Swirl-String-Theory Canon v0.8.36 — Canonical Reference and Research Framework

Abstract

Swirl-String-Theory Canon v0.8.36 is the formal reference document for Swirl-String Theory (SST), a continuum-based hydrodynamic and topological framework in which physical structure is modeled as arising from stable circulation-bearing configurations in an incompressible, inviscid medium. This edition consolidates the core axiomatic layer of the theory, defines a minimal primitive structure, and organizes the framework through an explicit epistemic classification that distinguishes orthodox input, internally derived consequences, and speculative extensions. The document is designed as a logically stratified canon rather than as a single-claim research article. Its primary purpose is to provide a stable source of definitions, canonical constants, dependency structure, master relations, and theory-internal consistency rules for subsequent SST papers, notes, simulations, and benchmarks. Version 0.8.36 places particular emphasis on non-circular closure, traceability of assumptions, and compatibility checks against established physics in appropriate limits. The canon includes: (i) formal foundations based on a minimal primitive set; (ii) an axiomatic framework for circulation, topology, delay dynamics, and relational time; (iii) a consistency and classification layer for epistemic status tracking; (iv) a geometric and topological sector; (v) delay-induced mode-selection theory as a route to spectral discreteness; (vi) a conservative atomic bridge model and spectroscopic constraints; (vii) a relational time framework with Swirl-Clock, foliation, and effective-field-theory bridge structures; and (viii) an integration layer that selectively recovers transferable material from earlier SST canon versions without treating those versions as external authorities. Compared with earlier canon releases, v0.8.36 strengthens the formal architecture of SST by separating canonical definitions from phenomenological bridge models and by explicitly labeling which statements are orthodox, derived within the present framework, or still speculative. It also preserves selected higher-level sectors—such as particle-candidate topology, hydrodynamic exchange barriers, benchmark structure, gauge-roadmap elements, and clock/gravity bridge constructions—while recasting them in a stricter and more transparent format. This edition (v0.8.36) adds on top of the prior canon line: Maxwell swirl-tonic, kinetic closure, dynamical-field / reciprocal-stress / mechanical falsifiers, and spectroscopic-response guards. This deposit is intended as a citable canonical reference for the SST framework in its v0.8.36 state. It is suitable for use as the primary background document for related technical notes, mass-functional derivations, atomic bridge analyses, topological classification work, and future computational or phenomenological developments. }$. Version changelog v0.8.2 — Horn/circulation radius, envelope density, highres terminology v0.8.3 — Framed-tube ontology, trefoil closure, particle dictionary, Pauli a_core v0.8.4 — EM–gravity bridge, finite-cell α obstruction, research-track extensions v0.8.5 — highres conversation audit + CALIBRATED circularity honesty v0.8.6 — framed self-linking and spinorial lepton ladder v0.8.7 — Z2 spinstats sector and CP1 substrate discipline v0.8.8 — Epistemic/notation audit v0.8.9 — triadic gravity-response corollary and diagnostics v0.8.10 — Round-2 calibration notation audit v0.8.11 — final notation hygiene pass v0.8.12 — Round-3 epistemic patch v0.8.13 — relativity emergence ladder (SR/GR audit) v0.8.14 — core-torsion / two-speed clock discipline v0.8.15 — Lorentz-type swirl-stress / EM correspondence v0.8.16 — pressure-optical locking and no-monopole audit v0.8.17 — T-foliation discipline and corpus integration bundle v0.8.18 — guardrails v2 + resolved-tube v3 + four-insights v2 + euler transport + time ontology + compton-horn + hybrid clock v0.8.19 — ropelength foundation + screening scalarization + thin-filament energy + mass audit + impedance bridge + audit bundle + Foucault RT + projected vorticity + dark taxonomy operator clock + claude audit cleanup + rhoF cosmological impedance + Taylor-column parity v0.8.20 — chronos kelvin + contact pressure + rank9 + SSDL + particle/clock ansatz v0.8.21 — eight-source curl/writhe/Gehring/Biot-Savart/Hodge/helicity-forms/isoperimetric/Ridgerunner series v0.8.22 — operational spacetime axiom + quasinormal swirl spectroscopy v0.8.23 — v0.8.23 integrates the Author's Origin Note and the Genesis/provenance architecture, records the rediscovered capacitance--impedance path with an explicit same-route guard, adds the Historical Notebook and Proto-Canon Provenance Register (A v0.8.24 — v0.8.24 corrects the core--torsion inertia target to the Lorentz-consistent normalization \( M_{ torsion}=E_0 I/c_T^2\), adds trace-based scale and anisotropy residuals, attributes the minimal compact link action to the orthodox Wilson/Kogu v0.8.25 — the KAM-caged knot-state stability programme and separates spatial vortex-line confinement (KAM-S) from temporal knot-shape stability (KAM-T); introduces the LIA and Hasimoto reference layer with full finite-core Biot--Savart correction as v0.8.26 — v0.8.26 corrects the boxed Rydberg form of () with an explicit [ERRATUM], retires the tautological in favour of in Eq.~, adds the transparency identity (Eq.~), records a provenance guard, tightens and spring-energy epistemic labels, and fen v0.8.27 — v0.8.27 completes the research-track de-duplication of the seven Selective-Recovery subsections (RT full-text replaced by main-canon pointers), strips pre-existing commented duplicate section labels ( / / / / ), introduces a macro for curre v0.8.28 — the action--phase mass--shell clock bridge \(H(P,I)= \), derives the internal carrier phase rate \( _0/ \) at fixed momentum, links the low-momentum expansion to the canonical inertia normalization \(M_0=E_0/c^2\), separates translational c v0.8.29 — the Fermat-metric optical-geometry guard (Eqs.~--), separates ray bending / optical caustics from circular light-ring candidates and horizon-like clock degeneracy, derives the conditional SST stationary-circumference gate, and extends Quasi v0.8.30 — v0.8.30 separates the unfixed material substrate density from the calibrated quasi-static effective response , introduces distinct notation for rotational microinertia and line inertia , corrects the historical provenance of the inherited d v0.8.31 — v0.8.31 audits the compact-rotor reinterpretation of the line-inertia sector: it labels the Compton-gap rotor normalization as a matching ansatz, records as a definitional identity rather than an independent validation, separates linear int v0.8.32 — v0.8.32 removes the inherited value from the primitive calibration set, registers it as [LEGACY REFERENCE NORMALIZATION / PROVENANCE INVALIDATED], leaves the physical numerically unfixed, records all four VAM-7 provenance defects, adds the v0.8.33 — the covariant vortex-worldsheet form-degree guard, including the correct distinction between a two-form worldsheet coupling and three-form flux integration; introduces a Research-Track Kalb--Ramond/worldsheet action with source, scale-separ v0.8.34 — ideal-knot regime guard, compact-to-slender carrier hypothesis, and Kirchhoff--Cosserat diagnostic guards v0.8.35 — transverse-projector 8pi/3 origin, alpha-blind finite-core response, helicity-constrained twist energy, and EM matching guards v0.8.36 — Maxwell swirl-tonic, kinetic closure, dynamical-field / reciprocal-stress / mechanical falsifiers, and spectroscopic-response guards