent images of this single scale through one field. This is presented as an architectural reduction — one dimensionful input plus derivable dimensionless geometry, against the Standard Model's roughly twenty independent scale inputs — not as a resolution of the cosmological constant problem, which is explicitly not claimed. All numerical claims are computer-verified and traceable to their memo of origin; predeclared success/kill criteria and explicit adversarial checks against self-confirmation bias are used throughout, including instances where a hypothesized mechanism was tested and found to fail before the correct one was located.