Datasets:

PureOne
/

Chisael-Nexythra

{"claim_id": "nonlinear_calendar", "title": "Exact finite nonlinear helicity-event calendar", "statement": "The manuscript presents a small-data global smooth unforced periodic incompressible Navier–Stokes realization, at fixed positive viscosity, of a finite helicity-zero calendar with specified finite positive multiplicities, a later nonzero anchor, nonzero initial projected advection and vortex stretching, and no additional nonnegative-time zeros.", "scope_and_limitations": "Finite calendar, sufficiently small specifically parameterized perturbation, smooth periodic incompressible setting. The entire between-event curve is not prescribed; allowable perturbation interval is existential.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/02_nonlinear.tex", "source_label": "ch:nonlinear", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "quadratic_retuning", "title": "Even analytic repair of an observable calendar", "statement": "For the specified transverse perturbation, carrier retuning is analytic and even in epsilon, with first allowed correction of order epsilon squared, whereas initial projected interaction already has a nonzero first-order term.", "scope_and_limitations": "Specific half-period translation symmetry and local implicit-function construction. No general robustness guarantee or certified numerical perturbation interval.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/02_nonlinear.tex", "source_label": "ch:retuning", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "triad_acceleration", "title": "Nonhelical triad helicity acceleration", "statement": "For the specified three linearly polarized waves, H(0)=H′(0)=0 and H″(0)=2 nu a b c cos(Phi).", "scope_and_limitations": "Specified wavevectors and polarizations with source Fourier normalization. A closed triad has only two independent wavevector directions.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:triad", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "triad_kernel", "title": "Exact third mixed amplitude response", "statement": "The third mixed amplitude derivative of helicity at zero amplitudes is exp(-6 nu t) [exp(4 nu t)-1-4 nu t] cos(Phi)/(8 nu). Its phase-independent factor is positive for nu>0 and t>0.", "scope_and_limitations": "An exact derivative of the solution map, not the complete finite-amplitude helicity history or a global positivity result for that history.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:triad", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "quadrature_extinction", "title": "Symmetry-protected total helicity extinction", "statement": "At quadrature phase Phi=pi/2 modulo pi, orientation-reversing symmetry forces total helicity to vanish throughout the smooth evolution, globally for sufficiently small data.", "scope_and_limitations": "Observable extinction does not imply stopped motion, zero interaction, or absence of energy dissipation.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:phase", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "energy_clock", "title": "Event multiplicity in the energy coordinate", "statement": "When energy and helicity share a common nondecreasing operational clock and underlying energy decreases strictly, the unparameterized energy–helicity curve and event multiplicities are preserved under retiming.", "scope_and_limitations": "Common clock and strictly decreasing underlying energy required. Pauses are an imposed process-clock model, not physical time freezing.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:clock", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "finite_optimizer", "title": "Finite-library weighted-L1 energy compiler", "statement": "The heat-carrier finite-library design problem admits a weighted-L1 primal and explicit dual certificate; some optimum uses the minimal M+1 carriers for total event multiplicity M with an anchor.", "scope_and_limitations": "Limited carrier library and scaffold class; not a global energy optimum over arbitrary nonlinear flows. Numerical certificates are floating point.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:resource", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "momentum_words", "title": "Selection rule for mixed Fourier responses", "statement": "Translation invariance restricts squarefree mixed derivatives by a zero-sum momentum-word condition; the construction supplies arbitrarily long minimal mixed words.", "scope_and_limitations": "Squarefree mixed responses only. Repeated parameters can appear earlier, and allowed momentum words may have zero coefficients.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:selection", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "mirror_twins", "title": "Energy-only handedness nonidentifiability", "statement": "Reflected flows have identical energy histories and parity-even quadratic observations while their helicities have opposite signs.", "scope_and_limitations": "Reflection is classical. This is an observability obstruction for the specified measurements, not invisibility to all measurements.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:stability", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "root_sensitivity", "title": "Multiplicity-dependent root sensitivity", "statement": "Near a root of multiplicity m, characteristic displacement under an observation perturbation can scale as the m-th root of the error.", "scope_and_limitations": "Local scaling under stated hypotheses. Table 15 is an illustrative power-law chart, not measured simulation errors.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:stability", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
{"claim_id": "exponential_compiler", "title": "Minimal exponential calendar scaffold", "statement": "Confluent exponential interpolation supplies a finite signed spectrum realizing the selected zeros and anchor, with minimal carrier count and strict exclusion of extra zeros in the scaffold.", "scope_and_limitations": "Chebyshev-system and exponential-interpolation ingredients are established mathematics; novelty is proposed for the combined nonlinear framework.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/01_foundations.tex", "source_label": "ch:exponentials", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}

	{"claim_id": "nonlinear_calendar", "title": "Exact finite nonlinear helicity-event calendar", "statement": "The manuscript presents a small-data global smooth unforced periodic incompressible Navier–Stokes realization, at fixed positive viscosity, of a finite helicity-zero calendar with specified finite positive multiplicities, a later nonzero anchor, nonzero initial projected advection and vortex stretching, and no additional nonnegative-time zeros.", "scope_and_limitations": "Finite calendar, sufficiently small specifically parameterized perturbation, smooth periodic incompressible setting. The entire between-event curve is not prescribed; allowable perturbation interval is existential.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/02_nonlinear.tex", "source_label": "ch:nonlinear", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "quadratic_retuning", "title": "Even analytic repair of an observable calendar", "statement": "For the specified transverse perturbation, carrier retuning is analytic and even in epsilon, with first allowed correction of order epsilon squared, whereas initial projected interaction already has a nonzero first-order term.", "scope_and_limitations": "Specific half-period translation symmetry and local implicit-function construction. No general robustness guarantee or certified numerical perturbation interval.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/02_nonlinear.tex", "source_label": "ch:retuning", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "triad_acceleration", "title": "Nonhelical triad helicity acceleration", "statement": "For the specified three linearly polarized waves, H(0)=H′(0)=0 and H″(0)=2 nu a b c cos(Phi).", "scope_and_limitations": "Specified wavevectors and polarizations with source Fourier normalization. A closed triad has only two independent wavevector directions.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:triad", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "triad_kernel", "title": "Exact third mixed amplitude response", "statement": "The third mixed amplitude derivative of helicity at zero amplitudes is exp(-6 nu t) [exp(4 nu t)-1-4 nu t] cos(Phi)/(8 nu). Its phase-independent factor is positive for nu>0 and t>0.", "scope_and_limitations": "An exact derivative of the solution map, not the complete finite-amplitude helicity history or a global positivity result for that history.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:triad", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "quadrature_extinction", "title": "Symmetry-protected total helicity extinction", "statement": "At quadrature phase Phi=pi/2 modulo pi, orientation-reversing symmetry forces total helicity to vanish throughout the smooth evolution, globally for sufficiently small data.", "scope_and_limitations": "Observable extinction does not imply stopped motion, zero interaction, or absence of energy dissipation.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:phase", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "energy_clock", "title": "Event multiplicity in the energy coordinate", "statement": "When energy and helicity share a common nondecreasing operational clock and underlying energy decreases strictly, the unparameterized energy–helicity curve and event multiplicities are preserved under retiming.", "scope_and_limitations": "Common clock and strictly decreasing underlying energy required. Pauses are an imposed process-clock model, not physical time freezing.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/03_triad_clock.tex", "source_label": "ch:clock", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "finite_optimizer", "title": "Finite-library weighted-L1 energy compiler", "statement": "The heat-carrier finite-library design problem admits a weighted-L1 primal and explicit dual certificate; some optimum uses the minimal M+1 carriers for total event multiplicity M with an anchor.", "scope_and_limitations": "Limited carrier library and scaffold class; not a global energy optimum over arbitrary nonlinear flows. Numerical certificates are floating point.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:resource", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "momentum_words", "title": "Selection rule for mixed Fourier responses", "statement": "Translation invariance restricts squarefree mixed derivatives by a zero-sum momentum-word condition; the construction supplies arbitrarily long minimal mixed words.", "scope_and_limitations": "Squarefree mixed responses only. Repeated parameters can appear earlier, and allowed momentum words may have zero coefficients.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:selection", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "mirror_twins", "title": "Energy-only handedness nonidentifiability", "statement": "Reflected flows have identical energy histories and parity-even quadratic observations while their helicities have opposite signs.", "scope_and_limitations": "Reflection is classical. This is an observability obstruction for the specified measurements, not invisibility to all measurements.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:stability", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "root_sensitivity", "title": "Multiplicity-dependent root sensitivity", "statement": "Near a root of multiplicity m, characteristic displacement under an observation perturbation can scale as the m-th root of the error.", "scope_and_limitations": "Local scaling under stated hypotheses. Table 15 is an illustrative power-law chart, not measured simulation errors.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/04_resources_selection.tex", "source_label": "ch:stability", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}
	{"claim_id": "exponential_compiler", "title": "Minimal exponential calendar scaffold", "statement": "Confluent exponential interpolation supplies a finite signed spectrum realizing the selected zeros and anchor, with minimal carrier count and strict exclusion of extra zeros in the scaffold.", "scope_and_limitations": "Chebyshev-system and exponential-interpolation ingredients are established mathematics; novelty is proposed for the combined nonlinear framework.", "proof_status": "analytical proof supplied in source draft; independent review pending", "novelty_status": "candidate combined construction; component mathematics established; historical priority unverified", "source_path": "research/chapters/01_foundations.tex", "source_label": "ch:exponentials", "audit_path": "research/CLAIM_AUDIT.md", "source_version": "1.0.0"}