Published Working Draft III · synchronized interactive companion
A triangularly addressed, scale-covariant plane geometry connecting reciprocal area, null coordinates, reciprocal metallic means, and Pell-optimal cell grids.
Shared address, separate theorem lineThe parent paper supplies the flattened triangular rank ρ(n,k). C-Geometry writes m = ρ(n,k) and forms t = qm. It inherits the chamber-step address, not the TFG divisor-band or totient-shell theorems.
No Desmos required
Choose a triangular address, move the shape parameter, or jump to an exact lock. The cell scale is frozen at q = 1/2 in address mode.
Core theorem line
Universal similarity
The original and centered rectangles are similar for every 0 < c < 1. Side, perimeter, diagonal, and area relations are the same law at different powers.
Projective null map
The half-normalized null transform acts projectively on slopes, and the induced slope map is an involution.
Pell bridge
The locks use continued fractions with period one after the zero integer part. The alternating geometric error is recorded as a consequence of the classical convergent determinant identity.
Attribution boundary
Null coordinates, rapidity, metallic means, continued fractions, Vieta-style determinant identities, and tangent geometry are classical and cited in the paper. The proved-here organizing result is the single-generator bundle at c = √5 − 2 and the native collision selection {1, 2, 4}, stated with the bounded-search wording that no exact prior appearance was located.
The fence is part of the result
An external target can be assigned an address and fitted c; recovering it is not prediction.
The address is lossless. Entropy requires a declared measure, ensemble, or coarse-graining.
Null coordinates and rapidity are exact mathematics. Physical claims additionally require units, dynamics, boundary data, and held-out tests.