I
Published preprint
Critical Schwarzschild Scalar Dynamics
A machine-checked operator theory of terminal self-adjoint laws and Friedrichs selection.
Program
A quantum sector is carried from operator law to gravitational ownership.
The sequence begins with the critical Schwarzschild scalar operator and its Friedrichs-selected terminal law. That choice is propagated into continuum Fock dynamics and then into action-derived local quantum matter. The geometry is next required to own the same matter law self-consistently rather than importing it from a background.
The middle papers move upstream into action and gauge structure. The self-consistent Einstein–scalar sector is bound to a Palatini master action, a square-zero BRST representation, and a regulated BV/QME program whose finite quantum complexes expose both positive substructures and explicit obstruction surfaces.
The eighth paper then separates two relations that gravity can otherwise tempt us to identify: physical ownership and gravitational visibility. Their quotient structures are globally incomparable, while intrinsic curvature data rigidly recover the source parameter on the realized nonlinear family.
When a quantum matter sector backreacts on geometry, which structures genuinely belong to the same physical owner, and which equivalences are visible only to gravity?
Paper sequence
Eight stages from scalar selection to relational gravity.
II
Published preprint
Friedrichs-Selected Schwarzschild Quantum Dynamics
A machine-checked continuum Fock theory and real-scalar physical Cauchy evolution.
III
Published preprint
Friedrichs-Selected Schwarzschild Quantum Matter
A machine-checked real-scalar stress theory, physical-clock coherence, and regulator-independent sources.
IV
Published preprint
A Self-Consistent Einstein–Scalar Quantum Sector
Friedrichs selection, native quantum evolution, and exact gravitational matter.
V
Published preprint
Master-Action Ownership of a Self-Consistent Einstein–Scalar Quantum Sector
Symmetric-projective BV closure, Palatini descent, and quantum Ward/source exchange.
VI
Published preprint
Quantum Gauge Structure of a Self-Consistent Einstein–Scalar Sector
Operator BRST representation, a retracted physical Hilbert sector, and projective gauge reduction.
VII
Published preprint
Regulated Palatini BV Quantization of a Self-Consistent Einstein–Scalar Sector
Quantum-master obstructions, finite Gaussian BV pushforwards, and restricted physical cohomology.
VIII
Published preprint
Relational Quantum Gravity in a Self-Consistent Einstein–Scalar Sector
Independent physical and gravitational quotients, nonlinear Einstein realization, and intrinsic gauge rigidity.