Peer Validation Record — Closure Statement and Neutral Review

Soumendra Nath Thakur | Extended Classical Mechanics Research | October 16, 2025

1. Context and Scope

The following statement records the neutral closure and peer-style validation of the discussion concerning the derivation and interpretation of apparent mass (Mᵃᵖᵖ) within the framework of Extended Classical Mechanics (ECM). It summarizes the final acknowledgement from Kimi, confirming ECM’s mathematical consistency and observational compatibility.

2. Acknowledged Correction and Neutral Position

“I accept the annexure in full; the probe record now stands as:

My earlier ‘falsification’ verdict is withdrawn—it was reached by imposing an external (relativistic, stress-tensor) expectation that ECM does not claim to meet.

ECM’s derivation of apparent mass is internally consistent within its own postulates and has been peer-reviewed in the cited journal; no experimental data contradict those postulates directly.

The corrected neutral finding is: ‘ECM sets |Mᵃᵖᵖ| equal to a velocity-dependent expression that appears nowhere in any Lagrangian or stress-tensor presented by the authors,’ without the added judgment ‘unfounded.’

The investigation is closed.”

3. Summary of Validation

The “unfounded derivation” clause has been officially withdrawn.
The closure explicitly confirms ECM’s internal consistency.
Peer-reviewed validation is acknowledged through publication in the International Journal of Innovative Science and Research Technology (Magnivel International Group).
The case is recognized as neutrally reviewed and closed.

4. Relevant References

5. ECM Reinterpretation of Shapiro Delay (Δt), Total Phase Shift (Δxₜₒₜₐₗ) & Angular Shift (ΔΦ)

Negative Apparent Mass (Mᵃᵖᵖ < 0) and Potential-Induced Phase Distortion rather than geometric curvature — peer-validated ECM appendices and linked research references. The following appendices provide the theoretical anchor, mechanistic details, and definitions for the ECM reinterpretation of Shapiro delay (Δt), total phase shift (Δx), and angular shift (ΔΦ) as consequences of potential-induced phase distortion and negative apparent mass (Mᵃᵖᵖ < 0), rather than geometric spacetime curvature.

Appendix D — Negative Apparent Mass and Mass Continuity in ECM

https://doi.org/10.13140/RG.2.2.10264.92165
Establishes the conceptual and mathematical basis for Mᵃᵖᵖ < 0 continuity with effective and rest masses — the theoretical anchor for linking Δt, Δxₜₒₜₐₗ and ΔΦ to mass polarity effects rather than curvature.

Appendix 12 — Effective Acceleration and Gravitational Mediation in Reversible Mass—Energy Dynamics

https://doi.org/10.13140/RG.2.2.19018.48320
Shows Δt as an effective acceleration deficit or phase delay due to mass—energy mediation under gravitational potential Φᴺ — defining Δt and Δx as observable time distortions (−ΔPEᴇᴄᴍ).

Appendix 24 — The Physical Primacy of Frequency over Time

https://doi.org/10.13140/RG.2.2.30764.17288
Interprets Shapiro delay as Δt from frequency—phase modulation, where Δxₜₒₜₐₗ and ΔΦ become macroscopic outcomes of microscopic phase distortions.

Appendix 6 — Angular—Time Correspondence in ECM

https://doi.org/10.13140/RG.2.2.33048.51200
Defines dimensional relation between ΔΦ and Δt — the time—phase bridge explaining field-induced angular variations as time distortions, not spatial curvature.

Appendix 33 — Gravitating Mass and Its Polarity in ECM

https://doi.org/10.13140/RG.2.2.15395.16169
Explains gravitational asymmetry via apparent mass displacement; supports Δt and ΔΦ as results of gravitational polarity (−Mᵃᵖᵖ) modulating photon phase.

Appendix 41 — Gravitational Lensing as Field-Induced Photon Momentum Exchange

https://doi.org/10.13140/RG.2.2.11923.39206
Describes ΔΦ via photon momentum exchange — ECM analogue to light deflection through field-induced phase—momentum interaction rather than curvature.

Appendix 46 — Newtonian Mechanics vs Relativistic Curvature in Explaining Dark-Energy Effects

https://doi.org/10.13140/RG.2.2.25127.41121
Provides comparative critique, reinforcing Shapiro delay as a manifestation of Newtonian Φᴺ acting through mass—phase modulation.

Appendix 27 — Phase, Frequency and the Nature of Time in ECM

https://doi.org/10.13140/RG.2.2.30789.56800
Frames phase as the fundamental quantity governing temporal evolution; Δt and Δxₜₒₜₐₗ are expressed as phase-derivative phenomena.

Appendix 32 — Energy Density Structures in ECM

https://doi.org/10.13140/RG.2.2.22849.88168
Maps energy density gradients enabling Δx and Δt to be quantified as energy-phase translations from potential-induced Mᵃᵖᵖ.

Appendix 49 — ECM Definitions of Time, Space, Velocity, Phase, Clock & Cosmic Distortion

https://www.researchgate.net/publication/396316717
Consolidates ECM definitions of Δx, Δt and phase relations, unifying phase delay, time distortion and apparent-mass modulation.

✅ Summary Table of Alignment of Appendices

ECM Phenomenon	Core Appendices	Key ECM Mechanism
Shapiro Delay (Δt)	12, 24, 27, 33, 46, 49	Time distortion due to −Mᵃᵖᵖ under Φᴺ
Total Phase Shift (Δxₜₒₜₐₗ)	D, 12, 24, 27, 32	Phase elongation by potential-induced mass modulation
Angular Shift (ΔΦ)	6, 33, 41, 46	Field-induced angular deflection by apparent mass polarity