What question did this study set out to answer?

The research aims to explore modulus and remainder predictions derived from multiple hierarchy levels to validate a theoretical framework.

April 23, 2026Open Access

Modulus and Remainder at Every Scale

Puntos clave

The research aims to explore modulus and remainder predictions derived from multiple hierarchy levels to validate a theoretical framework.
Conducted the giga remainder test with eleven derivations across seven hierarchy levels.
Computed predictions based on modulus/remainder frameworks and compared them to measured values within a pre-set tolerance.
Evaluated 3788 value nodes for accuracy, yielding outputs for registered comparisons.
Out of the eleven tested derivations, 8 passed the predictions while 2 failed.
The experiment produced 140 values from 11 successful derivations, indicating a robust predictive capacity.
Predictions include parameters from particle to cosmological scales, showcasing interrelated scientific concepts.

Resumen

The giga remainder test is a single experiment with eleven derivations sampling seven hierarchy levels simultaneously. Each derivation computes a specific numerical prediction from the framework's modulus/remainder decomposition. Each prediction is compared to a measured quantity through a pre-registered tolerance window. The framework committed before the computation ran. **Experiment: ** experimentgigaᵣemainderₜestᵥ0, run001. **Pool: ** 3788 value nodes. **Derivations: ** 11 OK, 0 errors. **Outputs: ** 140 values. **Pre-registered comparisons: ** 10. **Result: ** 8 PASS, 2 FAIL. The eleven derivations: | # | Derivation | Level | What it tests | |---|---|---|---| | 1 | CKM from integers | Particle | CKM elements as gauge-group fractions | | 2 | Cosmological closure | Cosmos | Ω_Λ = (251−22π) /264 | | 3 | Hubble tension | Cosmos | H₀ ratio = 12/11 | | 4 | Hadron Koide | Hadron | K for 9 particle triplets | | 5 | Nuclear binding | Nuclear | SEMF ratio aA/aV = 3/2 | | 6 | Hill sphere | Planetary | Decomposition into 1/3 + mass ratio | | 7 | Chandrasekhar | Stellar | Lane-Emden coefficient = 15π/8 | | 8 | Muon g-2 toroidal | Lepton | 4-loop toroidal = 40% of anomaly | | 9 | Koide amplitude map | All families | a² distribution across 4 sectors | | 10 | Filling fraction ladder | Math | R₃/R₂ unique rational | | 11 | Microscopic-cosmic bridge | QED↔Cosmos | cosmic/micro = 3 (MZ/mₑ) ² |

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