Theoretical study demonstrates universal obstruction cohomology in categorified spectral objects, indicating higher-order contextuality detection beyond single obstruction classes.
Key Points
To establish an intrinsic obstruction cohomology framework for admissible operator-semantic systems derived directly from their categorified spectra without requiring an external geometric model.
Constructed graded obstruction cohomology using canonical descent filtrations on categorified spectral objects.
Formulated an axiomatic framework satisfying generalized Eilenberg-Steenrod properties, including long exact sequences, Mayer-Vietoris sequences, and excision.
Derived dualities between the tangent complex and obstruction sheaves to analyze contextuality across all cohomological degrees.
Proved that the obstruction cohomology serves as the universal initial object through which all representable descent-compatible obstruction invariants uniquely factor.
Established a Representation Theorem identifying obstruction cohomology with shifted derived global sections of an intrinsic obstruction sheaf, yielding canonical duality with the tangent complex.
Demonstrated a Higher Contextuality Detection Theorem showing contextuality is governed across a graded spectrum of all positive cohomological degrees rather than a single degree-two class.