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Chamber-Lift Series.

Public front door for the chamber-lift papers and tools. The organizing rule is strict: shared shape is not shared mechanism. Edges belong in the atlas only when a shared construction, formula, gate, density machine, or explicitly dashed methodological connection can be written down.

Current release

Prime Numerators of the Triangular-Fractional Grid is the current settled result: a shell stratification and a lens for prime-in-progression density. The result is a lens, not a new prime law.

Local PDFZenodo recordOEIS draft A394477Prime-numerator rendererAtlas

Radial and shell companions

These records sit beside the chamber core but do not all share one shell law. The relation is stated explicitly rather than inferred from visual similarity.

Polar Shell Renderer — the exact reduced-fraction representation companion. Reduction gives the denominator shell, the polar map gives coordinates, and φ(n) gives population. Interactive plotLocal PDFDOI 21280464

Annular Shell Isolation Near Zeta Zeros — an analytic diagnostic sibling with a different generator, r_m(ρ) ≈ 1/(m|ζ′(ρ)|). Same shell metaphor, different shell law. Local PDFDOI 20564213

Canonical arithmetic parent: Divisor-Band Bijections and Totient Shells in the Triangular-Fractional Grid · DOI 21440877.

Zenodo records

Curated release links for the chamber-lift corpus, including the previously missed Odd Perfect Number, Goldbach, and Jordan records.

current

Prime Numerators of the Triangular-Fractional Grid: A Shell Stratification and a Lens for Prime-in-Progression Density

Zenodo 21200816

foundation

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

Zenodo 21440877

foundation

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

Zenodo 20580136

foundation

Divisor-Filtered Farey Chambers and Localized Discrepancy

Zenodo 20575700

residue-gate

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

Zenodo 20634306

residue-gate

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

Zenodo 20612902

geometry

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

Zenodo 20777503

quadratic sieve

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

Zenodo 20615213

method sibling

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

Zenodo 20601277

method sibling

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

Zenodo 20602122

method sibling

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

Zenodo 20607004

method sibling

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

Zenodo 20644786

method sibling

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

Zenodo 20635829

totient gate

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

Zenodo 20777470

Euler product

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

Zenodo 20634767

method warning

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

Zenodo 20644858

method keystone

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

Zenodo 20644917

geometry

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

Zenodo 20581459

discipline

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

Zenodo 20671738