BridgeTech Media · Research tool · v0.2

Photonica Live

Explore a structured record ⟨E, p, ℓ, t, f, μ, κ⟩ under repeated addition of a fixed seed. Compare two consistent arithmetic models and observe how the record’s nonzero coordinates change.

Changing the model, radix, or seed resets the run. Zero is a valid seed. Other seed coordinates are zero. Animation uses up to 10 updates per second and stops at one complete additive cycle.

Current coordinate labels

Bars show each label relative to its largest permitted label. Gold indicates a carry emitted during the most recent update; several additions may occur in one update. E is fixed at radix 1. A zero coordinate contributes the factor 1 to W.

Distinct support scores observed

The vertical axis counts distinct W values; the horizontal axis counts additions. Both axes are linear. This count cannot decrease and is bounded by the finite set of support scores. It is not the instantaneous score or an entropy-growth claim.

Support-score frequencies

Bars are ordered by W; height is the number of observations. Entropy is H = −Σ p(W) log₂ p(W) over the sampled steps 1…n. The initial zero record is excluded; zero at the cycle’s end is included. This empirical statistic is not quantum entropy or physical storage capacity.

What the labels mean

“Unit” means multiplicatively invertible in the selected ring. Zero is reported separately. Every other nonunit in these finite rings is a nonzero zero divisor. This class belongs to the full seed record, not only its time coordinate.

In carry mode the exact period is N/gcd(N,J(seed)). In coordinate mode it is the least common multiple of dᵢ/gcd(dᵢ,seedᵢ). Both trajectories are periodic. Changing between the models changes the arithmetic, rather than testing a different physical theory.