Foundations of Theory
Foundations of Theory gathers the core works of the Observer-Dependent Theory of Everything (ODTOE), Anton Pankratov's framework in which reality is not fixed but actualized by observers who select configurations from a single field H. These articles set out the founding ideas: how an observer first arises, the primordial distinction that separates something from nothing, and coherence B(O,C) as the central measurable quantity. Together they trace observers as self-referential strange loops and show why constants like pi and phi recur as structural invariants.
11 articles
Articles in this topic
- 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.
axiompostulatesformalismmetatheoryRead →PDF · RU + EN - 02
ODTOE - Simple Guide
Introduction to the theory for beginners without complex mathematics. Central formula R=O(Psi), three participants, belief as measurable quantity.
introductionbasicssimpleRead →PDF · RU + EN - 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 tableRead →PDF · RU + EN - 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 LambdaRead →PDF · RU - 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 dimensionalityegregoreRead →PDF · RU + EN - 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 theoremRead →PDF · RU + EN - 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 analogueRead →PDF · RU + EN - 08
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 pointRead →PDF · RU + EN - 09
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 compositionRead →PDF · RU + EN - 10
Observer-Dependent Realism: A Reply to Objections on Objectivity, the Observer, Testability, and Causation in Observer-Dependent Physics
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.
realismobjectivityintersubjectivityfixed pointRead →PDF · RU + EN - 11
The Unified Self-Observation Operator: From Physical Constants Through Toroidal Geometry to Language Structure
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.
unified operatorphysical constantstoroidal geometrylanguageRead →PDF · RU + EN
Other Topics
Physics
Pure physics through ODTOE: atom, light, gravity, the Einstein equations, the Standard Model, accelerators, black holes and the ether.
22 articles
Cosmology & Universe
Cosmological structure of ODTOE: dark energy and dark matter, the eternal expansion, cosmological fractions, the singularity boundary and the infinite-recursion universe.
6 articles
Mathematical Structures
Pi, golden ratio, information, memory, world lines
11 articles
Time and Space
Emergence of time, arrow of time, chirality, Kozyrev mechanics
5 articles
Technology & Engineering
Applied ODTOE: coherent CPU architecture, next-generation quantum computing, room-temperature superconductors, coherent fusion reactors and energy extraction.
6 articles
Consciousness and Observer
Evolution of observer, collective observation, dimensionality
8 articles
Education
Coherent education: theory and methodology of learning systems and the nonlinear dynamics of knowledge flows built on the observer-dependent framework.
5 articles
Social Applications
Business, teams, love, music, conflict resolution. Personal exploratory work and applied analyses. Not all materials are peer-reviewed.
15 articles
Philosophy & Meaning
Meaning, love, honesty, creativity and immortality through the observer: the philosophical and existential consequences of ODTOE.
6 articles
Personal Numerological Studies
The following studies explore numerological patterns from a critical and analytical perspective. They are personal research notes, not peer-reviewed scholarship. Where Tesla-related apocrypha or other folkloric claims are discussed, they are presented as objects of critical analysis, not as endorsed truths.
4 articles