Datasets:

PureOne
/

eve-3d-conductivity-function-closure-v6

id,title,audit_class,novelty_class,dependencies,location,scope
T01,"Physical compression, spectral representation and binary deficit",A,1,,main §2; supplement §1,All measurable gray periodic coefficients
T02,Joint mean-and-moment topology and compactness,G,1,T01,main §2; supplement §1,Mean must be retained when it varies
T03,Geometry-uniform response continuity,C,4,T01,main §3; supplement §2,Meyers qualitative route; compact-torus Riesz theorem for explicit constants
T04,Exact-fraction cubic whole-function density,C,0,T01;T02;T03,main §4; supplement §3,Finite-chamber local periodic homogenization is an explicit classical dependency
T05,Positive cubic Bernstein template density and exact operator polynomials,A,0,T01,main §7; supplement §4,Expanding Fourier support; no fixed-band PDE truncation
T06,Exact fraction-constrained bathtub rounding,A,1,,main §5,Nonatomic space; invariant quotient for cubic preservation
T07,Sharp variable-fraction mean/deficit rounding envelope,A,5,T06,main §5,"Sharp given m, B, theta; simple S penalty retained in compiler"
T08,Abstract calibrated closure distance and sharp universal factor,A,3,,main §6; supplement §7,Requires independently proved recovery and vanishing-penalty density
T09,Explicit full-cube reference-localizer convergence,A,1,,main §9; supplement §6,Known full-support reference measure; no Putinar or convexity hypothesis
T10,Response-only calibrated physical-distance hierarchy,A,4,T01;T02;T03;T04;T05;T06;T08;T09,main §1 statement; §9 proof,Unrestricted periodic isotropic function closure; exhaustive infinite normal form
T11,Single running hierarchy for exact squared physical distance,A,3,T10,"main §§1,6,9; supplement §7",Running minimum includes positive integer penalty; raw rescaled sequence need not be monotone
T12,Finite complex observations without latent spectral extension,A,4,T03;T05;T09;T10,main §8 and §9,Fixed nodes anywhere in slit plane; value data and Taylor-at-one modes
T13,Finite strict approximation certificates and binary extraction,A,4,T06;T09;T10;T11,main §9; supplement §8,"Finite error bound, not a finite exact membership verdict"
T14,Convex contact dual without convexifying physical attainability,A,3,T10,main §10; supplement §7,Underlying real Hilbert pairing for complex data
T15,"Noise, fraction continuity and bounded-data uniform penalty limit",A,3,T03;T08;T10,"main §§6,10",Penalty convergence is not template/localizer complexity convergence
T16,Finite-information separation of nonphysical analytic candidates,A,3,T02;T04,main §10,No effective prefix-size bound or complete finite computational separator grammar
T17,Universal unit-circle inequality and exact midpoint rejection,A,0,T01;T02,main §11; supplement §12,"L2 quadratic proof, no determinant weak-continuity premise"
T18,Rank-escape and measurable high-frequency tail obstruction,A,0,T01;T02;T03;T06,supplement §11,Anisotropic tensor target; no BV; example itself laminated
T19,Independent boundary-compatible finite-certificate route,C,0,T01;T02,supplement §9,Alternative qualitative equivalence with spatial witnesses retained
T20,Failure of automatic stationary/GNS spatial completion,A,3,,supplement §10,Counterexamples to stochastic continuity and continuity of response under local laws
T21,Independent finite symbolic and physical regression checks,D,0,T01;T03;T05;T07;T09;T11;T17;T18,tests/ and verification/,Finite arithmetic and numerical evidence only

	id,title,audit_class,novelty_class,dependencies,location,scope
	T01,"Physical compression, spectral representation and binary deficit",A,1,,main §2; supplement §1,All measurable gray periodic coefficients
	T02,Joint mean-and-moment topology and compactness,G,1,T01,main §2; supplement §1,Mean must be retained when it varies
	T03,Geometry-uniform response continuity,C,4,T01,main §3; supplement §2,Meyers qualitative route; compact-torus Riesz theorem for explicit constants
	T04,Exact-fraction cubic whole-function density,C,0,T01;T02;T03,main §4; supplement §3,Finite-chamber local periodic homogenization is an explicit classical dependency
	T05,Positive cubic Bernstein template density and exact operator polynomials,A,0,T01,main §7; supplement §4,Expanding Fourier support; no fixed-band PDE truncation
	T06,Exact fraction-constrained bathtub rounding,A,1,,main §5,Nonatomic space; invariant quotient for cubic preservation
	T07,Sharp variable-fraction mean/deficit rounding envelope,A,5,T06,main §5,"Sharp given m, B, theta; simple S penalty retained in compiler"
	T08,Abstract calibrated closure distance and sharp universal factor,A,3,,main §6; supplement §7,Requires independently proved recovery and vanishing-penalty density
	T09,Explicit full-cube reference-localizer convergence,A,1,,main §9; supplement §6,Known full-support reference measure; no Putinar or convexity hypothesis
	T10,Response-only calibrated physical-distance hierarchy,A,4,T01;T02;T03;T04;T05;T06;T08;T09,main §1 statement; §9 proof,Unrestricted periodic isotropic function closure; exhaustive infinite normal form
	T11,Single running hierarchy for exact squared physical distance,A,3,T10,"main §§1,6,9; supplement §7",Running minimum includes positive integer penalty; raw rescaled sequence need not be monotone
	T12,Finite complex observations without latent spectral extension,A,4,T03;T05;T09;T10,main §8 and §9,Fixed nodes anywhere in slit plane; value data and Taylor-at-one modes
	T13,Finite strict approximation certificates and binary extraction,A,4,T06;T09;T10;T11,main §9; supplement §8,"Finite error bound, not a finite exact membership verdict"
	T14,Convex contact dual without convexifying physical attainability,A,3,T10,main §10; supplement §7,Underlying real Hilbert pairing for complex data
	T15,"Noise, fraction continuity and bounded-data uniform penalty limit",A,3,T03;T08;T10,"main §§6,10",Penalty convergence is not template/localizer complexity convergence
	T16,Finite-information separation of nonphysical analytic candidates,A,3,T02;T04,main §10,No effective prefix-size bound or complete finite computational separator grammar
	T17,Universal unit-circle inequality and exact midpoint rejection,A,0,T01;T02,main §11; supplement §12,"L2 quadratic proof, no determinant weak-continuity premise"
	T18,Rank-escape and measurable high-frequency tail obstruction,A,0,T01;T02;T03;T06,supplement §11,Anisotropic tensor target; no BV; example itself laminated
	T19,Independent boundary-compatible finite-certificate route,C,0,T01;T02,supplement §9,Alternative qualitative equivalence with spatial witnesses retained
	T20,Failure of automatic stationary/GNS spatial completion,A,3,,supplement §10,Counterexamples to stochastic continuity and continuity of response under local laws
	T21,Independent finite symbolic and physical regression checks,D,0,T01;T03;T05;T07;T09;T11;T17;T18,tests/ and verification/,Finite arithmetic and numerical evidence only