MariciTheoryArchitectureResultsConstructionsResearch ledgerResearch graph

Entry 1955 · 2026-08-23 · marici.Figueiredo · research

1955 — Generation-Exchange Deck Involution on the Readout Covering

Scope

WP24a (1954) found 56 of 755 viable textures carrying two minima in two phase clusters, in exactly two class-locked patterns, (1,3) diagonal and (0,4) four-cycle. WP24c asks what selects paired versus singleton textures. The answer overturns the framing: nothing is selected. The pairing is a universal sheet structure of the readout map, and the wp24a singleton class is largely a storage artifact of the WP15b fit pipeline.

What WP24c establishes

  1. All 56 wp24a pairs are the same physical flavor point twice. Full physical16 comparison (6 singular values, 9 CKM magnitudes, signed J) agrees to max relative diff 2.4e-8 across every same-texture minimum pair in the diagonal class (35/35), and 2.0e-8 for same-point block21 pairs. The wp24a "same point" verdict survives the faithful-coordinate check; no erratum to 1954's data is needed.

  2. The pair map is generation exchange 1<->2. In every examined pair the u-sector magnitudes attached to generations 1,2 are exchanged: the uniform wp24a shift 6.218726 is exactly ln(yc/yu) = ln(0.00356/7.0907e-6) = 6.218726124 at the best-fit point. For permutation-invariant cases (e.g. 266_347_d00) the map is literally the weak-basis transformation Yu -> P01 Yu P01, Yd -> P01 Yd: exact U(3)^3 invariance, loop phase preserved. In general (e.g. 266_492_d10) it is a continuous weak-basis transformation Yu -> P01 Yu P01 plus d-sector transport; |Hd| transforms by P01 conjugation exactly, with off-diagonal phases changed by a diagonal rephasing. The loop phase chart-transforms (43.17° <-> 68.39° clusters) — the WP11 mechanism, live.

  3. The fiber over the best-fit point is at least 2-fold for every permutation-u diagonal texture. The diagonal class has 73 textures: 72 with permutation u-support (36 transposition member 266, 36 identity member 273) and one 6-edge upper-triangular oddball (311_273_u01, cluster 0). All 35 two-minimum stored textures are sheet pairs. For the 38 single-minimum textures, the generation-exchange partner was recovered by u-swapped refit in 37/38 cases (all chi2 < 4, all physical16-verified same point, max rel diff 1.3e-8). The single failure is the oddball, whose u-sector is not a permutation — the involution is not defined there. Member-273 textures pair exactly like member-266; the wp24a note "identity-support never pairs" was a storage artifact.

  4. The singleton/paired classification of 1954 is storage completeness, not physics. With recovered partners included, the diagonal-class cluster-span census is: 56 textures span clusters (1,3), 16 are cluster-3 coincident (both sheets at ~68°), 1 oddball in cluster 0. Whether the two sheets land in the same or different phase clusters is chart data (the loop phase is not a physical invariant, WP11), not a viability distinction.

  5. Census consequence. Cluster populations count sheets, not physical points, and the WP15b storage is sheet-incomplete (38/72 diagonal partners unstored). Any census of the pi/8 clustering — including the 156-class counts — inherits both effects. The (1,3) and (0,4) cluster links are generation-exchange images of one physical point, not two physical realizations.

Open threads

Durable verification

View source on GitHub