The research catalogue.

Triangular n Postmaster: From the Discrete Primitive to the Completed Source Frontier

The current Reading Volume follows the triangular primitive through the completed zeta source, the Widder ladder and the remaining all-order source estimate. The volume explicitly keeps RH open.

Attached document: Reading Volume v4.2. The repository record is labelled v32; these are separate version numbers.

Triangular n Postmaster Research Volume I v0.5: Definitive Master Union

An earlier Postmaster synthesis preserving source layers, arithmetic gates and an audited research ledger. Read for the development trail; use v4.2 for the current reading route and status table.

Triangular n Master Volume

A master-volume stage joining counting and spectral constructions with reciprocal coordinates and finite-resource comparisons. It separates exact bridges from unproved positivity targets.

Counting, Positive Degree, Reciprocal Uniformization, and Mellin-Fourier Reflection of a Spherical Casimir Spectrum

A spherical Casimir construction linking positive degree, reflection, determinants and Mellin-Fourier coordinates. Its operator and comparison models are not identified with the completed zeta source.

Two-Term Asymptotics for the Total Variation of Exponentially Weighted Laguerre Polynomials

Two-term asymptotics for the total variation of exponentially weighted Laguerre polynomials, with a Bessel-profile leading constant and a stated correction.

One Reflection, Two Renderings: The Terminal Fold in the Pair Plane and on Reduced Polar Shells

One terminal reflection is expressed in the arithmetic pair plane and in reduced polar shells. The paper distinguishes that shared reflection from an obstructed geometry-preserving whitening transfer.

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

A reading guide to vortex stretching, concentration and the distinction between the engine of amplification and the mechanisms that may restrain it.

Also indexed: the other supplied record with this title. No unverified DOI version relation is asserted.

Vorticity-Aligned Stretching in Null Coordinates: A Cauchy--Euler Hyperbolic Normal Form

A null-coordinate description of vorticity-aligned stretching built from the Cauchy vorticity formula. It is a bounded reduction, not an Euler closure or a blow-up criterion.

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

Triangular addresses, null coordinates and reciprocal-metallic locks in a scale-covariant plane construction. Address inheritance is distinct from a shared theorem.

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

Finite radial-wave bookkeeping, exact semidiscrete scattering and configuration-bound numerical checks. Exact identities and empirical certificates are kept separate.

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

The arithmetic foundation: divisor-band bijections, reduced-denominator shell counts and the triangular-fractional grid.

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

Reduced fractions placed at radius sqrt(n) and angle 2 pi k/n. Each denominator shell contains phi(n) points and has an assigned equal-area annulus.

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

A finite-observer architecture coupling phase-changing memory, reusable sensing volume, pressure control and apparatus costs.

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

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

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

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

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

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

Also indexed: the other supplied record with this title. No unverified DOI version relation is asserted.

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

Transient Phase Atlas: Short-Orbit Modular Fingerprints of Constants

A computational atlas of short modular orbits with diagnostics and explicit limits on what transient patterns establish.

Moments of Memory: An address is not the past

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

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

The Line Game | Surprise Is Not Meaning

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

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

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

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

Volume I: Exact Geometry and Symbolic Foundations

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Divisor-Filtered Farey Chambers and Localized Discrepancy

Annular Shell Isolation Near Zeta Zeros

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

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

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

Part II: Taxonomy and Structural Symmetries of Transient Rational Locking

Transient Rational Locking in Modular Logarithmic Orbits

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