FIRST-HIT STOPPING AND BIAS-CORRECTED SCORE INFERENCE IN DIMENSION THREE
Scott Schubr | Luminary Oddities | October 20, 2026

The paper proves a corrected same-sample score limit at the actual first
residual hit of the symmetric self-transport iteration in dimension three.
Formal Gaussian range: 2/17 < kappa < 4/9, with 0 < gamma < 3/4.
Consistent estimation and shrinking uncertainty: 2/17 < kappa < 2/5.
The strict upper 4/9 endpoint is sufficient; its necessity is not asserted.
The lower 2/17 obstruction applies to the stated two-scale estimator.
Residual constants 1/2 and 1 are sharp in the stated subsequential sense.

Contents
  First_Hit_and_Corrected_Score_Dimension_Three_v2_1.pdf: complete paper
  manuscript/*.tex: complete editable source
  code/build_pdf.py: portable local build helper
  CITATION.bib: citation metadata
  MANIFEST.sha256: SHA-256 checksums of the files listed above

Rebuild
Requires Python 3.9+ and Tectonic with its LaTeX resources installed.
  python code/build_pdf.py --output-dir ../dimension-three-build
The output directory must be new. If needed pass --tectonic PATH_TO_TECTONIC.
For offline builds add --only-cached and optionally --cache-dir CACHE_PATH.
Build products and compiler logs are written outside these source files.

The analytic results assume a fixed positive C8 probability density on
the unit three-dimensional torus, a fixed spatial query, the exact periodic
heat kernel and shared observations at both scales. The sharp-clock theorem
states its separate bandwidth hypotheses. This is one consolidated paper
following the cited one- and two-dimensional residual-stopping analysis.
