WILL Jupyter Notebook Catalog

Overview

Total Notebooks: 37

Colab_Notebooks (Main Research)

25 notebooks

1. Ab_Initio_CMB_Spectrum_Derivation

File: Ab_Initio_CMB_Spectrum_Derivation.ipynb Colab: Ab_Initio_CMB_Spectrum_Derivation

Purpose: Calculates CMB acoustic peak positions (ℓ₁, ℓ₂, ℓ₃) from WILL Relational Geometry topological principles (S2 Surface Tension) using Bessel function analysis

Claim: WILL RG can predict CMB acoustic peak positions from first principles without fitting

Datasets: CMB Planck data

Key Result: Compares predicted peak positions vs observed Planck CMB spectrum

2. Baryonic_Escape_Threshold

File: Baryonic_Escape_Threshold.ipynb Colab: Baryonic_Escape_Threshold

Purpose: Tests galaxy escape velocity predictions comparing WILL RG framework vs observations with zero free parameters

Claim: WILL RG predicts galaxy escape velocity without dark matter or fitting parameters

Datasets: Galaxy observation data

Key Result: Escape velocity predictions for multiple galaxy types

3. Dark_Lensing

File: Dark_Lensing.ipynb Colab: Dark_Lensing

Purpose: Analyzes gravitational lensing predictions under WILL RG framework compared to GR

Claim: WILL RG predicts gravitational lensing effects differently from GR

Datasets: H0 and cosmological parameters

Key Result: Lensing angle and magnitude predictions from WILL RG vs GR

4. Galactic_Clusters_DM_Killer

File: Galactic_Clusters_DM_Killer.ipynb Colab: Galactic_Clusters_DM_Killer

Purpose: Predicts galaxy cluster velocity dispersion using WILL RG Machian scale (a_κ) without dark matter

Claim: WILL RG accounts for galaxy cluster dynamics without dark matter via horizon acceleration

Datasets: Coma, Virgo, Fornax clusters

Key Result: Observed vs predicted velocity dispersion for galactic clusters

5. Galactic_Rotation_Protocol_Independent_SPARC

File: Galactic_Rotation_Protocol_Independent_SPARC.ipynb Colab: Galactic_Rotation_Protocol_Independent_SPARC

Purpose: Tests galactic rotation curves using SPARC dataset with protocol-independent analysis

Claim: WILL RG predicts galaxy rotation curves without dark matter (protocol-independent)

Datasets: SPARC (Spitzer Photometry and Accurate Rotation Curves)

Key Result: Comparison of predicted vs observed rotation curves across SPARC galaxies

6. Geometric_expansion_Pantheon

File: Geometric_expansion_Pantheon.ipynb Colab: Geometric_expansion_Pantheon

Purpose: Derives cosmological parameters (H0, Ω) from Pantheon+ supernova data using WILL RG geometric expansion model

Claim: WILL RG geometric expansion fits Pantheon+ supernova luminosity distances

Datasets: Pantheon+ Type Ia supernovae

Key Result: H0 value and matter density parameter derived from supernovae

7. Gravitational_Deflection

File: Gravitational_Deflection.ipynb Colab: Gravitational_Deflection

Purpose: Calculates light deflection angle under WILL RG vs GR predictions

Claim: WILL RG predicts different photon deflection than GR

Datasets: Solar parameters

Key Result: Deflection angle comparison: WILL RG vs GR

8. Gravitational_Lensing

File: Gravitational_Lensing.ipynb Colab: Gravitational_Lensing

Purpose: Tests gravitational lensing predictions in WILL Relational Geometry framework

Claim: WILL RG framework predicts lensing effects consistent with observations

Datasets: Lensing system parameters

Key Result: Lensing magnification and geometry predictions

9. H_0_from_T_CMB_and_alpha

File: H_0_from_T_CMB_and_alpha.ipynb Colab: H_0_from_T_CMB_and_alpha

Purpose: Derives Hubble constant (H0) from CMB temperature and fine structure constant using WILL RG

Claim: H0 can be derived from fundamental constants (T_CMB, alpha) via WILL RG

Datasets: CMB temperature (Fixsen 2009, Planck 2018), fine structure constant (CODATA)

Key Result: H0 ≈ 68.15 km/s/Mpc derived from first principles

10. Low_Quadrupole_Suppression

File: Low_Quadrupole_Suppression.ipynb Colab: Low_Quadrupole_Suppression

Purpose: Explains CMB quadrupole suppression (anomalously low ℓ=2 mode) via WILL RG Surface Tension model

Claim: WILL RG Surface Tension mechanism explains observed CMB quadrupole deficit

Datasets: CMB Planck angular power spectrum

Key Result: Predicted suppression of CMB quadrupole moment

11. Mercury-Sun_Relational_Parameterization

File: Mercury-Sun_Relational_Parameterization.ipynb Colab: Mercury-Sun_Relational_Parameterization

Purpose: Derives Mercury’s orbital parameters using WILL RG relational geometry without GR

Claim: WILL RG can derive Mercury’s orbital elements without general relativity

Datasets: Mercury orbital period, eccentricity

Key Result: Orbital parameters computed via WILL RG relational scale factor

12. OJ_287_WILL_RG_ORBITAL_ANALYSIS_AND_FLARE_TIMING

File: OJ_287_WILL_RG_ORBITAL_ANALYSIS_AND_FLARE_TIMING.ipynb Colab: OJ_287_WILL_RG_ORBITAL_ANALYSIS_AND_FLARE_TIMING

Purpose: Analyzes OJ 287 binary black hole orbital mechanics and flare timing predictions under WILL RG

Claim: WILL RG predicts flare timing and orbital dynamics of OJ 287 binary system

Datasets: OJ 287 black hole binary system observations

Key Result: Predicted flare timing and orbital precession for OJ 287

13. PHOTON_DEFLECTION

File: PHOTON_DEFLECTION.ipynb Colab: PHOTON_DEFLECTION

Purpose: Symbolic algebra comparison of photon deflection predictions: massive particles vs photons in WILL RG

Claim: WILL RG predicts different deflection for massless photons vs massive particles

Datasets: None (symbolic analysis)

Key Result: Symbolic expressions for photon deflection in WILL RG

14. RAR_test

File: RAR_test.ipynb Colab: RAR_test

Purpose: Tests Radial Acceleration Relation (RAR) of galaxies: WILL RG predictions vs observational data

Claim: WILL RG accounts for galaxy RAR (correlation between centripetal and observed acceleration)

Datasets: Galaxy observational data

Key Result: WILL RG RAR prediction vs observed galaxy accelerations

15. RGvsGR_ISCO_Photon_Horizon

File: RGvsGR_ISCO_Photon_Horizon.ipynb Colab: RGvsGR_ISCO_Photon_Horizon

Purpose: Symbolic algebra comparison of ISCO (Inner-most Stable Circular Orbit) and photon horizon between WILL RG and GR

Claim: WILL RG predicts different ISCO radius and photon orbit than GR

Datasets: None (symbolic/algebraic analysis)

Key Result: Symbolic comparison showing WILL RG has simpler expressions (fewer operations, shorter strings)

16. ROM_HOLOGRAPHIC_REALITY_DECODER

File: ROM_HOLOGRAPHIC_REALITY_DECODER.ipynb Colab: ROM_HOLOGRAPHIC_REALITY_DECODER

Purpose: Three-stage inversion algorithm: reconstructs orbital parameters from observed redshift time series using R.O.M.

Claim: R.O.M. (Relational Orbital Mechanics) can recover orbital geometry from 1D redshift data

Datasets: Synthetic 1PN orbital data

Key Result: Recovered period, eccentricity, inclination from redshift signal via MCMC

17. ROM_MCMC_POSTERIORS_vs_GRAVITY_COLLABORATION

File: ROM_MCMC_POSTERIORS_vs_GRAVITY_COLLABORATION.ipynb Colab: ROM_MCMC_POSTERIORS_vs_GRAVITY_COLLABORATION

Purpose: MCMC posterior analysis of R.O.M. parameters vs Gravity Collaboration observational constraints

Claim: R.O.M. posterior parameter distributions agree with or improve upon GR constraints

Datasets: Gravity Collaboration orbital observations

Key Result: Parameter posterior distributions and comparison with GR

18. ROM_S2_SOLVER

File: ROM_S2_SOLVER.ipynb Colab: ROM_S2_SOLVER

Purpose: Solves for S2 star orbital parameters (period, eccentricity, inclination) using R.O.M. inverse solution method

Claim: R.O.M. inverse solution recovers S2 star parameters from radial velocity measurements

Datasets: S2 star radial velocity data

Key Result: S2 orbital parameters (P, e, i) extracted via R.O.M. inversion

19. Recombination__Model_Independent_Atomic_Physics

File: Recombination__Model_Independent_Atomic_Physics.ipynb Colab: Recombination__Model_Independent_Atomic_Physics

Purpose: Model-independent atomic physics analysis of CMB recombination without assuming Lambda-CDM

Claim: CMB recombination epoch can be derived from atomic physics alone without cosmological model assumptions

Datasets: CMB temperature, fine structure constant

Key Result: Recombination redshift z_rec derived from first-principles atomic physics

20. Suspiciously_Perfect_CMB

File: Suspiciously_Perfect_CMB.ipynb Colab: Suspiciously_Perfect_CMB

Purpose: Tests whether WILL RG predicts anomalously perfect CMB spectrum matching observations

Claim: WILL RG produces CMB spectrum predictions that fit observations better than expected

Datasets: CMB Planck temperature and polarization spectra

Key Result: CMB power spectrum predictions and fit quality assessment

21. Topological_ruler

File: Topological_ruler.ipynb Colab: Topological_ruler

Purpose: Compares WILL RG galactic rotation predictions against SPARC data using topological ruler metric

Claim: WILL RG topological model predicts galaxy rotation curves across SPARC sample

Datasets: SPARC galaxy rotation curves

Key Result: WILL/SPARC prediction ratio across galaxies using topological scale

22. WILL-relativistic-tests-gps-mercury-s2

File: WILL-relativistic-tests-gps-mercury-s2.ipynb Colab: WILL-relativistic-tests-gps-mercury-s2

Purpose: High-precision verification of WILL RG predictions: GPS time dilation, Mercury precession, S2 star orbit

Claim: WILL RG accurately predicts solar system relativistic effects with high precision

Datasets: GPS satellite parameters, Mercury orbit, S2 star orbital data

Key Result: Five key WILL RG predictions verified to high decimal precision (50+ digits)

23. Wide_binary_Chae_2023

File: Wide_binary_Chae_2023.ipynb Colab: Wide_binary_Chae_2023

Purpose: Tests wide binary dynamics (Chae 2023 data) under WILL RG framework

Claim: WILL RG predicts wide binary orbital mechanics without dark matter

Datasets: Chae 2023 wide binary star systems

Key Result: WILL RG predictions for wide binary orbital separations and dynamics

24. Wisper_ATT

File: Wisper_ATT.ipynb Colab: Wisper_ATT

Purpose: Audio transcription tool using OpenAI Whisper model and Gradio interface

Claim: N/A (utility/tool notebook)

Datasets: Audio files (user-provided)

Key Result: Transcribed text from audio input

25. beta_i_comparison

File: beta_i_comparison.ipynb Colab: beta_i_comparison

Purpose: Compares inclination parameter (β_i / K*sin(i)) between R.O.M. and observational data via MCMC

Claim: R.O.M. inclination predictions (β_i) match observational constraints

Datasets: Observational orbital inclination data

Key Result: MCMC posterior distributions for inclination parameter comparisons

Holster (Advanced Tests)

12 notebooks

1. RELATIONAL_ORBITAL_HOLOGRAPHY

File: RELATIONAL_ORBITAL_HOLOGRAPHY.ipynb Colab: RELATIONAL_ORBITAL_HOLOGRAPHY

Purpose: Tests holographic principle: recovers orbital parameters (period, eccentricity) from 1D redshift signal using R.O.M. with MCMC

Claim: R.O.M. holographic principle: 3D orbital geometry encoded in 1D time series can be inverted

Datasets: Synthetic 1PN redshift data

Key Result: Recovered orbital parameters (P, e) from synthetic redshift signal with MCMC analysis

2. ROM_APP

File: ROM_APP.ipynb Colab: ROM_APP

Purpose: Interactive SymPy module computing complete R.O.M. (Relational Orbital Mechanics) orbital state system

Claim: R.O.M. forms a closed algebraic system solvable from minimal inputs

Datasets: None (symbolic computation)

Key Result: Complete orbital state computation and consistency verification using SymPy

3. ROM_Ksin_i_vs_Synthetic_1PN_Data

File: ROM_Ksin_i_vs_Synthetic_1PN_Data.ipynb Colab: ROM_Ksin_i_vs_Synthetic_1PN_Data

Purpose: Compares R.O.M. predictions of K*sin(i) parameter against synthetic 1PN relativistic orbital data via MCMC

Claim: R.O.M. K*sin(i) predictions match 1PN predictions for relativistic orbits

Datasets: Synthetic 1PN orbital data

Key Result: MCMC parameter recovery: K*sin(i) comparison between R.O.M. and 1PN

4. Double_Pulsar_orbital_decay_rate

File: Double_Pulsar_orbital_decay_rate.ipynb Colab: Double_Pulsar_orbital_decay_rate

Purpose: Calculates orbital decay rate (Pdot_b) for double pulsar system using WILL RG energy symmetry principle

Claim: WILL RG predicts orbital decay rate consistent with double pulsar observations

Datasets: Double pulsar binary parameters

Key Result: Predicted orbital period decay rate (Pdot_b) from WILL RG

5. HULSE_TAYLOR_PULSAR_DATA_FOR_R_O_M_

File: HULSE_TAYLOR_PULSAR_DATA_FOR_R_O_M_ (1).ipynb Colab: HULSE_TAYLOR_PULSAR_DATA_FOR_R_O_M_

Purpose: Fetches Hulse-Taylor pulsar orbital parameters and generates synthetic redshift signal for R.O.M. testing

Claim: R.O.M. can process real pulsar data for orbital parameter recovery

Datasets: Hulse-Taylor pulsar (PSR B1913+16) orbital data

Key Result: Synthetic redshift time series generated from Hulse-Taylor pulsar parameters

6. RELATIONAL_INERTIA_TEST

File: RELATIONAL_INERTIA_TEST.ipynb Colab: RELATIONAL_INERTIA_TEST

Purpose: Tests relational inertia (Q shift) predictions under WILL RG vs observational data

Claim: WILL RG relational shift factor (Q) predicts inertial effects observed in data

Datasets: Observational data with inertial measurements

Key Result: Observed vs predicted relational shift (Q) comparison

7. ROM_TEST_GR

File: ROM_TEST_GR.ipynb Colab: ROM_TEST_GR

Purpose: Generates standard Keplerian/GR orbital benchmark data for comparison against R.O.M.

Claim: R.O.M. can be benchmarked against standard GR orbital predictions

Datasets: User-input orbital parameters

Key Result: GR orbital benchmark data for R.O.M. validation

8. ROM_vs_GR_7p

File: ROM_vs_GR_7p.ipynb Colab: ROM_vs_GR_7p

Purpose: Compares R.O.M. vs strict GR orbital predictions across multiple test scenarios (7-parameter test)

Claim: R.O.M. predictions differ from GR in measurable ways across orbital parameter space

Datasets: Synthetic orbital data across 7-parameter space

Key Result: R.O.M. vs GR predictions comparison across parameter variations

9. R_O_M_SMOOTH_PHASE__INVERSE_SOLUTION

File: R_O_M_SMOOTH_PHASE__INVERSE_SOLUTION.ipynb Colab: R_O_M_SMOOTH_PHASE__INVERSE_SOLUTION

Purpose: Tests R.O.M. strong-field inverse solution: recovers e and kp from redshift signal at peri/apocenter

Claim: R.O.M. inverse solution can recover orbital parameters from smooth redshift phase

Datasets: Synthetic redshift phase data

Key Result: Recovered eccentricity (e) and potential (kp) from signal extrema

10. R_O_M__INVERSE_SOLUTION

File: R_O_M__INVERSE_SOLUTION.ipynb Colab: R_O_M__INVERSE_SOLUTION

Purpose: Proof of concept: signal decomposition and parameter recovery from scalar redshift data using R.O.M.

Claim: R.O.M. hidden orbital geometry (e, kp) can be recovered from 1D redshift signal alone

Datasets: Synthetic redshift time series

Key Result: Parameter recovery demonstration showing e and kp extraction from redshift

11. WILL_Geometry_absolute_scale_cosmology

File: WILL_Geometry_absolute_scale_cosmology.ipynb Colab: WILL_Geometry_absolute_scale_cosmology

Purpose: Derives absolute-scale cosmology from WILL RG fundamental constant (κ² = 2/3) closure condition

Claim: WILL RG κ² = 2/3 constraint uniquely determines cosmological parameters

Datasets: None (first-principles derivation)

Key Result: H0, matter density, and other cosmological parameters from κ² condition

12. WILL_Qcenter_mirror_test

File: WILL_Qcenter_mirror_test.ipynb Colab: WILL_Qcenter_mirror_test

Purpose: Tests relational symmetry: observer ↔ object equivalence (GPS satellite ↔ Earth surface) under WILL RG

Claim: WILL RG exhibits perfect relational symmetry between observer and object positions

Datasets: GPS satellite and Earth surface parameters

Key Result: Verification of relational symmetry through Q-center mirror test