Can a Two-Symbol Algebra Add Predictive Power to Galaxy Dynamics?

(A minimal, test-only demonstration — MVP IA/NOP 2.1, Freeze)

Status: canonical
Audience: physics-facing / internal method / narrative

Canonical entry point is here – Non-ontic Physics and IA (Interdiscrete Algebra): Definitions, Boundary Discipline, and Near-Term Applications.

Important Notes (Scope & Verification)

• This is a test-grade MVP demonstration, not a full scientific study of all available galaxies.
• The computations were performed with a modern LLM-assisted workflow and have not yet been audited by a fundamental-physics expert. We invite independent verification of both data handling and methodology.
• If the scientific community finds this direction interesting, we are ready to continue by expanding the protocol, running stronger falsification tests, and applying the NOP/IA capsule to other physics problems.

Dataset

We used the public SPARC RAR dataset file RAR.mrt, which contains
log10(g_bar), e_gbar, log10(g_obs), e_gobs.
Source: SPARC (Case Western Reserve University): RAR.mrt.

Canonical Capsule (NOP/IA ↔ DISCRETE Separation)

Freeze conditions (NOP/IA 2.1, Slim):

• Π-readout-version: 2.1
• Allowed-Exports: { I_scale }
• SV-set: { SV-A, SV-B, SV-C } (names only in NOF/IA; implementation stays in DISCRETE)
• kill_flags: { feature_leak, meta_dependence, scale_leak }
• Baseline procedure: mandatory

NOP/IA contains no arithmetic. All numeric fitting, metrics, and statistics live strictly inside the DISCRETE block.

DISCRETE Block (All Ontic Computation)

Minimal sample for MVP

• We selected N = 600 points, stratified evenly across log10(g_bar) after sorting, to avoid “one-corner” sampling.

Models

• Baseline: g_obs = g_bar
• Main: a standard one-parameter RAR/MOND-like mapping with g† (as given in the RAR literature; see eq. (4) in the arXiv preprint).

Fit result

• Fitted parameter: g† ≈ 1.05 × 10⁻¹⁰ m/s² (on this 600-point MVP sample)

Classical accuracy (weighted RMSE in log10(g))

• Baseline RMSE ≈ 0.538
• Main RMSE ≈ 0.116
• Improvement factor ≈ 4.64×

Where IA Adds Non-Decorative Value

Beyond RMSE, we computed an IA-native structural indicator on residuals that targets
“hidden coherent failure modes” (systematic sign patterns) across scales.
This produces value-data that a single RMSE number does not capture.

IA construction (inside DISCRETE, but using IA grammar)

• Sort points by g_bar to define an index frame K.
• Define Bnd as adjacency pairs on K.
• Define configuration C from the sign of residuals (Ø₀ / Ø∞ as a binary label).
• Compute DID_density = fraction of adjacent flips on Bnd.
• Define IA_structure = 2·(DID_density − 0.5)², in [0, 0.5].
• Evaluate across SV-operators (SV-A, SV-B, SV-C) as a scale-stability probe for I_scale.

Measured IA indicators

Interpretation:
Baseline residuals show a strongly coherent sign pattern (very low flip density),
while the main model removes that structure (flip density approaches ~0.5, i.e. noise-like under this test).
This is a different notion of predictive strength than “smaller RMSE”:
it is about reducing structured residual modes that often reappear under resampling or new subsamples.

Noise sanity check (permutation test)

To avoid “hand-wavy 0.5 claims”, we ran a permutation test that shuffles the residual-sign labels and
compares the observed IA_structure to the null distribution. In this MVP run, baseline shows
significant structure under SV-A (p≈0.025), while the main model is close to the null.

Conclusion

This first MVP run demonstrates a clean NOP/IA capsule where IA contributes non-decorative value:
it produces a scale-checked structural diagnostic of residuals that complements classical fit error.
Next steps depend on community interest and expert review: strengthening falsification (meta_dependence),
expanding readout tests, and running larger subsets or full SPARC data under the same frozen protocol.