[yonghakim]

Independent layer permittivity inputs at the complex-angle knife edge in #21 can still give order-one errors after the shared-material fixes. For a homogeneous nonmagnetic region stack, this change keeps each independent material and uses rationalized Fresnel interfaces, a two-face recursion, and compensated normal-root residuals. Reflection, transmission, field reconstruction and both SMM ports come from the same calculation. ETM and SMM use this direct homogeneous path under material transformations; concrete eager solves retain their existing path.

The same work fixes a Torch material-response narrowing: a Python wavelength must not cast a float64 material through complex64 and overflow its otherwise finite cotangent.

Validation:

• New 120-digit ordinary-Fresnel references cover equal and adjacent float64 permittivities, separated values, both polarizations/sides, R/T, pointwise fields and their independent material tangents. Reference generation imports no solver code; CI needs no mpmath dependency.
• The unmodified base fails 11 of the 19 new stack tests; its eight ordinary multilayer controls pass.
• Selected solver regressions: 324 passed and one existing xfail across the uniform-interface, half-space merge, evanescent incidence, compiled field and public lifecycle tests; two subsequently added answer-contract tests passed separately (326 passed total). All 21 new stack tests pass.
• Material regressions: 97 passed, including three new precision tests. Docs: 165 passed and one existing skip; quick profile: 17 passed; Ruff and diff checks pass.
• The numerical candidate 7fff018 preserves all 1,952 recorded eager entries byte-for-byte, with four existing refusals, against the previously recorded PR97 tree (identical to this PR's base). No claim to rerun that baseline corpus or the historical research-tier discrepancies.
• Self-review complete; no outstanding review threads. No tolerances or reference values were changed to make failures pass. An exact layer-cutoff probe remains NaN on both candidate and unmodified base; this inherited limit is not claimed fixed.

Scope: second-order, single-plane-wave, scalar nonmagnetic region stacks with no shapes. Patterned/raster, magnetic/tensor, first-order and coherent-source cases retain their existing limits. Physical poles, cutoffs and values beyond floating-point range are not resolved generally. This partially addresses #21 and does not close it. No release changes.

CI follow-up: the first Ready run failed the license inventory step and installed-distribution checks. Failure annotations identified an unreviewed installed tzdata 2026.5 package, also confirmed in the macOS installed check. The base inventory reproduces the same missing-entry error. The official wheel METADATA and Apache-2.0 license files were reviewed and recorded with the wheel hash; no dependency requirement or license policy was weakened. License/doc tests: 194 passed, one existing skip. Replacement required CI passed.

Ports: 72c5266ff4f21a6104d413550593f230b6755328

Full CI then exposed a Torch wavelength-derivative regression in the new homogeneous path: constant Python-scalar exterior materials reached tensor-only real/imag operations. The existing test reproduces the failure on bd237a6 and passes on the unmodified base. Commit7fff0185 promotes those constants through the root array without detaching the graph; the unchanged existing test now passes. Related material/uniform tests passed76, including all21 uniform cases. The exact7fff0185 eager corpus remains byte-identical for all1,952 entries with four existing refusals. Replacement full CI39717299468 passed all eight required gates (52 successful jobs, one existing diagnostic-only skip).

Integrated by Rebase and merge as ca5d27750a88810efe9329aee62794795241ffb3, tree-identical to the reviewed candidate. Exact-main tests39718968235 and CodeQL39718967784 succeeded. No release was made.