Reusable result
Reuse the operational future quotient
Minimality is proved for fixed r and a fixed experiment alphabet.
For a new attempt: Do not infer a physical Hilbert space or TFPT source selector from it.
Read the question and its evidenceExplore the foundations and current research.
Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
What has been tried, and what follows
Reusable result
Reuse conditional positive GNS reconstruction
Cyclic GNS construction and uniqueness are reusable under explicit K conditions.
For a new attempt: It remains open which complete K the original source supplies.
Read the question and its evidenceInsufficient for the goal
Polynomial degree as a physical source selector
The cited original seed definition assumes A_loc, tau_t, Theta, omega, [u_Sigma], and D_coll as data and shows only their collar completion. This cited evidence supplies no rule selecting the common physical source from a polynomial degree.
For a new attempt: Provide an explicit original-source rule mapping degree to source selection before assessing the strategy as a selector.
Read the question and its evidenceReusable result
Order-four markings from given time and full charge
The whole family is completed by lattice saturation and exact classification, including an original-frame control.
For a new attempt: New knowledge requires a justified change to the original source operator or its field/sector map; further phases of the same family are already covered.
Read the question and its evidenceInsufficient for the goal
Use an internal character hit as physical source selection
All candidates retain the missing original field/state identification. The composed marking does not prove that identification.
For a new attempt: Identify the actual original seam action on the same collar/field core, including domain, state and full time.
Read the question and its evidenceInsufficient for the goal
Infer unique source from minimal defect
The proof does not classify the minimal operator fiber.
For a new attempt: Actually classify operator structures in the minimal fiber; do not relabel well-ordering or presentation invariance as uniqueness.
Read the question and its evidenceReusable result
Scan further scalar Hardy isometries
The whole continuous class is covered analytically; more Blaschke parameters provide no new selection.
For a new attempt: Supply a P1-grounded change of source class or actual operator action.
Read the question and its evidenceReusable result
Minimize seam energy within the same scalar source
The entire H1 class is solved by E=alpha+Var(phi prime)/2; additional genotypes or GPU grids are unnecessary.
For a new attempt: Derive the physical source and least-excitation rule from P1; do not replace their selection with optimization inside a supplied source.
Read the question and its evidenceInsufficient for the goal
Use the downstream master functional as an original selector
The allowed source is already named in the zero/infinity barrier. A minimum on that restricted branch does not prove this upstream selection.
For a new attempt: Supply a selection rule computable from original data without a presumed B_min and prove its relation to the actual field/state/time operator.
Read the question and its evidenceScoped exclusion
Identify geometric deck lift with boundary polarization
The general implication from reflection regularity is disproved by a compact Dirac counterexample; carrier restrictions built on it need their actual operator map established again.
For a new attempt: Keep geometric lift, normal Clifford action and Calderon polarization distinct. For dynamics retain the full two-face relation and use the already verified inverse reader.
Read the question and its evidenceScoped exclusion
Obtain mixed carrier by restriction to the positive-only space
The actual restriction is identity; the negative sector has already been removed. Additional spectral tests cannot repair this type error.
For a new attempt: Retain field space and internal marking action before state projection. Check an actual embedding W with (2G−I)W=W epsilon if that polarization is intended; for a separate internal involution supply its source origin. Do not count an inserted 3+2 matrix as a derivation.
Read the question and its evidenceScoped exclusion
Invariant-ring primitiveness as rank selector
The explicit minimum-degree primitive 5+2 tensor satisfies even fermion degrees and the same invariance. The local argument does not exclude it.
For a new attempt: Prove tensor support, a degree bound or global-minimality rule actually derived from the original source; do not again identify primitiveness with contraction surjectivity.
Read the question and its evidence