Fixed grids, ticks and shadows: what a discrete model can reveal

Can a fixed spatial grid, a universal time tick or a hidden extra dimension be identified from what an observer can actually measure?

The programme proposed a fixed grid, a tick and extra dimensions. Whether observations could identify them decides whether those ideas can become testable physical claims.

1. Independently checked

   Step 1

   What was built. Fixed Grid String Lab 0.1 (20 September; revision 1.43): a tick-rejection rule against measured intervals and an exact reversible four-coordinate integer string, with a typed claim ledger.

   What was found. Three candidate ticks fail; the Planck-time tick passes only trivially. Any small enough tick fits finite data, and decimal rounding can fake a common tick.

   What it opens. The proposed next test was a gauge-consistent hydrogen Hamiltonian; the next release froze a narrower radial Coulomb benchmark without gauge dynamics.

   • Fixed Grid String Lab 0.1.0 results Public
   • Fixed Grid String Lab claim ledger Public

2. Independently checked

   Step 2

   What was built. 0.2.0 (21 September; revision 1.77): a foundation contract separating mathematics, computation, measurement, hypothesis and theology, and a frozen radial Coulomb benchmark with an exact half-line spectrum.

   What was found. The spectrum matches within 4.7e-14 Hartree; exact tick evolution cannot reveal whether time is discrete. Two manuscript claims (minimum memory, Markov closure) were corrected.

   What it opens. The l = 1 sector with a dipole operator.

   • Foundation contract — Fixed Grid String Lab 0.2.0 Public
   • Radial Coulomb foundation: operator, exact spectrum, and limits Public
   • Fixed Grid String Lab 0.2.0 — bounded results Public

3. Independently checked

   Step 3

   What was built. 0.3.0 (revision 1.78): an exact 1S→2P electric-dipole derivation and a refinement protocol frozen before the run, with sources and provenance.

   What was found. All gates passed first time, with second-order convergence observed toward the exact oscillator strength (not a general proof); this is imported quantum mechanics, not a derivation from strings.

   What it opens. A requirement for a project-specific interaction giving a numerical contrast with standard physics.

   • Hydrogen 1S→2P electric-dipole benchmark Public
   • Sources and provenance for release 0.3.0 Public
   • Fixed Grid String Lab 0.3.0 — 1S→2P benchmark results Public

4. Independently checked

   Step 4

   What was built. 0.7 (revision 1.82): labelled 3D slices, axis projections and a scalar generator tested exactly; an earlier standalone 24-shape atlas (prepared 5 September) multiplies planar regions into 4D.

   What was found. Labelled slices rebuild a 4D set exactly, but two different sets share all four axis projections; a 3D shadow hides a collapsed direction. A scalar-curve claim was corrected.

   What it opens. Comparing frozen bridge models, internal state against an extra coordinate, on calibrated outcomes.

   • Dimensional slices, shadows and regular generators Public
   • Sources for release 0.7 Public
   • Results 0.7 — dimensional slices and aliases Public
   • Multiplying shapes: 24-shape atlas Public

5. Independently checked

   Step 5

   What was built. Releases 0.4–0.22: acoustic support, an exceptional-mathematics audit, a wave formulation, U(1) gauge modules, coupled ring and plaquettes, dispersion and optical-tail countermodels, and paired-reference calibration.

   What was found. Each is a bounded benchmark or exact countermodel; corrections in 0.5, 0.6 and 0.12 and the failed 0.14 run are kept. No real measured dataset yet meets the gate.

   What it opens. The 0.22 boundary: a sample/reference ratio identifies a material kernel when detector and path kernels are shared; with a path mismatch, an exact countermodel mimics the delay.

   • Version 0.22.0 — paired-reference calibration boundary Public

6. Independently checked

   Step 6

   What was built. An optics line: exact matrix reconstruction from Fourier rotor pairs (19 September), a spectral studio whose validation still checks that reconstruction (27 September), and a Yee-grid Maxwell mode.

   What was found. Rotor count is a basis-dependent measure, not universal complexity or proof of randomness; the studio cannot make UV literally visible; the diffraction checks establish neither convergence nor experimental agreement.

   What it opens. Open convergence and measured-comparison questions for the optics line.

   • Rotational Complexity of Matrices — Theory and Experimental Results Public
   • Spectral engine validation Public
   • Maxwell diffraction build — v0.3 Public

The next question. Can a project-specific interaction make a frozen, precision-complete prediction that differs from standard physics and survives unused measured data?

Editorial guide