Active research index.

The complete active publication shelf supplied by the author. The relationship Atlas remains selective: a title can belong here without earning an edge there.

Catalog rule: records in this master list are active. Restricted records and other records still served by Zenodo are deprecated or historical and are not promoted as current work.

Rational grids & geometry 11

July 19, 2026 · v2 · Preprint

Triangular Addressing, Null Coordinates, and Reciprocal-Metallic Locks in a Scale-Covariant Plane Geometry

July 19, 2026 · v5 · Peer review

Divisor-Band Bijections and Totient Shells in the Triangular-Fractional Grid

July 9, 2026 · v2 · Working paper

The Polar Shell Renderer: Equal-Area Denominator Shells for Reduced Fractions and Primitive Roots of Unity

July 5, 2026 · v1 · Preprint

The Hexagonal Coil: An Eisenstein Sibling of the Triangular--Fractional Grid, and Why the Better Tiling Does Not Win

July 5, 2026 · v5 · Preprint

Prime Numerators of the Triangular-Fractional Grid: A shell stratification and a lens for prime-in-progression density

July 4, 2026 · v4 · Preprint

The Prime-Numerator Distribution of the Triangular-Fractional Grid: A supplement on divisor-driven prime structure and a Ulam-family comparison

July 4, 2026 · v4 · Preprint

A Radial Coordinatization of the Triangular-Fractional Grid: Integer Boundaries, a Phase-Pole Center, and a Tiling–Phase Obstruction

June 19, 2026 · v7 · Peer review

Volume I: Exact Geometry and Symbolic Foundations

June 17, 2026 · v4 · Peer review

Scalarstack Geometry in a 45◦ Cone: Exact Cone/Sphere Operators, Rational Void, Silver Gears, and a Heuristic Near-7/8 Note

June 7, 2026 · v2 · Peer review

Alternating Interstitial Geometry of Ball–Cube Recursions: A Bridge Note from Jordan Chambers to Boundary-Conditioned Bodies

March 17, 2026 · v1 · Peer review

Scalarstack Geometry in a 45◦ Cone: Rational Void, Silver Gears, Concentric Compression, and a Near 7/8 Resonance

Open-problem chamber lifts 15

June 20, 2026 · v2 · Peer review

The Prime-Square Chamber Lift: Short-Interval Occupancy via Quadratic Boundary Windows

June 20, 2026 · v2 · Peer review

The Lehmer Totient Chamber Lift: Product Totient Gates via Korselt Supports

June 11, 2026 · v2 · Peer review

The Exponent Chamber Lift: Beal, Reciprocal Shells, and the First Hyperbolic Shadow

June 11, 2026 · v1 · Peer review

The Radical Chamber Lift: abc, Valuation Excess, and Additive Closure

June 11, 2026 · v1 · Peer review

The Zeta-Exponent Chamber Lift: Dimensional Visibility, Jordan Shadows, and Valuation Mirrors

June 11, 2026 · v1 · Peer review

The Goldbach Chamber Lift: Midpoint Prime Occupancy via Symmetric Residue Gates

June 11, 2026 · v1 · Peer review

The Twin Prime Chamber Lift: Residue-Pair Survival via Two-Point Sieve Gates

June 11, 2026 · v1 · Peer review

The Primitive Ray Chamber Lift: Lattice Visibility via Tolled Conformal Scale

June 9, 2026 · v1 · Peer review

N^2+1 Chamber Lift: Quadratic Residue Sieve for Landau's Problem

June 9, 2026 · v1 · Peer review

The Odd Perfect Number Chamber Lift: Abundancy Balance via Euler Prime Form

June 9, 2026 · v1 · Peer review

The Erdős–Straus Chamber Lift: Reciprocal Defect Routing via Completing-the-Rectangle Divisor Gates

June 9, 2026 · v1 · Peer review

The Congruent Number Chamber Lift: Rational Triangle Areas via Tunnell Lattice Counts

June 9, 2026 · v1 · Peer review

The Collatz Chamber Lift: Parity-Vector Descent via Affine Residue Geometry

June 7, 2026 · v4 · Peer review

The Jordan Chamber Lift: Higher-Dimensional Denominator Shells via the GCD Collapse

June 7, 2026 · v2 · Peer review

Divisor-Filtered Farey Chambers and Localized Discrepancy

Analytic diagnostics 7

June 25, 2026 · v2 · Peer review

Transient Phase Atlas: Short-Orbit Modular Fingerprints of Constants

June 11, 2026 · v1 · Peer review

One Euler Product, Many Coordinates: Bernoulli, Sine, Zeta Continuation, and Radial Layer-Counting as Shared Analytic Infrastructure

June 5, 2026 · v1 · Peer review

Annular Shell Isolation Near Zeta Zeros

May 23, 2026 · v4 · Peer review

A Finite-Count Search for a Morphology-Structured Projection Ridge Near 2.75 in Riemann-Zero Gap Coordinates

May 4, 2026 · v20 · Peer review

Terminal Altitude Architecture and Post-Selection Artifacts in Adjacent Zeta-Zero Spacing

May 4, 2026 · v5 · Peer review

A Search-Adjusted Audit of Row-Sector Modulus Signals in Terminal Zeta-Zero Spacing Residuals

March 18, 2026 · v1 · Preprint

Transient Rational Locking in Modular Logarithmic Orbits

Meaning, memory & reconstruction 12

July 9, 2026 · v4 · Preprint

The Phase-Change Ledger: Why a Finite Observer Must Melt Memory to Keep Reading

June 29, 2026 · v3 · Peer review

One Ledger, and the Withholding of the Second: Count, Order, and Why a Black Hole Is Black: a staging of established results at the extreme

June 28, 2026 · v4 · Working paper

The Ledger: Records, Seals, Winding, and the Cost of Recovery

June 24, 2026 · v2 · Working paper

Moments of Memory: An address is not the past

June 24, 2026 · v2 · Working paper

The Price of Construction: Cancer, entropy, and the cost of carrying convention

June 24, 2026 · v2 · Working paper

The Cost of Surprise: Entropy, recognition memory, and the loop that neither side controls

June 22, 2026 · v2 · Working paper

The Line Game | Surprise Is Not Meaning

June 22, 2026 · v1 · Working paper

The Sense of Things: A working paper on the senses through which structure is read, and the discipline of not mistaking the reading for the knowing

June 20, 2026 · v2 · Peer review

Addresses Are Not Meanings: A Dialogue on One Structure, Three Vocabularies, and the Discipline of Comprehension

June 14, 2026 · v2 · Peer review

The Toll, the Rule, and the Iota: A compression of one night's thinking on memory, transmission, and meaning

June 14, 2026 · v3 · Peer review

Two Readings, One Construction: A short map to a three-paper set, and where the readings meet

June 13, 2026 · v8 · Peer review

A Message Hidden as an Address: Where a Theorem Recovers a Number, and Only You Recover the Letter: A hand-computable demonstration, built to be climbed

Measurement & physical systems 4

July 19, 2026 · v4 · Preprint

From Measure to Flux: Energy-Conjugate Bookkeeping and Exact Semidiscrete Scattering in Finite Radial Wave Models

June 29, 2026 · v2 · Working paper

Vortex Stretching and the Edge of Blow-Up: The engine that concentrates a spin, the brakes that might hold it back, and what is actually proven

June 17, 2026 · v2 · Preprint

Kitchen-Scale Breath Figures and Coalescence Events: Preliminary Measured Outputs from a Phone-Camera Condensation Run

June 12, 2026 · v1 · Peer review

Ledger-Preserving Forms of Explicit Formulae: Typed Bookkeeping and Instrument Calibration

Methods & bridges 2

June 11, 2026 · v2 · Peer review

Tolled Dilation Scale and Lattice Visibility: A Discrete Atlas for Primitive Rays, Logarithmic Obstruction Cost, and Square-Free Mirrors

March 18, 2026 · v2 · Preprint

Part II: Taxonomy and Structural Symmetries of Transient Rational Locking