Theorem · Chain 56/192
T8.1
Sign Invariance Theorem
Knowledge
🔷 Theorem
7Q
0.925
9
Bridges
Ontological
Category
Physics; Theolog
Domain
gold
Status
None
Collapse Radius
Boundary Layer
Physics
Divine law/covenant
Theology
—
Scripture
—
Kills
Judge & Jury
Claims
Complete theory must satisfy boundary conditions.
Identity
Formal
Formal Statement
** For any self-generated unitary Û: [σ̂, Û] = 0. Proof 8.1: Û generated by system Hamiltonian → Û preserves system symmetries → sigma-hat eigenvalue unchanged.
Plain English
In Plain Words
Why This Type
Classification
Formal Architecture
Equation 1
$$\hat{U}(t) = e^{-iHt/\hbar}$$Equation 2
$$[\hat{\sigma}, H] = 0 \implies [\hat{\sigma}, e^{-iHt/\hbar}] = 0$$Equation 3
$$H_{self} = H_0 + V_{self}(\Psi_S)$$+1 more equations
Objections & Defense
Objection
This assumes unitarity—what if evolution isn't unitary?
"Real moral change might involve non-unitary processes from the start." Response: Self-operations are unitary by definition. Non-unitary evolution requires coupling to external systems (Lindblad…
Objection
Commutators can be zero accidentally
"Just because [σ̂, Û] = 0 doesn't mean σ is preserved. Eigenvalues could still change." Response: When two Hermitian operators commute, they share eigenstates.
Objection
What if the Hamiltonian is unbounded?
"Unbounded operators have domain issues. The theorem might not apply." Response: For physically realistic Hamiltonians (bounded below, finite energy), the generated unitaries are well-defined.
Collapse Analysis
Collapse Radius: None
If T8.1 fails: - Self-flip becomes possible (contradicts empirical observation) - C8.1 (Self-Flip Impossible) loses its proof - C8.2 (Works-Salvation Impossible) collapses - The entire soteriology of grace-dependence fails - People can save themselves (Pelagianism wins) - The external intervention argument (A9.1) is unmotivated T8.1 is the mathematical firewall against self-salvation.
Snapshot
Formal Statement
** For any self-generated unitary Û: [σ̂, Û] = 0. Proof 8.1: Û generated by system Hamiltonian → Û preserves system symmetries → sigma-hat eigenvalue unchanged. ---
Plain English