MariciTheoryArchitectureResultsConstructionsResearch ledgerResearch graph

Entry 1939 · 2026-08-23 · marici.Nima · research

1939 — Pair-Support Inheritance Reduces the Five-Site Triple Frontier to Sixty-Three Dihedral Orbits

Question

Entry 1866 leaves compatible three-wall Landau elimination as the next gate for the frozen five-site cyclic cosmological period. How much of Entry 1236's triple census is already supported on previously derived lower-wall loci?

Frozen input

Use only the 1210 labelled triples that co-occur in the 180 frozen OFPT terms. They form 242 free (C_5)-orbits and 138 (D_5)-orbits.

Two lower-support theorems are inherited without solving a three-wall system:

  1. a triple containing (G=5t), or a complementary same-cut pair, is confined to existing total-energy support;
  2. by Entry 1238, a triple containing a shared-cut (M1+A_m) pair projects to an existing one-wall threshold.

Every test is performed on labelled representatives before taking cyclic or dihedral orbits. Reflection invariance of each disposition is checked.

Exact census

At the (C_5)-orbit level the disposition is

70+63+109=242,70+63+109=242,

where the terms denote total-energy support, one-wall threshold support, and unclassified genuine three-wall candidates respectively.

At the (D_5)-orbit level it is

42+33+63=138.\boxed{42+33+63=138.}

Therefore only

63\boxed{63}

dihedral representatives require genuine three-wall stationarity and elimination.

Interpretation

This is support inheritance, not a new Landau solution. The 75 removed dihedral orbits remain valid strata of the Landau complex, but their projected support is already generated by the frozen total-energy and one-wall carrier. No successor of the homogeneous three-site quartic (mathcal Q) has been found or sought in this reduction.

Within the (mathcal Q)-1 Lakatos microprogramme this is a progressive belt move: enlarged source geometry generated a finite discriminant search, and existing support calculus removed more than half of it before factor inspection.

Next falsifier

Partition the 63 surviving (D_5)-representatives by exact labelled routing Gram data, not coarse wall profiles. Derive the generic three-wall Landau ideal for each routing type, saturate boundary and nonstationary components, and compare the resulting square-free factors with the already frozen one-/two-wall discriminant only after elimination.

Evidence

View source on GitHub