Symmetry Without Rules: A Meta-Ontological Framework — Working Paper v2.4 (Bilingual)

Symmetry Without Rules (SWR) is a meta-ontological framework that proposes the only regress-free answer to the question *why does anything exist at all? * Every proposed initial condition — a quantum field, a mathematical structure, a deity — generates infinite regress (what established it? ) or terminates in brute fact (it just is). SWR demonstrates that the sole initial condition requiring no further explanation is the complete absence of any condition: absolute lawlessness. This is not "nothing" in the physicist's sense (a quantum vacuum is replete with structure) but the total absence of rules, structure, and content. From this single axiom, the framework derives — without additional assumptions — why change is inevitable (changelessness would itself be a rule), why the change takes the form of symmetric polarization (0 = (+n) + (−n), the identity of zero), and why the resulting structure exhibits descriptive regularities rather than prescriptive laws. The distinction between descriptive and prescriptive is the framework's central conceptual move: the regularities we observe are not external commands imposed on reality but intrinsic structural features of the polarization — like the angles of a triangle summing to 180°, which is not a "law" the triangle obeys but a description of what a triangle is. The main document (13 chapters) develops the full ontological architecture — a monist relational network with emergent local clusters — and applies it to five classical philosophical problems: consciousness (the hard problem as a category error), entropy and the arrow of time (irreversibility from the adjunction asymmetry F ⊣ U), free will (genuine agency from self-referential incompleteness via Gödel), causation (real connections without necessitation), and mathematics (the relational structure of polarization in symbolic form, dissolving Wigner's "unreasonable effectiveness"). Each application resolves its respective problem by identifying the same hidden premise: the conflation of "real" with "prescriptive. " Version 2. 4 adds a formal inter-level constraint (§1. 3: CHANGE/INSTANTIATE/DESCRIBE trichotomy) proving that level 0 lacks NNO, hence the endofunctor Σ: C₀ → C₀ is categorically impossible. The axiom is formalized as a necessary identity — not a posited axiom — of a self-dual simple object A ≅ A* in a semiadditive †-compact ℂ-enriched category. The self-duality isomorphism provides pair-creation and pair-annihilation morphisms (η: I → A ⊗ A, ε: A ⊗ A → I), encoding the zero-sum principle 0 = (+n) + (−n) categorically. In v2. 4, the R2 item of the Gödelian residuum has been closed: the question "why A ≅ A* and not some other axiom? " dissolves because absolute nothingness has exactly one self-consistent identity. Six technical appendices provide the detailed derivation chains: (A) The Standard Model gauge symmetries U (1) × SU (2) × SU (3) derived from the self-dual axiom A ≅ A* alone in six steps, via Schur's lemma, endomorphism algebras, and the symmetric tensor product Sym². The Higgs doublet is identified with the axiom's biproduct A ⊕ A ≅ ℂ². Five negative predictions (no second scalar boson, no Z'/W', no proton decay via GUT mechanism, no supersymmetric partners, no extra spatial dimensions), two positive predictions (Higgs self-coupling λ ≠ 0, coupling constant independence), and two derived consequences are formulated. The V₃ = Sym² (ℂ³) = ℂ⁶ representation is identified as a speculative dark matter candidate. (B) Polarization formalization: uniqueness of U (1) via Hurwitz's theorem, quantum measurement as the forgetful functor U, and the Born rule as P (a) ∝ f†f. Cross-reference to Level Placement Test (LPT) in Appendix D §13. (C) Quantitative predictions: the Bekenstein-Hawking S = A/4 from the self-dual constraint (with the dS/dτ mechanism connecting to black hole analysis), the β₀-ratio b₀ (SU (3) ) /b₀ (SU (2) ) = 3/2 confirmed from level structure, the origin of matter from the tensor product decomposition ∧² (ℂ³) = ℂ³, the cosmological constant as a dynamical η-ε surplus Λ (t) = Γ_η (t) − Γ_ε (t) consistent with DESI 2024 results, and the V₃ dark matter candidate with five observational consistency checks. (D) Polarization mechanics: the structural inevitability of dynamics proved via reductio (suppressing η or ε would impose a rule on the pre-structural state I ≡ 0), the gravitational cascade (dS/dτ mechanism for time dilation, black hole analysis, no-hair theorem reinterpretation), zero-sum invariance, stability as the †-norm, the CHANGE/INSTANTIATE/DESCRIBE trichotomy (§5b), timeless vs. static distinction (§12), Level Placement Test LPT (§13), and Cₘeta as a finite 2-category with Gödelian residuum narrowing (§11a). Seven testable hypotheses. (E) Bidirectional correspondence between the intuitive axiom 0 = (+n) + (−n) and its category-theoretic formalization via the Grothendieck group K₀, proving the formalization is the unique categorification of the axiom. R2-correction: the "why A ≅ A*? " question dissolved. Cₘeta scope and three-row Gödelian residuum status table added (§5). (F) Extended application notes: detailed technical summaries of five forthcoming companion essays applying the SWR framework's necessary identity A ≅ A* to consciousness (the hard problem as a category error, four structural conditions, IIT integration), entropy (low initial entropy as identity, Boltzmann brain elimination), free will (the hidden prescriptive premise dissolving the trilemma), mathematics (Wigner dissolved, Tegmark divergence, H-NEW-6: mathematical branches as emergent-level identities with TIER A–D classification), and causation (the third way between Humean and anti-Humean traditions, Kim's exclusion problem dissolved). All predictions are consistent with current experimental observations. No prediction has been falsified. Version 2. 4 adds expert cross-audit corrections (terminology hardening, inter-level constraint, Cₘeta finite 2-category, R2 closure, H-NEW-6 mathematical branches) across all 14 documents. Appendix F (added in v2. 1) formally timestamps the core innovations of five forthcoming essays to establish intellectual priority without prematurely releasing the full manuscripts.