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, argues that an internal C*-observer's choice of idempotent and complex structure simultaneously yields the Standard Model gauge group (U(1)×SU(2)×SU(3))/Z6 and left-handed chirality. Matches the Todorov-Drenska F4∩Spin(9) result. The complexification step is argued, not proved — this is the paper's central weakness.
6. The Self-Modeling Basin Is Exceptional Supergravity exploratory
An identification theorem, not a derivation of GR. h3(O) uniquely matches the exceptional entry in the GST classification of N=2 Maxwell-Einstein supergravity, whose Lagrangian contains −R/2. This tells you that if the basin carries field-theoretic dynamics on a smooth manifold, the Lagrangian is determined. Why the basin should carry smooth-manifold dynamics in the first place is the paper's main open problem and I don't have an answer.
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.