Certified answers from imperfect experiments
Query Geometry follows uncertainty through to the answer itself: three passing real-query degree-eleven contracts, fourfold spatial calibration area, and an exact attained ambiguity threshold.
Research · Mathematics
Operational Geometry & Arithmetic
The current home for operational geometry, arithmetic observability, reproducible experiments and clearly bounded interpretations. Formerly Number Geometry.
Global Geometry · How Local Rules Make Worlds
A reproducible Global Geometry article and browser laboratory, now extended by a content-addressed Global Geometry II evaluation checkpoint whose U2 status remains unresolved.
Read Global Geometry Explore the Lab
Evaluation checkpoint: Global Geometry II · U2 UNRESOLVED · exact cross-host replication FAIL · authority NONE
Operational Information Geometry — From Response Limits to Certified Experiments
A resolution-aware theory and executable certificate engine that selects measurements for a declared query, removes exact nuisance directions, preserves structured uncertainty, and proves what information survives finite approximation.
Double-Pendulum OIG Wind Tunnel · Ensemble Calibration Chamber
A dependency-free browser laboratory that freezes an Operational Information Geometry forecast before independently integrating held-out double-pendulum outcomes, finite ensembles, and background calibration studies.
Arithmetic Observability Atlas
A ten-manuscript theory of when incomplete global harmonic measurements determine local arithmetic structure, when they cannot, how stable recovery can be, and what geometry the measurements impose.
The Geometry Arithmetic Remembers
What remains of numerical geometry after coordinate artifacts are removed? Exact rigidity theorems, adelic harmonic analysis, finite reconstruction, spectral models, and a class-group obstruction reveal a layered answer.
Order–Factorization Geometry
The earlier bounded exploration of ordered-monoid rigidity, finite logarithmic constraints and a conditional spectral hypothesis.
Arithmetic Sensing: Recovering Number Patterns—and Knowing the Limits
A rigorous sensing theory for recovering finite arithmetic data from global Dirichlet traces—complete with deterministic tail certificates, noise bounds, sampling aliases, and explicit cases where recovery is impossible.
Arithmetic Sensing III — Optimized Quadrature and Unavoidable Aliases
A technical continuation that designs positive cosine-series quadratures for logarithmic arithmetic frequencies while proving that fixed midpoint grids retain exact unit-magnitude aliases.
Arithmetic Sensing IV — Continuum Positivity, Alias-Band Tails, and Local Information
A technical continuation that strengthens optimized arithmetic sensing with continuum positivity, alias-by-alias divisor tails, fixed-degree bounds and a mathematically explicit local channel beyond Dedekind zeta data.
Arithmetic Sensing V — From Log-Mellin Certificates to a Finite Multiscale Stopping Theorem
Arithmetic Sensing V consolidates the log-Mellin certificate, cancellation correction, degree-fourteen resource law, nested multiscale design, and finite target-50 residual stopping theorem into one reproducible publication.
Operational Information Geometry V — Scale Flow, Continuum Response, and Protocol Boundaries
Operational Information Geometry V studies which features of a finite directed response survive refinement and which depend on preparation, regularity, sensor protocol, or order of limits.
Operational Information Geometry VIII — The Uniform Three-Parameter Atlas
Operational Information Geometry VIII replaces an iterated continuum picture with a uniform three-parameter atlas for resolved smooth, finite-cell lattice, atomic-tail, and reflecting-boundary response charts.