Fixedness
What must remain invariant for a changing system to remain itself, and how measurement keeps hold of identity through transformation.
Theme archive
18 current works connected to this question.
This page is a cross-corpus projection: technical papers and notebook pieces remain distinct objects, but can be browsed together when they address the same durable research question.
18 works
Reading the living boundary
A relational account of gradients, exchange, laminarity, reconstruction, and what an instrument can learn from a living surface.
Residue and residual
Two different remainders: what a living boundary retains, and what remains after a model has been tested against a law.
The making of an observable
How calibration, reconstruction, residual analysis, transport preservation, and claim maturity turn a signal into an observable.
Endpoint Rigidity in Periodic Navier–Stokes Flow
Terminal magnification, intrinsic restart, and analytic rigidity at the L∞t L³x boundary.
Bounded terminal L³ forces global continuation, while finite maximal time forces infinite terminal L³ limsup through magnification, restart, backward identification, and rigidity.
Critical Schwarzschild Scalar Dynamics
A machine-checked operator theory of terminal self-adjoint laws and Friedrichs selection.
A Hardy-critical radial operator with a genuine family of self-adjoint terminal laws is reduced by a ground-state form to the Friedrichs-selected no-log realization.
Friedrichs-Selected Schwarzschild Quantum Dynamics
A machine-checked continuum Fock theory and real-scalar physical Cauchy evolution.
Friedrichs selection is propagated into positive one-particle frequency, continuum bosonic Fock dynamics, and an independently action-derived physical Cauchy theory.
Friedrichs-Selected Schwarzschild Quantum Matter
A machine-checked real-scalar stress theory, physical-clock coherence, and regulator-independent sources.
The selected scalar is promoted from quantum dynamics to local spacetime matter through action-derived stress, coherent Fock moments, regulator removal, and explicit quantum sources.
A Self-Consistent Einstein–Scalar Quantum Sector
Friedrichs selection, native quantum evolution, and exact gravitational matter.
The changed nonlinear geometry owns its own selected quantum law, Fock/Cauchy dynamics, conserved stress, and exact quantum-source branches satisfying Einstein's equation on that same geometry.
Quantum Gauge Structure of a Self-Consistent Einstein–Scalar Sector
Operator BRST representation, a retracted physical Hilbert sector, and projective gauge reduction.
A square-zero BRST charge realizes physical cohomology, embeds the native scalar Fock space faithfully, descends native evolution, and removes the Palatini projective quartet cohomologically.
Regulated Palatini BV Quantization of a Self-Consistent Einstein–Scalar Sector
Quantum-master obstructions, finite Gaussian BV pushforwards, and restricted physical cohomology.
Finite BV regulators support genuine quantum complexes, while Gaussian refinement exposes a first-shell Hamiltonian descent obstruction and canonically leaves a greatest compatible restricted physical complex.
Relational Quantum Gravity in a Self-Consistent Einstein–Scalar Sector
Independent physical and gravitational quotients, nonlinear Einstein realization, and intrinsic gauge rigidity.
Physical-owner and gravity-visible equivalence relations are globally incomparable, while intrinsic curvature data rigidly recover the source parameter and represented geometry class on the fixed nonlinear family.
Closed Matter-Current Constraints and Gaussian Physical Moduli
Bounded-particle exclusion and all-orders Fock structure in a machine-checked gauge-field model.
Every nonzero joint closed-current state extends beyond every finite particle cutoff while the same kernel contains an injectively parametrized positive-orthant Gaussian family.
Pair-Generated Completion of Gaussian Physical States
Closed quadratic generators, faithful two-particle seeds, and nontruncatable current physicality in a machine-checked gauge-field model.
A symmetric pair kernel and canonical quadratic creator reconstruct every even sector; the normalized two-particle seed faithfully recovers the Gaussian modulus.
From Pair-Generated Fock Structure to Physical Particle Semantics
Completed Bose/Fock representations, analytic carrier realization, and the boundary of asymptotic particle identity in a machine-checked gauge-field model.
The Gaussian pair receives an exact completed Bose/Fock realization with intertwined Poincaré symmetry while asymptotic-particle identification remains a separate boundary.
Gaussian Pair Geometry and Physical Radiative Response
Quadratic-sector variational stress, physical-helicity response, and exact information compression in a machine-checked gauge-field model.
A faithful three-parameter covariance passes through response maps that retain less information: zero variational stress, one-parameter radiative response, and finally a scale-independent normalized Bose pair.
Source-Aware Weyl-Reduced Celestial Representation
Joint source-output symmetry and positive-measure obstruction to fixed-source isometry for radiative two-particle Clebsch–Gordan kernels.
Source-aware Weyl reflection admits an exact joint Hilbert reduction, while a positive-measure Gram defect rules out almost-everywhere fixed-source isometric realization of the normalized physical kernel.
The Physical Celestial Clebsch–Gordan Transform of a Radiative Bose Pair
Direct-integral completion, source-Weyl geometry, and all-label uniqueness on the intrinsic physical source range.
On the intrinsic physical source range, the cross-ratio and full signed principal-series transforms are injective for every physical external-label pair, while the retained bounded completion remains conditional on one explicit uniform core estimate.