Algebra before AI
Why formal structure, admissibility, and claim authority have to exist before learned inference is allowed to act.
Theme archive
17 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.
17 works
What is genuinely new, precisely.
A proof-checked living algebra of physical observables, situated carefully against the fields nearest to it.
A boundary-observable certification algebra
How mathematical freedom is progressively admitted through physical consistency, closure, witness, and evidentiary maturity.
The temperament of a bespoke algebra
What repeated behavior under proof reveals about the character of a mathematical object built for measurement.
Continuation Anatomy of Periodic Navier–Stokes Breakdown
A machine-checked H² theory of finite-energy regularity escape.
Finite maximality is resolved into bounded kinetic energy, eventual H² divergence, escape beyond every fixed Fourier cutoff, positive-scale regularity, and collapse of uniform continuation reserve.
Critical Regularity Anatomy of Periodic Navier–Stokes Breakdown
Spectral transfer, terminal nonlinear H² work, and simultaneous failure of nonendpoint continuation controls.
The continuation anatomy is sharpened through finite-annulus spectral budgets, unbounded terminal nonlinear H² work, and simultaneous failure of nonendpoint continuation regimes.
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.
Master-Action Ownership of a Self-Consistent Einstein–Scalar Quantum Sector
Symmetric-projective BV closure, Palatini descent, and quantum Ward/source exchange.
The completed Einstein–scalar sector is traced upstream to an intrinsic symmetric/projective Palatini BV theory whose classical projection binds back to the same native action, source, and clock.
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.
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.
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.