Research program and papers
All consistent mathematical structures exist. Isomorphic copies collapse to a single point in structure space. The kind of structure we are is a self-modeler: a system containing a faithful copy of itself, using it to probe its own state. We don't just happen to be self-modelers. We find ourselves inside the basin of self-modeling, pointed at its fixed point, because self-modeling concentrates experiential measure.
The main result: a finite-dimensional system admitting a faithful self-model is necessarily governed by complex quantum mechanics. The complex field, the C*-involution, and local tomography are all derived, not assumed.
Project status
This work has not been peer-reviewed. We have no contacts in academia and haven't had any luck getting in touch with anyone in the field. In lieu of human review, we have stress-tested the results through independent adversarial review sessions using every frontier LLM (Claude, Gemini, GPT, Grok), each instructed to find fatal flaws. No fatal flaws were found. Real issues were identified and fixed. The proofs are numerically verified (844+ SymPy tests). All source is public.
If you have the background to evaluate this and are willing to look, we would genuinely appreciate it. The strongest objections we have found so far are documented in the discussion section of the QM paper (#5 below).
Papers
7. The Standard Model from Self-Modeling: Gauge Structure from the Observer-Universe Interface 2026
The universe, as the unique non-composable self-modeling structure, necessarily contains the exceptional Jordan algebra h3(O). An internal observer, being a C*-algebra subsystem, simultaneously selects a rank-1 idempotent (breaking F4 to Spin(9)) and a complex structure (breaking F4 to [SU(3)×SU(3)]/Z3). The intersection is (U(1)×SU(2)×SU(3))/Z6 — the Standard Model gauge group with correct chirality.
6. Spacetime from Self-Modeling: Einstein's Equations from a Self-Modeling Lattice via Jacobson's Thermodynamic Argument 2026
Self-modeling forces the isotropic Heisenberg Hamiltonian via diagonal U(n) covariance and Schur-Weyl duality, producing area-law entanglement. Jacobson's 1995 thermodynamic argument (Clausius on local Rindler horizons) converts this to Einstein's equations in d+1 ≥ 3 dimensions. Four gaps identified: emergent Lorentz invariance, lattice Bisognano-Wichmann, local equilibrium, continuum limit.
5. Quantum Mechanics from Self-Modeling: Deriving Complex C*-Algebraic Structure from a Single Operational Premise 2026
One operational premise plus four structural assumptions derive finite-dimensional complex quantum mechanics. Self-modeling produces a sequential product satisfying van de Wetering's axioms, forcing Euclidean Jordan algebra structure. Faithful tracking implies local tomography, excluding all non-complex types.
1. Experiential Measure on the Structure Space of Self-Modeling Systems
Defines the experiential density functional on self-referential dynamical systems. Conditional theorem for Boltzmann brain negligibility. Toy model validation.
2. Exponential Suppression of Transient-Basin Contributions in Trajectory-Weighted Markov Chain Measures
Rigorous proof of Boltzmann brain negligibility via 7-lemma composition from metastability theory. Explicit error scaling.
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 cleanly falsifies the conjecture that Born-rule probabilities are dynamically selected by the experiential density. 1900+ Lindblad trajectories. The Born rule instead follows from Gleason's theorem applied to the C*-algebra that self-modeling forces.