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.

Theorem V* on temporal asymmetry of past and future states in H. Past is indestructible (norm conservation under Φ-iterations), future is constructible (not fixed). Resolves the «arrow of time» problem from first principles. Temporal projectors π_past and π_future with mutual orthogonality. Connection to Penrose's CCC and Wheeler's delayed-choice.

Places ODTOE coherence B(O,C) and observer-correlator metric on a single statistical manifold. Three results: (i) −logB = D_KL(p_θ||p*) as exact identity; (ii) Fisher metric coincides with observer-correlator formula F1; (iii) Archimedean isoperimetric defect (π−3)² as PL-invariant. Direct proof of simply-connectedness of the bootstrap-closure stratum via Banach chain.

Formalizes A.F. Losev's hyletic number doctrine (in V.B. Kudrin's reconstruction) within ODTOE. μL-mapping: hyletic number → Ψ∈H. Weak indestructibility theorem proved via lemmas L1-L4. Adele bridge from ultrametrics to φ-torus. Kudrin's «mirror sphere» as special case of matryoshka configuration. Closes open task §VII.1 (Bugaev's law of conservation of the past).

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.

Theorem 1: on the spectrum of Φ-iteration frequencies, points ν_Φ=0 (light in own rest frame) and ν_Φ=∞ (light everywhere simultaneously) are identical, forming projective point [0:1]∈RP¹. Speed of light c=r₀/τ₀ is unique continuous extension. Key premise: τ₀ calibrated INDEPENDENTLY of c via P2 inertia formula. Resolves paradox «light stands still ↔ light is everywhere».

Closes four related questions: (i) time and space emerge simultaneously with observer Ô birth as structural consequences of SSB+KAM selection; (ii) both temporal projectors π_past and π_future instantiated symmetrically at τ_obs=τ₀; (iii) formal resolution of chicken-and-egg paradox via anti-circularity audit; (iv) teleological selection of realized world-line via goal-functional A_goal [CONJECTURE]. Composite theorem ST.T1 in five claims.

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).