Informativity Institute · Press release archive
MQ’s kinetic-energy check distinguishes two density-gradient functionals
Reciprocal-density weighting distinguishes the source kinetic expectation from an unweighted gradient functional.
· Recorded source version · Retrospective release
CHICAGO — The current MQ realization study evaluates a proposed density-gradient energy against the source Hamiltonian. With constant phase and zero potential, the normalized wave function has modulus equal to the square root of normalized availability. The corresponding kinetic expectation weights the squared density gradient by the reciprocal density.
Figure 1 summarizes the source result and its evidentiary scope.
The result and its scope
Source kinetic expectation
Squared density gradient weighted by reciprocal density
Different candidate
Unweighted squared-gradient functional
Conditional result
The two normalizations need not agree
An unweighted squared-gradient integral divided by total inventory is a different functional. Agreement for a specially chosen profile does not establish equality for all admissible positive densities. The source tests the difference using an explicit periodic positive-density construction.
This distinction matters when converting a count-smoothing measure into physical energy. A valid energy identification must reproduce the Hamiltonian’s density dependence, normalization, and action prefactor. Calling both expressions kinetic does not supply that derivation.
The result is a conditional mathematical obstruction to the proposed identification, not an experiment measuring a new energy effect or a general disproof of MQ. It identifies an additional requirement for a source-selected realization. The October 23 date is source-version provenance. The available record does not establish an original announcement date for this particular comparison.
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These institute pages provide further explanation and source material. Their claims retain the research-status qualifications stated in this release.
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