Symmetry Without Rules: A Meta-Ontological Framework — Working Paper v2.1 (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 = A ⊕ A*, 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 (12 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." The axiom is formalized as the zero-sum identity 0 ≅ A ⊕ A* within a semiadditive †-compact category. Six technical appendices provide the detailed derivation chains: (A) The Standard Model gauge symmetries U(1) × SU(2) × SU(3) derived from the axiom alone in six steps, via Schur's lemma, endomorphism algebras, and the symmetric tensor product Sym². Seven theorems proven, nine testable predictions formulated — including proton stability, absence of supersymmetry, and exact CPT symmetry. (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. (C) Quantitative predictions: the β₀-ratio b₀(SU(3))/b₀(SU(2)) = 3/2 confirmed from level structure, the Bekenstein-Hawking S = A/4 from zero-sum constraints, and dynamical dark energy Λ(t) ∝ 1/a(t)². (D) Polarization mechanics: zero-sum invariance, stability as the †-norm, the chance → regularity → confinement developmental arc, and 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. (F) Extended application notes: detailed technical summaries of five forthcoming companion essays applying the SWR axiom 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), and causation (the third way between Humean and anti-Humean traditions, Kim’s exclusion problem dissolved). All nine predictions are consistent with current experimental observations. No prediction has been falsified. Version 2.1 adds Appendix F, which formally timestamps the core innovations of five forthcoming essays to establish intellectual priority without prematurely releasing the full manuscripts.