| digraph FloquetV2 { |
| rankdir=LR |
| node [shape=box] |
| "foundation:maxwell" [label="Stated nondispersive canonical Maxwell model and positive material parameters."] |
| "foundation:projective" [label="Direct polar identities, common positive angular velocity, and projective winding."] |
| "foundation:ode" [label="Bounded measurable linear ODEs, determinant one, continuity of transfer matrices."] |
| "foundation:fractional" [label="Exact fractional-linear pointwise subtraction and derivative identities."] |
| "foundation:segments" [label="Explicit constant-generator transfer matrices and their products."] |
| "foundation:convex" [label="Compact convex moment fibers, finite-dimensional support, and weak-* compactness."] |
| "foundation:linear_algebra" [label="Cayley\u2013Hamilton, Vandermonde, Hankel, and singular-value identities."] |
| "foundation:inverse_function" [label="Inverse/constant-rank theorem and local derivative estimates."] |
| "foundation:analytic_jets" [label="Analytic transfer family and finite polynomial/exponential expansions."] |
| "external:real_QE" [label="Effective real-closed-field quantifier elimination; Collins CAD is an external algorithmic input."] |
| "lem:linearize" [label="3.1 An exact, unrelaxed linearization"] |
| "lem:boundary" [label="3.2 Boundary moments cannot carry positive gain"] |
| "lem:normal" [label="3.3 Finite normal duals at every interior moment"] |
| "thm:resource" [label="4.1 Global resource-constrained extremality and equality"] |
| "thm:resourceDefect" [label="4.2 Resource defect and unique dual parameters"] |
| "thm:concavity" [label="5.1 Strict concavity and at most two adjacent winning windings"] |
| "thm:resourceFree" [label="5.2 Free-period optimum with a fixed long-run resource"] |
| "lem:margin" [label="6.1 A two-multiplier switching margin"] |
| "thm:phasestability" [label="6.2 Phase and clock stability from the exact defect"] |
| "thm:globalstability" [label="6.3 Global resource-constrained square-root rigidity"] |
| "prop:resourceSharp" [label="6.4 Sharpness while preserving the resource exactly"] |
| "thm:main" [label="7.1 Preserved exact bounds-only optimum"] |
| "thm:defect" [label="7.2 Preserved bounds-only exact defect"] |
| "cor:boundstability" [label="7.3 Preserved bounds-only global stability"] |
| "prop:sharp" [label="7.4 The exponent $1/2$ cannot generally be improved"] |
| "thm:free" [label="8.1 Sharp growth per unit time"] |
| "thm:quantum" [label="9.1 Exact finite-cycle and asymptotic quantum laws"] |
| "cor:quantumargmax" [label="9.2 Resource-constrained classical--quantum extremality"] |
| "prop:quantumfinite" [label="9.3 Finite-cycle photon optimization is a different problem"] |
| "thm:quantumstability" [label="9.4 Finite-observation quantum rigidity"] |
| "lem:boxselector" [label="10.1 The exact corner selector"] |
| "lem:boxclock" [label="10.2 A strictly monotone clock"] |
| "thm:boxfixed" [label="10.3 Complete fixed-period Maxwell corner-purity theorem"] |
| "cor:boxfree" [label="10.4 Free-period rectangle rate and quantum optimum"] |
| "prop:boxstability" [label="10.5 Rectangle structural stability"] |
| "lem:polylinear" [label="11.1 Fractional barycentric linearization"] |
| "thm:polyresource" [label="11.2 Affine-resource calibration, purity, and finite switching"] |
| "thm:abstract" [label="11.3 Preserved calibrated rotating-polytope extremality"] |
| "thm:boxresource" [label="12.1 Explicit two-resource Maxwell extremality"] |
| "lem:boxnormal" [label="12.2 Boundary moments and normal duals for two Maxwell resources"] |
| "lem:boxpalindrome" [label="12.3 Time reversal locks the two diagonal visits"] |
| "prop:boxresourceconcavity" [label="12.4 Resource-ray concavity and rate calibration"] |
| "cor:boxresourceStability" [label="12.5 Two-resource Maxwell stability and quantum extremality"] |
| "prop:inversefailure" [label="13.1 Exact two-layer isodiscriminant counterexample"] |
| "thm:inverse" [label="14.1 Finite derivatives determine every reduced layer"] |
| "lem:prony" [label="14.2 Finite exponential determination"] |
| "lem:peel" [label="14.3 Recovering the leading temporal layer"] |
| "prop:datacount" [label="15.1 Preserved regular-data lower bound"] |
| "lem:projection" [label="15.2 A direct generic projection bound"] |
| "thm:jetCompression" [label="15.3 Linear-count compression of exact transfer data"] |
| "prop:CAD" [label="15.4 Certified projection search for algebraic inputs"] |
| "prop:localInverse" [label="15.5 Local inverse conditioning at regular points"] |
| "thm:rigidityCompression" [label="15.6 Saturation is an inverse certificate"] |
| "prop:nearNoGo" [label="15.7 No finite exact inverse for the entire near-extremal class"] |
| "foundation:projective" -> "lem:linearize" |
| "foundation:fractional" -> "lem:linearize" |
| "lem:linearize" -> "lem:boundary" |
| "foundation:convex" -> "lem:boundary" |
| "lem:linearize" -> "lem:normal" |
| "lem:boundary" -> "lem:normal" |
| "foundation:convex" -> "lem:normal" |
| "lem:normal" -> "thm:resource" |
| "foundation:fractional" -> "thm:resource" |
| "foundation:segments" -> "thm:resource" |
| "thm:resource" -> "thm:resourceDefect" |
| "lem:normal" -> "thm:resourceDefect" |
| "foundation:fractional" -> "thm:resourceDefect" |
| "lem:normal" -> "thm:concavity" |
| "thm:resource" -> "thm:concavity" |
| "foundation:convex" -> "thm:concavity" |
| "thm:concavity" -> "thm:resourceFree" |
| "thm:resourceDefect" -> "thm:resourceFree" |
| "foundation:fractional" -> "lem:margin" |
| "lem:margin" -> "thm:phasestability" |
| "thm:resourceDefect" -> "thm:phasestability" |
| "foundation:projective" -> "thm:phasestability" |
| "thm:phasestability" -> "thm:globalstability" |
| "thm:resource" -> "thm:globalstability" |
| "foundation:segments" -> "prop:resourceSharp" |
| "thm:resource" -> "prop:resourceSharp" |
| "foundation:projective" -> "thm:main" |
| "foundation:fractional" -> "thm:main" |
| "foundation:segments" -> "thm:main" |
| "thm:main" -> "thm:defect" |
| "foundation:fractional" -> "thm:defect" |
| "thm:main" -> "cor:boundstability" |
| "thm:defect" -> "cor:boundstability" |
| "thm:phasestability" -> "cor:boundstability" |
| "foundation:segments" -> "prop:sharp" |
| "thm:main" -> "prop:sharp" |
| "thm:main" -> "thm:free" |
| "thm:defect" -> "thm:free" |
| "foundation:maxwell" -> "thm:quantum" |
| "foundation:linear_algebra" -> "thm:quantum" |
| "thm:quantum" -> "cor:quantumargmax" |
| "thm:resource" -> "cor:quantumargmax" |
| "thm:globalstability" -> "cor:quantumargmax" |
| "foundation:segments" -> "prop:quantumfinite" |
| "thm:quantum" -> "prop:quantumfinite" |
| "thm:resource" -> "prop:quantumfinite" |
| "thm:quantum" -> "thm:quantumstability" |
| "thm:globalstability" -> "thm:quantumstability" |
| "foundation:ode" -> "thm:quantumstability" |
| "foundation:maxwell" -> "lem:boxselector" |
| "foundation:fractional" -> "lem:boxselector" |
| "lem:boxselector" -> "lem:boxclock" |
| "lem:boxclock" -> "thm:boxfixed" |
| "lem:boxselector" -> "thm:boxfixed" |
| "foundation:projective" -> "thm:boxfixed" |
| "thm:boxfixed" -> "cor:boxfree" |
| "thm:quantum" -> "cor:boxfree" |
| "thm:boxfixed" -> "prop:boxstability" |
| "thm:phasestability" -> "prop:boxstability" |
| "thm:quantumstability" -> "prop:boxstability" |
| "foundation:projective" -> "lem:polylinear" |
| "foundation:fractional" -> "lem:polylinear" |
| "lem:polylinear" -> "thm:polyresource" |
| "foundation:convex" -> "thm:polyresource" |
| "thm:polyresource" -> "thm:abstract" |
| "lem:polylinear" -> "lem:boxnormal" |
| "foundation:convex" -> "lem:boxnormal" |
| "lem:boxselector" -> "lem:boxnormal" |
| "lem:boxnormal" -> "lem:boxpalindrome" |
| "foundation:segments" -> "lem:boxpalindrome" |
| "foundation:projective" -> "lem:boxpalindrome" |
| "lem:boxnormal" -> "prop:boxresourceconcavity" |
| "lem:boxpalindrome" -> "prop:boxresourceconcavity" |
| "foundation:convex" -> "prop:boxresourceconcavity" |
| "lem:boxnormal" -> "thm:boxresource" |
| "lem:boxpalindrome" -> "thm:boxresource" |
| "prop:boxresourceconcavity" -> "thm:boxresource" |
| "foundation:projective" -> "thm:boxresource" |
| "thm:boxresource" -> "cor:boxresourceStability" |
| "prop:boxstability" -> "cor:boxresourceStability" |
| "thm:quantum" -> "cor:boxresourceStability" |
| "thm:quantumstability" -> "cor:boxresourceStability" |
| "foundation:segments" -> "prop:inversefailure" |
| "foundation:linear_algebra" -> "lem:prony" |
| "foundation:analytic_jets" -> "lem:peel" |
| "foundation:segments" -> "lem:peel" |
| "lem:prony" -> "thm:inverse" |
| "lem:peel" -> "thm:inverse" |
| "foundation:analytic_jets" -> "thm:inverse" |
| "thm:inverse" -> "prop:datacount" |
| "foundation:inverse_function" -> "prop:datacount" |
| "foundation:inverse_function" -> "lem:projection" |
| "thm:inverse" -> "thm:jetCompression" |
| "lem:projection" -> "thm:jetCompression" |
| "prop:datacount" -> "thm:jetCompression" |
| "thm:jetCompression" -> "prop:CAD" |
| "foundation:analytic_jets" -> "prop:CAD" |
| "external:real_QE" -> "prop:CAD" |
| "prop:datacount" -> "prop:localInverse" |
| "thm:inverse" -> "prop:localInverse" |
| "thm:jetCompression" -> "prop:localInverse" |
| "foundation:inverse_function" -> "prop:localInverse" |
| "thm:resource" -> "thm:rigidityCompression" |
| "thm:concavity" -> "thm:rigidityCompression" |
| "thm:quantum" -> "thm:rigidityCompression" |
| "thm:boxresource" -> "thm:rigidityCompression" |
| "thm:resource" -> "prop:nearNoGo" |
| "prop:datacount" -> "prop:nearNoGo" |
| "foundation:ode" -> "prop:nearNoGo" |
| } |
|
|
