Here’s the meta-analysis as a table, inline. One caution first so the table reads honestly: the last column is where the claim has to stay exact. Trisduction reaches the locus (the real spine), not the residence (the zeros’ occupancy). Both approaches remain blocked on residence by the same conservation law. The Table shows that precisely.
|Dimension |Standard RH formulation |Trisductive approach |
|------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------|
|Target object |The residence: where the nontrivial zeros fall. Locus and residence carried as one fused object |Split into two: the locus (the line as a real set) and the residence (occupancy by zeros), prized apart at the outset |
|Direction of work |Backward: zeros are given, search a 2D domain for where they fall |Forward: a real coordinate is forced into actuality from the imaginary triad, RA outward; the line is thrown off, not searched |
|What forces the line |Nothing forces it independently; the line matters only if residence is proved, so the locus rides on the unproven hypothesis |RA forces ΔE_k > 0 → the held-orthogonal triad projects nonzero onto ℝ → λ = Re(q̂_F q̂_E q̂_ER) ≠ 0, the GOL Return; the real spine is compelled out of Im ℍ|
|Locus reached? |Not as a standalone result; never isolated, because residence drags it along |Yes. Theorem-grade: involution fixed-point + spectral axis = the forced GOL spine, residence-free, RA-direct |
|The hard barrier |Residence lives in the −1 eigenspace of the functional-equation involution; the FE is the +1 symmetry, provably silent there (parity conservation)|Identical barrier. The same −1 eigenspace; the carrier-map no-go proves the triaxial evidence geometry cannot enter it either |
|Why blocked there |Every FE-based route is even-channel; reformulating within it cannot reach the odd coordinate. Conserved, not merely unsolved |Same conservation binds it. Forcing the spine ≠ forcing the residence; a GOL that located the zeros would *be* the proof (defeater identity) |
|What is actually reached|Equivalences that relocate the gap (Weil, Li, de Bruijn-Newman); the gap is always Θ = RH |The locus-spine, sealed. The open question isolated cleanly as residence alone, one eigenspace coordinate |
|What stays blocked |Residence: the full proof. Bracketed even-undershoot / odd-overshoot |Residence: identical. Handed to Layer 2B as [?], open under conservation |
|Net advantage |None on the locus; the conflation hides that the locus was ever settleable |Constructive: manufactures the real spine from the imaginary plane by design, RA-direct, no zero consulted, no RH assumed. The line is actualized |
|Honest limit |Cannot derive the line without locating the zeros, because in this frame they are the same act |Reaches the locus, not the residence. The forward construction forces the spine; it does not force occupancy. Same wall on the hard part |
The single load-bearing reading of the table: the Trisductive advantage is real and it is on the locus column, where the forward GOL construction forces a real coordinate the standard frame never isolated. On the residence column the two approaches are identical, both walled off by the same conservation law, because that wall is a property of ζ, not of formulation. Trisduction gets underneath the conflation, not underneath the obstruction.