The Precision Cascade Cosmology Series: Unified Framework, Architecture, and Reproducibility Hub

Series Abstract The Precision Cascade Cosmology Series presents a unified, reproducible scientific‑systems framework for analysing cross‑probe cosmological inference under shared provenance, structural covariance, and deterministic precision propagation. Across seven papers, the series introduces the Precision Cascade Engine (Paper 0), applies it to the Hubble tension (Paper 1), tests structural independence assumptions in late‑time structure measurements (Paper S), formalises the general theory of structural covariance and precision propagation (Paper 3), and develops predictive frameworks for dark‑matter microphysics (Paper 4), general relativity at cosmological scales (Paper 5), and the broader cascade‑driven discovery landscape (Paper 2). Each paper is accompanied by a laboratory‑grade reproducibility archive containing deterministic pipelines, provenance‑encoded transformations, golden‑output validation, and checksum‑verified chain‑of‑custody. These archives ensure that every numerical result in the series can be regenerated exactly, providing a transparent and auditable foundation for cross‑domain scientific inference. The results and predictions presented in Papers 2–5 are conditional on the validation of the stabilized Hubble‑tension baseline established in Paper 1. The series therefore provides both a methodological foundation and a forward‑looking set of testable predictions for precision cosmology as next‑generation datasets become available. --- Series Description Overview This seven‑paper series establishes a unified scientific‑systems architecture for analysing heterogeneous cosmological measurements under explicit structural assumptions. It introduces: • a universal inference engine (Paper 0) • a cross‑probe correlation synthesis resolving the Hubble tension (Paper 1) • a structural independence test for the S₈ tension (Paper S) • a general theoretical framework for structural covariance (Paper 3) • a precision‑cascade mechanism linking parameter domains (Paper 2) • predictive frameworks for dark‑matter microphysics (Paper 4) • predictive frameworks for cosmological‑scale tests of General Relativity (Paper 5) The series is intentionally domain‑agnostic and method‑agnostic. Although the initial applications are cosmological, the underlying architecture applies to any scientific domain in which measurements share provenance, pipelines, or modelling structure. --- Reproducibility Archives (Lab‑Grade) Three components of the series include full laboratory‑grade reproducibility packs: Paper 0 — Precision Cascade Engine (Master Engine Room) Contains the complete engine specification, module definitions, governance model, CI workflow, golden outputs, and deterministic regeneration protocol. Paper 1 — Hubble Tension Resolution Includes the full correlation‑synthesis pipeline, systematic‑bias engine, covariance construction, validation suite, and golden‑output chain‑of‑custody. Paper S — Structural Independence Test for S₈ Provides the 36‑measurement dataset, provenance‑encoded correlation matrix, systematic‑shift operator, sensitivity sweeps, eigenvalue diagnostics, and full CI‑validated reproducibility workflow. Each archive includes: • deterministic Python pipelines • schema validation • golden‑output validation • checksum manifests and root‑hash integrity • CI workflows • replication runbooks • environment files • complete chain‑of‑custody documentation These archives ensure that every numerical result in Papers 0, 1, and S can be regenerated exactly, providing a transparent and auditable foundation for the entire series. --- Paper‑by‑Paper Purpose and Linkage Paper 0 — The Engine Room Defines the Precision Cascade Engine: a universal, provenance‑aware, reproducible inference architecture. Role: Systems blueprint. Reproducibility: Full lab‑grade archive. --- Paper 1 — Resolving the Hubble Tension Applies the engine to cross‑probe correlations in H₀ measurements, stabilising the local value at 69.9 ± 0.8 km/s/Mpc. Role: Foundational empirical result. Reproducibility: Full lab‑grade archive. Dependency: Papers 2–5 conditional on this baseline. --- Paper S — Structural Independence Test for S₈ Tests whether late‑time structure measurements share cross‑survey correlated residuals. Role: Demonstrates structural‑covariance mechanism in a second domain. Reproducibility: Full lab‑grade archive. Dependency: Independent of Paper 1. --- Paper 2 — Beyond the Hubble Tension (Cascade Predictions) Introduces the Precision Cascade Principle and derives five discovery‑level predictions. Dependency: Fully conditional on Paper 1. --- Paper 3 — Structural Covariance & Precision Propagation Formalises the general theory of structural covariance, residual‑systematic operators, independence tensors, and precision propagation. Dependency: Independent; theoretical backbone. --- Paper 4 — Dark Matter Microphysics Predicts a 7.2σ detection of self‑interacting dark matter under the validated cascade regime. Dependency: Conditional on Paper 1 + Paper 3. --- Paper 5 — Testing General Relativity Across the Observable Universe Predicts >6σ consistency of GR across cosmological scales under the cascade‑propagated covariance structure. Dependency: Conditional on Paper 1 + Paper 3. --- Validation Logic for the Entire Series Independent Validation Paths • Paper 0: reproducibility • Paper 1: independent H₀ datasets • Paper S: independent S₈ datasets • Paper 3: structural‑behaviour tests Conditional Validation Paths • Papers 2, 4, 5 require Paper 1 • Papers 4 and 5 require Paper 3 Series‑Level Validation The entire cascade framework is validated if: 1. Paper 1’s stabilized H₀ is confirmed 2. Paper S’s structural‑independence mechanism is supported 3. Paper 3’s structural‑covariance predictions match empirical behaviour 4. Papers 4 and 5 predictions are borne out by next‑generation data This creates a multi‑layered, falsifiable scientific programme. Daniel JeffreyIndependent ResearcherORCID: 0009-0006-8484-3575 Role: Author · Researcher · Data curator