Bryan Ehrlich
Axioms
A. Self-modeling. A system is self-modeling if it contains a structure-preserving representation of its own operationally accessible state and effect structure.
B. Relativity of isomorphism. Physical counting is over equivalence classes under structure-preserving isomorphism; each presentation x is weighted by 1/|Aut(x)|.
Under review
5. Quantum Mechanics from Self-Modeling: Deriving Complex C*-Algebraic Structure from a Single Operational Premise submitted to JMP
The one result in this program I'd defend as peer-review ready. Four structural conditions on a finite-dimensional system (spectral state space, faithful internal tracking, minimal body-model composite, simplicity) force it to be isomorphic to Mn(ℂ)sa with the Lüders product. The complex field and C*-involution are derived, not assumed. The downstream chain is machine-verified in Lean 4 (0 sorry, 16 axioms, each citing a published theorem). Currently at the Journal of Mathematical Physics.
Exploratory — where the program might go
These papers ask: if Paper 5's theorem is right, what else does self-modeling force? The answers are speculative. Each paper has been through multiple rounds of adversarial review and survives at a conditional level (“if you grant X, then Y”). None is ready for peer review. They're here as scaffolding for a research program and to make the current gaps visible.
7. The Standard Model from Self-Modeling: Gauge Structure from the Observer-Universe Interface exploratory
Conditional on h3(O) being the arena, it houses — rather than derives — the Standard Model gauge group (U(1)×SU(2)×SU(3))/Z6 (matching the Todorov-Drenska F4∩Spin(9) result) and produces genuine parity violation (the left/right labeling is conventional, and reducing the verified left-right-symmetric content to the Standard Model's chiral form takes an extra input). The complexification step is argued, not proved — the paper's central weakness.
6. The Self-Modeling Basin Is Exceptional Supergravity retracted
Retracted. This paper matched the self-modeling basin h3(O) to the exceptional entry in the GST classification of N=2 Maxwell-Einstein supergravity, and read the Einstein-Hilbert term (−R/2) in that theory's Lagrangian as a derivation of gravity. The error was conflating kinematics with dynamics. The algebra does force the kinematic structure — the 4D arena, the matter content, the cubic coupling constants. It does not force the dynamics — that the metric is a field obeying Einstein's equations. Supergravity has gravity built in by definition, so matching our kinematic data to it and finding −R/2 there recovers an assumption rather than deriving anything. Later (unpublished) work asks the algebra for the dynamics directly: a matter-sourced spin-2 mode does appear, but nothing forces the metric to obey a field equation. Honest position: self-modeling forces the arena, quantum mechanics, and the matter content — the kinematics — but gravity's dynamical law looks genuinely separate. An incomplete theory, not a theory of everything. The PDF stays up as the original; a revised Paper 6 will come out of the current work.
1. Experiential Measure on the Structure Space of Self-Modeling Systems exploratory
Defines a density functional ρ on self-modeling structures and conjectures a connection to phenomenal experience. Section 10 (Lean verified) proves that ρJ = det(X)(Tr(X2)−1/3) is the unique lowest-degree F4-invariant with specific boundary conditions on h3(O). The math is clean; the interpretation as an experiential measure is a philosophical claim on top of the math, not a theorem.
Supporting & earlier results
2. Exponential Suppression of Transient-Basin Contributions in Trajectory-Weighted Markov Chain Measures
Boltzmann brain negligibility via 7-lemma composition from metastability theory. Verified.
2b. Theorem A: Lemma Assembly
All 7 constituent lemmas with error terms, citations, and dependency graph.
3. Lipschitz Stability of the Experiential Density Functional
Proves the density is Lipschitz continuous under kernel perturbations. 3000-perturbation numerical validation.
4. Falsification of the Born-Fisher-Experiential Conjecture in a Qubit Toy Model negative result
Tests and falsifies an earlier conjecture I had about ρ dynamically selecting Born probabilities. The Born rule follows from Gleason's theorem once Paper 5's C*-algebra structure is in place, not from the experiential measure. Published here because killing your own conjectures is part of the work.