R$^8$ Core Kit (Rev.\ 2.0) / Infrared EFT, Bank Quantization, Metric Elasticity \& Clause--U} / `Constitution'' of the R$^8$ Framework/ Appendix P/S: POLARIS--24 Ring--Harmonic Sensitivity /Statistical Stacking, and Systematics Floor

R$^8$ Core Kit (Rev.\ 2.0) / Infrared EFT, Bank Quantization, Metric Elasticity \& Clause--U} / `Constitution'' of the R$^8$ Framework/ Appendix P/S: POLARIS--24 Ring--Harmonic Sensitivity /Statistical Stacking, and Systematics Floor # Abstract We present **Constitution v3.0** of the **R$^8$ framework** as a fully self-contained **Infrared Effective Field Theory (IR–EFT)** defined on a 4D observable spacetime (“leaf”) carrying **General Relativity (GR)** and the **Standard Model (SM)**, coupled to an internal bosonic dark sector (“bank”). The purpose of the Constitution is not to assert a unique ultraviolet (UV) completion, but to **define an admissible operator class**—a protected locus in EFT space—within which (i) current gravitational and equivalence-principle constraints are satisfied **by construction**, (ii) radiative stability is promoted from a slogan to a mechanism, and (iii) the framework remains **falsifiable** through quantized signatures and cosmological dynamics beyond a featureless $\Lambda$CDM parameterization. The bank is modeled as a multi-scalar system truncated in the IR to two effective combinations: a **heavy mode** $\phi_H$ that behaves as a clustering dark component (CDM-like) and a **light mode** $\phi_L$ that can source late-time acceleration (DE-like) or ultralight dark-sector dynamics depending on parameters. A central architectural principle is the separation of **dynamics** (propagating degrees of freedom) from **governance** (topological constraints and admissibility rules). In particular, the Constitution introduces a discrete governance structure realized as a **discrete gauge symmetry $\mathbb{Z}_k$** implemented by a **BF topological sector**. This sector adds no local propagating degrees of freedom but enforces **quantized selection rules** (schematically $m \in k\mathbb{Z}$) that can imprint discrete “teeth” in appropriate spectra. While $k=24$ is used as a UV-motivated benchmark, the IR Constitution treats $k$ as an integer parameter that is, in principle, **measurable** through such quantized signatures. Radiative robustness of the leaf–bank coupling is enforced via an explicit **Portal Protection Mechanism**. The light mode is taken to be **axion-like** with a (discretely gauged) shift symmetry, so that low-dimension operators that would generate unscreened fifth forces or reintroduce dangerous SM-trace couplings are **forbidden** in the admissible basis (e.g., $\phi_L T^\mu{}_\mu/\Mp$, $\phi_L|H|^2$, $\phi_L\bar\psi\psi$). The allowed portals are restricted to derivative and/or higher-dimensional operators suppressed by a cutoff scale, such that loops can only regenerate symmetry-consistent structures. This converts the earlier “Trace-Free” requirement from an apparent cancellation into an **operator-level protection statement**. The Constitution also includes a **vacuum-offset sequester** implemented by a 3-form/4-form global-constraint sector. The sequester is used strictly as a **renormalized vacuum-offset filter**: it cancels the **spacetime-constant zero-mode** contribution to curvature (the renormalized “DC” component) while leaving the time-dependent (“AC”) bank dynamics intact. This is formalized through a spacetime averaging projector $\langle X\rangle$, where the sequester fixes the vacuum integration constant as a **boundary-set parameter** rather than a local degree of freedom. To avoid infrared ambiguities in idealized infinite-volume settings, the Constitution treats the global constraint within a **regulated four-volume/measure** (e.g., causal patch regularization), emphasizing that this is a cosmological, not laboratory, mechanism. An important implication is that if the light mode were exactly frozen, it would be indistinguishable from a pure constant and would be routed into the offset sector; therefore, dynamical dark-energy realizations generically predict **$w(z)\neq -1$** at some level. Clause–U—originally motivated by post–GW170817 constraints and equivalence-principle tests—is reformulated as an **operator class definition** rather than a post-hoc viability filter. The admissible locus restricts the gravity–scalar sector to **minimal Einstein–Hilbert gravity** plus **canonical/minimally coupled scalars**, explicitly excluding curvature–derivative scalar operators (Horndeski-type terms) that would modify tensor propagation. Within this class, **$c_T=c$** holds at tree level by construction, and radiatively induced deviations remain suppressed by the EFT cutoff and/or Planck scale within the regime of validity. WEP safety is enforced by the portal restrictions on $\phi_L$, while parity-violating gravitational couplings (e.g., effective gCS terms) are excluded or symmetry-suppressed for cosmologically accessible modes. Because the light mode is axion-like, the Constitution explicitly records UV-consistency awareness regarding **Swampland/WGC** considerations. Rather than adopting a single-field trans-Planckian cosine as baseline, admissible realizations include: (i) **alignment/clockwork** mechanisms yielding an effective large field range from multiple sub-Planckian axions, (ii) **monodromy** constructions where the potential “unwinds” while preserving local shift structure, and (iii) **dissipative/friction-driven slow evolution** (e.g., via $\phi_L F\tilde F$ backreaction) enabling $w\simeq -1$ without requiring an ultra-flat trans-Planckian decay constant. The ultralight mass scale $m_L\sim H_0$ is treated as technically natural, with explicit emphasis that the symmetry-breaking potential arises **non-perturbatively** and can generate **exponential smallness** (e.g., $m_L^2\sim \mu^2 e^{-S_{\rm inst}}$), avoiding continuous fine-tuning. For the heavy mode, the Constitution adopts **misalignment** and/or **freeze-in** as direct-detection-safe defaults; visible-strength Higgs portals are optional and constrained rather than assumed. Finally, the Constitution summarizes falsifiability handles beyond “DM + DE”: (a) measurable departures from a pure cosmological constant through $w(z)$ evolution, (b) quantized governance signatures that can, in principle, determine the integer $k$, (c) correlated dark-sector perturbations and associated isocurvature/structure-growth constraints, and (d) potential topological relic channels associated with discrete gauge structure. Constitution v3.0 therefore defines a concrete, mechanism-explicit IR–EFT locus that is both observationally hygienic and testable, while remaining honest about which aspects are IR definitions and which require dedicated UV technical modules. ## Abstract We present **R⁸ (Leaf–Bank)** as an infrared effective field theory (IR–EFT) on a single 4D Lorentzian *leaf* (GR+SM) coupled to a structured bosonic *bank*. The **Constitution v3.0** defines an admissible operator locus 𝓜₍c₎ by four non‑negotiable pillars: **(i)** a minimal leaf+bank truncation with a heavy clustering mode (CDM‑like) and a **protected ultralight** mode (DE‑like/ultralight), **(ii)** discrete **governance** realized by a BF ℤₖ sector (benchmark k=24) that constrains the IR operator basis and implies *quantized selection rules* (“teeth”), **(iii)** a **vacuum‑offset sequester** that cancels the *renormalized spacetime‑constant* (DC) stress‑energy offset via a global constraint while preserving time‑dependent (AC) dynamics, and **(iv)** **Clause‑U**, an operator‑class definition that enforces luminal tensor propagation and WEP safety by construction (excluding, e.g., curvature‑derivative scalar operators that shift c_T and parity‑odd gravitational propagation terms). To prevent “hidden preferred frames” in realizations that use internal selection channels, we attach a **Lorentz‑consistency module**: a projector‑bundle description with an induced connection, together with **governor certification** metrics (idempotency error, late‑time jitter, and locality‑commutator decay) that act as PASS/FAIL hygiene tests for projector stability and locality compatibility. A central falsifiability hook is an **audit‑grade teeth pipeline** for phase‑transport proxies in EHT‑style data: either (a) harmonic extraction at m={24,48} or (b) closure‑loop invariants (closure phases), followed by **Gold–Soft** HMM/Viterbi decoding into a Z₄₈ discrete cover and a sliding **Z₃ coherence detector** on decoded residuals. Statistical claims are assessed with matched null families, geometry‑destruction kill tests, hero‑kill and station‑jackknife resilience, and strict look‑elsewhere correction (global max‑over‑grid). We formalize this into a pre‑registered **Court Stability Gate (CSG‑1.0)** that fixes (1) a baseline **Cell0** configuration, (2) an explicit **Sweep** grid, and (3) an **Exploratory** tier whose results are non‑court‑admissible unless promoted into a new registered gate. CSG‑1.0 additionally introduces a **Complexity Governance Clause** for any maximization over discrete assignments (decoder paths, Z₂ flips, etc.), with two *equal* judicial routes: **(i)** a fixed‑λ penalized objective maxₓ[T(x)−λ|x|] (Gold–Soft default), or **(ii)** the **minimal‑support** solution achieving at least (1−ε) of the global maximum. The same complexity rule must be applied inside every null realization (“optimized‑null” requirement), and the final court p‑value is computed on the resulting super‑global max statistic (time grid × sweep grid). The intent is a forkable framework whose weakest points are not rhetorical but empirical: luminality/WEP gates (Clause‑U), leakage/portal closure, quantized‑teeth observability under CSG‑1.0, and module‑specific mappings to collider/cosmology/astrophysical data.