Scope
Chapter “The admissibility frontier”, section “the screened field is not the whole carrier”. This is assertion 3 of 3 in that section.
Expanded claim page · assertion 3 of 3
the screened field is not the whole carrier
ConditionalTranslator
Works after a named field, coefficient, boundary condition or control is supplied. moves a structure between mathematical, physical or ordinary languages.
Exact assertion
Screening reveals the missing thing. In the minimal local scalar completion of a static kernel \(1/(q^2+\kappa^2)\), the electric-gradient share of mode energy is \(q^2/(q^2+\kappa^2)\), while the non-gradient screening sector holds \(\kappa^2/(q^2+\kappa^2)\). At \(q\ll\kappa\), adding Maxwell \(E^2\) alone omits almost all the energy in that completion. A physical model must identify the sector represented by the \(\kappa\) term and give it dynamics, energy and flux; the fractions are not asserted for every microscopic screening theory. The look-here calculation is now concrete: build matched finite-speed and explicit-screening completions of the projected lattice model, integrate them out to recover the same Ewald kernel, and compare total KMS transport under one order of size, wavevector, screening, frequency and light-speed limits. Agreement gives a robust engineered heat-current definition; disagreement before matching diagnoses a missing carrier, not new physics.
What this commits us to
The construction is admitted only after the named additional input is supplied. The page records the dependency instead of hiding it inside the conclusion.
Logical anatomy
Evidence posture
Identify the named external input and verify that the construction follows after it is supplied.
Research move
moves a structure between mathematical, physical or ordinary languages.
Verification route
- Recover the declared objects and assumptions from the controlling documents.
- Check the calculation, construction, obstruction or stopping rule on those same objects.
- Compare the source conclusion with the exact assertion above; do not strengthen its verbs or enlarge its domain.
- Apply the status rule and retain every named external dependency.
What would move or defeat this claim
Show that the named input is inconsistent, insufficient, unavailable, or fails to imply the claimed construction.
Source map
Controlling documents
- admissibility 119 the field closes continuity but screening needs its own carrierOpen controlling document →
- admissibility 44 finite q energy continuity kernel and gauge boundaryOpen controlling document →
- admissibility 46 screened finite q order of limits ladderOpen controlling document →