Cosmology & Universe
The Cosmology & Universe cluster gathers ODTOE's account of the large-scale cosmos, in which the universe is not a fixed backdrop but a configuration of field H continuously actualized by observers, with its proportions and expansion fixed by the structural invariants pi and phi. Inside, geometry does the work that fine-tuning usually does: the dark-energy, dark-matter and baryonic fractions fall out as phi-squared to 1 to Z, the Hubble tension resolves as a difference in coherence rather than a crisis, and the transcendence of pi drives an expansion that never exhausts itself. The result is a picture where cosmic age, structure, and acceleration become observer-dependent readings of one infinite, self-observing recursion.
6 articles
Articles in this topic
- 01
Cosmological Fractions from Toroidal Architecture: Deriving Dark Energy, Dark Matter and Baryonic Matter from π and φ
Within the toroidal ODTOE model, the cosmological fractions of dark energy, dark matter and baryonic matter are derived from two structural invariants: π and φ. The φ-torus possesses three topological sectors: inter-level (R², gravitational inertia), intra-level (r²=1), and gap sector (Z=(π−3)/[1−(π−3)φ]). Normalized fractions: ΩΛ:ΩDM:Ωb = φ²:1:Z = 68.86%:26.30%:4.83%. Planck 2018 comparison: dark energy 0.54σ, dark matter 0.32σ, baryonic 1.64σ. Zero adjustable parameters.
cosmological fractionsdark energydark matterbaryonic matterRead →PDF - 02
A Geometric Resolution of the Hubble Tension: Dark-Energy and Dark-Matter Unification via Parent-Proton Mergers in the ODTOE Matryoshka
Geometric mechanism simultaneously resolving cosmological constant problem and H₀ tension within single one-parameter framework. Postulate of Geometric Primacy (GP) fixes asymptotic dark-sector attractor φ²:1:Z as topological invariant. Hubble tension between Planck 2018 H₀=67.4 and SH0ES H₀=73.04 at ~5σ level. Dark energy identified with merger process of parent-protons at level d=12. Merger rate regulated by scalar field χ(x,t). Three claims: χ-regimes classify expansion histories; anisotropic Δχ reproduces H₀ tension; dark sector unified with Ω_DM and Ω_Λ as two aspects of 2%-residue (π−3)². Merger limit N^{local}_{max}=Ω_DM/(π−3)²≈13.12. Single fitting parameter η.
dark energyHubble tensiondark matterparent-proton mergerRead →PDF - 03
Eternal Expansion: Transcendence of π as Proof of the Inexhaustibility of Reality
The mechanism of Universe expansion is formalized within the toroidal ODTOE model. The Lindemann theorem (1882) on the transcendence of π proves that the trajectory on the φ-torus never closes, making expansion infinite and inexhaustible. Potentiality pressure F=(π−3)²·|H|/|C| acts at every observation cycle. A scale factor a(n)=(1+ε/(2πφ))ⁿ describes exponential growth of the effective φ-torus radius. Accelerated expansion (ä>0) follows from (π−3)⁴>0 without invoking Λ as a free parameter. Dark energy fraction ΩΛ=φ²/(φ²+1+Z)=68.86% matches Planck 2018 within 0.54σ.
expansiontranscendence of πLindemann theorempotentiality pressureRead →PDF - 04
B-Zero Boundary Topology and the Full ODTOE Singularity Theorem
Closing the B-zero boundary topology marker of Article C. Topological structure of boundary ∂_B C of configuration space C at B→0. Criterion of finite-affine-parameter termination of Φ-iteration sequence (Theorem E.T2). Formal definition of trapped ODTOE-configuration via causal cone J⁺_O (Definition E.D1). Full ODTOE singularity theorem E.T1 as structural analog of Hawking–Penrose theorem. Five anti-circular proof steps: ODTOE Raychaudhuri inequality (E.L1), focusing along null directions (E.L2), finite-parameter focusing (E.L3), Φ-iteration behavior near ∂_B C (E.L4), Φ-iteration incompleteness as vanishing of causal future J⁺_O.
singularity theoremB-zero boundaryconformal compactificationΦ-iterationRead →PDF - 05
Methuselah Star Paradox: Age of Universe as Observer-Dependent Configuration
HD 140283 star age paradox. Different dating methods reflect different observation operators applied to unified field of potential states.
MethuselahstarageuniverseRead →PDF - 06
The Vertical Universe: Life, Time, and Navigation Across Infinite Recursion Levels
Reality as infinite recursion of self-observation cycle Φ=ι∘Ô. Each dimensionality level d contains 17 structural roles, two-level observer window spans 39 configurations. Life as recursion invariant inevitably emerging at every level d from −∞ to +∞. Time as strange-loop iteration flowing differently at each level. Five levels of inter-level navigation through field H. Threshold permeability P(d→d+1|S) with width δS=(π−3)². Observer trichotomy (B,A,H)=(spirit,soul,body). Cosmological proportions ΩΛ:ΩDM:Ωb=φ²:1:Z match Planck 2018 within 1.2σ. All formulas verified to 50+ significant digits.
vertical universeinfinite recursionlife invarianttimeRead →PDF
Other Topics
Foundations of Theory
Core ODTOE articles: axiom, postulates, mathematical formalism
11 articles
Physics
Pure physics through ODTOE: atom, light, gravity, the Einstein equations, the Standard Model, accelerators, black holes and the ether.
22 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