Mathematical Path
Produce a checkable derivation with equation IDs, premises, retained orders, remainders and validity conditions.
Reading and research guide
For readers who want to check premises, elimination, variation, approximations and limits in sequence.
Prerequisites Vector calculus and ordinary differential equations; later steps use variational methods, Fourier analysis and linear partial differential equations.
Outcome Produce a checkable derivation with equation IDs, premises, retained orders, remainders and validity conditions.
The checkboxes below record your own reading on this device. Every source retains its own version, scope and scientific status.
011. Fix definitions and measurement maps
Separate operational constraints from physical inputs used to close spatial relations.
Read in this order: Metrological Foundations → Time · Clocks and Frequency.
Checkpoint Which equalities are definitions, and which require physical constitutive relations?
Next action Build a symbol table with units, reference conditions and the final readings to be compared.
022. Check LVE step by step
Check path relations, elimination and review conditions in the original derivation.
Read in this order: Length Vector Effect · Full Derivation → Experimental Relations and Tests.
Checkpoint Does eliminating a variable require an additional independence or configuration condition?
Next action Open an equation detail from the article and record its upstream dependencies and one limiting-case check.
033. From action to dynamical quantities
Check momentum, energy, force and work using the existing dynamical relations.
Read in this order: Dynamics · Inertia and Momentum → Dynamics · Energy and Action → Dynamics · Force and Work.
Checkpoint Which variables and reference conditions are held fixed when derivatives are taken?
Next action Independently recalculate one low-speed limit and separate source steps from your added calculations.
044. Check rays and orbits in a background
Distinguish reference length, physical spatial length, optical-path weighting and action.
Read in this order: Light Deflection · From Optical Path to Rays → Shapiro Delay · Excess Optical Path and Propagation Counts → Orbital Dynamics · Action, Conservation and Precession.
Checkpoint Is a coordinate conversion counted twice in the optical path? Are endpoints and approximation orders consistent?
Next action Check one integral’s endpoints, dimensions and weak-field limit, retaining the stated status of higher-order differences.
055. Decompose propagation sectors
Check mode decomposition, propagation speeds and required constitutive conditions from continuum degrees of freedom.
Read in this order: Wave Propagation and the Equal-Speed Condition → Continuum Dynamics → Longitudinal–Transverse Coupling.
Checkpoint Under which conditions is equal longitudinal/transverse speed obtained, and what closure relations are still missing for coupling?
Next action Separate established linear results from candidate coupling terms; do not use candidates to claim a closed master equation.
066. Check the envelope and statistical boundary
Keep the exact remainder after carrier substitution, then check approximation, matching and conditional detection relations.
Read in this order: How Does a Spatial Field Yield an Effective Wave Equation? → Uncertainty: Fourier Width Bounds for Wave Packets → How Can Continuous Fields Yield Discrete Detection Statistics?.
Checkpoint What scale conditions justify dropping a term? What is needed to turn Fourier width into momentum width?
Next action Export a contextual equation task and use Critique mode to examine remainders and validity; retain human review of the result.
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