Ordered Mantissa Correspondences in the Theta Matrix

This exploratory preprint studies ordered numerical correspondences between mantissas generated by the logarithmic Theta matrix and reference values associated with physical constants, an astronomical scale and particle masses. The construction uses A(i,j) = k_B ln(i/j), examined on a 127 × 137 domain and at the refined denominator 137.03566. Here, “mantissa” means the normalized base-10 significand of the absolute value; numerical correspondences depend on the chosen units. The analysis compares fixed-row, free-row and ordered consecutive-block searches. Free-row matches are not unique to column 137: 91 integer columns admit seven distinct-row matches within 2%. In the ordered-block comparison, rows 122–127 at the terminal denominator rank first in each of the two tested grids. Each grid contains 16,714 candidate blocks, and only the best block matches all five defined references within 1%. The sixth position has no unambiguous reference and is excluded from scoring. These findings concern a retrospectively selected catalogue and ordering. They do not establish a chance probability, uniqueness outside the tested domains, or a derivation of physical constants. The manuscript also examines particle-mass mantissas in the eV/K chart and describes the Theta entropic-clock and crystallization interpretation, explicitly separating reproducible arithmetic results from conditional theoretical assumptions. Refining the denominator improves six of twelve particle associations and worsens six; the mean error does not improve overall. The supplement includes original Excel workbooks, CSV matrices, JSON results and standalone Python replay code. Original workbook labels are retained, with an English glossary. Version 0.1, exploratory preprint; not independently peer reviewed. AI assistance in editorial preparation and computational checks is disclosed. Text and documentation: CC BY-NC 4.0. Code: separate noncommercial terms specified in LICENSES.md. Commercial-use permission requests: [email protected].