Foundations of Theory

Core ODTOE articles: axiom, postulates, mathematical formalism

14 articles

Articles in this topic

  1. 01

    Observer-Dependent Theory of Everything (ODTOE)

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

    axiompostulatesformalismmetatheory
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  2. 02

    ODTOE - Simple Guide

    Introduction to the theory for beginners without complex mathematics. Central formula R=O(Psi), three participants, belief as measurable quantity.

    introductionbasicssimple
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  3. 03

    Modern Physical Theories as Configurations within ODTOE

    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.

    QMGRunificationperiodic table
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  4. 04

    Four Components of Cognitive Coherence

    B(O,C) = F^w1 * E^w2 * (1-sigma)^w3 * Lambda^w4. Operationalization and measurement of contextual belief. Interaction with environment.

    beliefcoherenceF E sigma Lambda
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  5. 05

    Supplements to the ODTOE Corpus: Anti-Coherence, Fractional Dimensionality, Egregore and Consciousness Oscillation

    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.

    anti-coherencedestructive clusterfractional dimensionalityegregore
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  6. 06

    Origin of the Observer in ODTOE: Existence Theorems for the Self-Observation Fixed Point

    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*.

    fixed pointself-observation operatorSchauder theoremBanach theorem
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  7. 07

    Primordial Distinction in ODTOE: Spontaneous Symmetry Breaking Mechanism and KAM Selection of the φ-Resonance

    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.

    primordial distinctionSpencer-Brownspontaneous symmetry breakingHiggs analogue
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  8. 08

    Temporal Asymmetry of Indestructibility in ODTOE: Theorem V* on Conservation of the Past and Constructibility of the Future

    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.

    temporal asymmetrytheorem V*indestructibilityarrow of time
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  9. 09

    Information Geometry of B(O,C): Connection to Perelman's S³ Topology, KL-Identity and Archimedean Isoperimetric Defect (π−3)²

    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.

    information geometryFisher metricKL-divergenceRicci flow
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  10. 10

    Losev's Hyletic Number in ODTOE: μL-Mapping, Weak Indestructibility Theorem, and Adele Bridge

    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).

    hyletic numberμL-mappingLosevKudrin
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  11. 11

    Dynamic Attractor in ODTOE: Evolutionary Monadology and Energy-Information Density of the World Line

    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.

    evolutionary monadologydynamic attractorBugaevfixed point
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  12. 12

    The Intrinsic Rest Frame of Light in ODTOE: Projective Identity 0≡∞ on the Φ-Iteration Spectrum

    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».

    speed of lightprojective geometryself-observation operatorΦ-iterations
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  13. 13

    Birth of Time and Space at Observer Birth: Composite Spacetime Genesis Theorem in ODTOE

    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.

    spacetime genesisobserver birthtemporal projectorstheorem V*
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  14. 14

    ODTOE: Parameter Λ as a Data-Quality Metric in the Coherence Formula B(O,C)

    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).

    cognitive coherenceparameter Λdata qualitymultiplicative composition
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