ODTOE Articles

Formal metatheory of reality based on the observer principle. One axiom: observer constitutes the observed. Six postulates with mathematical formalization.

Introduction to the theory for beginners without complex mathematics. Central formula , three participants, belief as measurable quantity.

Unified map of physics: QM, GR, string theory, LQG, QBism as configurations in field H. Periodic table of theories organized by coherence S and observer dimensionality d.

. Operationalization and measurement of contextual belief. Interaction with environment.

Systematization of ODTOE extensions affecting sixteen articles. Destructive collective probability P_destr(E)=1−∏(1−σᵢᵏ) for anti-coherent clusters. Fractional dimensionality hypothesis d∈R: intermediate values correspond to unstable transitional states (sleep, trance, altered consciousness). Threshold permeability P(d→d+1|S)=Θ(S−Sᶜ)·[1−exp(−(S−Sᶜ)/δS)]. Egregore as emergent meta-observer O_meta with B_meta, A_meta, H_meta. Sleep-wake dimensionality oscillation d_eff(t)=d₀+Δd·f(t). Theorem: T→∞ requires dd/dt>0, otherwise coherent stagnation trap (F→0). Zero adjustable parameters.

Closes the «open task of first priority» from the base ODTOE article: sufficient conditions for existence (and uniqueness under contraction) of the fixed point Ψ*=Φ(Ψ*). Schauder theorem (existence without uniqueness) and Banach theorem (uniqueness under contraction). Explicit contraction constant q_contract(B,S). Anti-circularity audit confirms Φ definition does not presuppose Ψ*.

Resolves Spencer-Brown's «first spark» bootstrap problem without pre-existing observer. Higgs-analogue spontaneous symmetry breaking of primordial field Ψ plus KAM filter selecting stable vacuum via Diophantine condition. Golden ratio φ as universal inherited invariant. E8 symmetry in quantum-critical chains CoNb₂O₆. Hardy nonlocality probability φ⁻⁵.

Extension of ODTOE to dynamic regime: from asymptotic limits (B→1, S→1) to evolutionary trajectories with derivatives dB/dt, dS_ij/dt. Bugaev's monadological lineage from Leibniz gets quantitative closure: law of solidarity → P5 collective observation, law of conservation of past → H_hist hierarchy. Conditional reachability theorem. Integral world-line density metric P(W). Two-level observer stratification.

Deepens operational structure of the fourth component Λ in B(O,C)=F^w1·E^w2·(1−σ)^w3·Λ^w4. Λ decomposed into three operational components: recency A(t), density/relevance D, and purity P. Primary multiplicative form Λ_B=A^a·D^d·P^p preserves weakest-link principle. Information-theoretic interpretation Λ_B=exp(−H(noise|signal)). Bridge to Datasheets for Datasets, Data Cascades, pedagogy (Vygotsky ZPD, Bandura mastery).

ODTOE as observer-dependent realism: reality is objective at the level of an intersubjective fixed point, and objectivity is reconstructed as the limit of high coherence. A conditional reply to five objections — hidden idealism, the undefined observer, untestability, causation, and the observability ceiling — via the corpus's existence/uniqueness theorems for the self-observation fixed point, an explicit operator algebra, and an instrument-level protocol for measuring B.

The unified self-observation operator Ψ∗ = Φ(Ψ∗) as a generative principle from which the structures of three seemingly unrelated domains are derived: physical constants, toroidal geometry, and natural-language architecture. π is the invariant of the operator's continuous spectrum (the phase period of cyclic processes); the golden ratio φ governs discrete recursion. A synthesis of 39 studies, including the 3-6-9 pattern and the architecture of alphabets as projections of the strange loop.