This is the central roadmap and reference document for the Relational Field Theory (RFT) series. It contains the complete list of all nine papers with full titles, short descriptions, and live DOIs. It serves as the official hub for the series, allowing readers to navigate the progression from the minimal ontological axiom to concrete downstream empirical results. All papers maintain the terminal reduction and anti-drift boundary of RFT. Related Preprints • Paper I: https://doi.org/10.17605/OSF.IO/EDJQC • Paper II: https://doi.org/10.17605/OSF.IO/R8VJ6 • Paper III: https://doi.org/10.17605/OSF.IO/VCSZN • Paper IV: https://doi.org/10.17605/OSF.IO/Z3P84 • Paper V: https://doi.org/10.17605/OSF.IO/9SXN5 • Paper VI: https://doi.org/10.17605/OSF.IO/6BGH2 • Paper VII: https://doi.org/10.17605/OSF.IO/724CN • Paper VIII: https://doi.org/10.17605/OSF.IO/NQ4DJ • Paper IX: https://doi.org/10.17605/OSF.IO/UYD4R
This wrapper paper provides a high-level overview of the RP-series (RP0–RP21), summarizing the logical structure, motivation, and progression of the axioms. It is intended as an orientation guide for readers, clarifying how the axioms build from a minimal substrate and asymmetric relations to irreversible δ-transitions, coarse-graining, relaxation dynamics, and the emergence of classical time. The wrapper does not replace the technical content of the RP papers; it offers conceptual summaries only, and readers should consult the individual RP manuscripts for complete definitions, derivations, and formal arguments. The wrapper establishes the context and roadmap for the full Relaxation–Measurement framework.
This book is an educational companion volume to the UNIFICATION series and provides a clear, step-by-step introduction to the Chi Framework designed to be accessible to a broad audience, including motivated readers at the high-school level and beyond.Written for curious students, independent thinkers, and readers with an interest in physics, this textbook explores the possibility that Special Relativity and Quantum Mechanics may share a common structural boundary: the lightlike boundary.Across eight lessons, the reader is introduced gradually to the key ideas of the framework, including: * the shared lightlike boundary between relativistic and quantum descriptions, * the Chi parameter (χ) as a measure of closeness to that boundary, * the Delta parameter (δ) as a measure of deviation from it, * the interpretation of proper time as internal phase evolution, * the relationship between phase amplification and relativistic effects, * the coupled appearance of zero-like and infinity-like limiting behavior, * and possible future directions involving governing equations, curvature, and unification.The lessons are written in plain language and require only algebra-level mathematics. Each concept is developed carefully, with equations explained step by step, beginner-friendly examples, glossary sections, and visual interpretations.This textbook does not claim to present a complete or experimentally verified theory of physics. Rather, it serves two purposes: 1. to teach established concepts from relativity and quantum mechanics in an accessible way; and 2. to introduce the Chi Framework as an exploratory structural interpretation that may point toward deeper unification.Whether the Chi Framework ultimately proves to be a lasting contribution or simply a useful way of thinking, the goal of this book is to encourage curiosity, critical thinking, and exploration.This work is intended as a conceptual and educational companion to the technical UNIFICATION papers available separately. Currently Available: UNIFICATION 0 - A Shared Lightlike Boundary for Relativity and Quantum Theory - v1.00 https://doi.org/10.5281/zenodo.19860494 UNIFICATION I - Phase Structure and the Lightlike Boundary - v1.00 https://doi.org/10.5281/zenodo.19862660 UNIFICATION II - Implications of the Lightlike Boundary and Phase Structure - v1.00 https://doi.org/10.5281/zenodo.19863301 UNIFICATION III - Toward a Dynamical Formulation of the Lightlike Boundary Framework - v1.00 https://doi.org/10.5281/zenodo.19895578 UNIFICATION IV - Consequences and Implications of the Chi Framework - v1.00 https://doi.org/10.5281/zenodo.19896296 UNIFICATION V - Concerning the Current Absence of a Governing Equation for the Chi Framework - v1.00 https://doi.org/10.5281/zenodo.19921182 UNIFICATION VI: The Chi Boundary Method and Structural Invariants - v1.00 https://doi.org/10.5281/zenodo.19925550 UNIFICATION VII - A BOUNDED UNIVERSE 0 - Reciprocal Boundary Structure and the Reinterpretation of Zero and Infinity https://doi.org/10.5281/zenodo.20090590 UNIFICATION VIII - A BOUNDED UNIVERSE I - Math of Counting vs a New Zed/Irony Math - v1.01 https://doi.org/10.5281/zenodo.20128424 UNIFICATION IX - A BOUNDED UNIVERSE II - Toward a Bounded Interpretation of Relativistic Extremes - v1.00 https://doi.org/10.5281/zenodo.20160715 UNIFICATION X - A BOUNDED UNIVERSE III - Reciprocal Discernment and the Quantum Boundary - v1.00 https://doi.org/10.5281/zenodo.20171582 UNIFICATION - The Chi Framework - Eight Lessons on the Boundary Between Relativity and Quantum Mechanics - v1.00 https://doi.org/10.5281/zenodo.19863601 A public project archive containing all PDFs in the UNIFICATION series is also available through the Open Science Framework (OSF): UNIFICATION SERIES: https://osf.io/mpvgj/files/osfstorage/
NOTE · Observational Record — "The η Corridor". A paper of the framework's research as it stood when written, kept as printed; its computations stand and were re-verified at the September 2026 reprint. The corpus is now read through One coordinate up (DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)). The η Corridor in 3D Wilson–Fisher Critical Phenomena — Empirical Observation. The anomalous dimension η at d = 3 critical points of the Wilson–Fisher family is observed to be bounded above by 2G ≈ 0.039484, where G = 1 − K_AUD and K_AUD = √2·ln(2). The bound is tested across ten universality classes — O(N) for N = 0–4, cubic anisotropy at N = 3, 4, MN cubic at N = 2, 3, and randomly dilute Ising — and holds in every case, with σ-margins from +2.2σ (randomly dilute Ising, the tightest unitary case) to +1593σ (3D Ising, conformal bootstrap). Three classes outside the family's scope (RFIM, deconfined SU(2) QCP, disordered Potts at large q) have η > 2G and are excluded by independent physical structure. The bound is offered as a falsifiable empirical observation, not a derived result; the priority falsification target is a higher-precision η at d = 3 randomly dilute Ising. Part I presents the observation. Part II develops a structural reading on the dome function g(x) = tanh(x)/cosh(2x), known from hyperbolic-3-manifold geometry as the Hodgson–Kerckhoff tube-packing function. Ten theorems: the factorization g = (1/2)·sech²·tanh(2x); the golden polynomial u² − u − 1 in the logarithmic derivative; the self-reference uniqueness at u = √2; the dome integral ∫g dx = ln(2)/2; the Mellin spectrum M_g(s) = (s−1)!·η(s)·(2^s − 1)/2^(2s−1) with its rational/π closed forms and A002105 × Mersenne integer-ratio factorizations; the descent-to-K identity at R₀ where cosh(2R₀) = 2; the two algebraic environments at the HK landmarks; and the corridor-margin identity 1/ln 2 − √2 = G·log₂(e). A zero-parameter model based on the dome fits the resummation factor R(N) for the O(N) anomalous dimensions to 0.77 % RMS. The Central Synchronization Conjecture (§11) is flagged as a conjecture; derivation targets are listed as open. The paper claims no derivation of the bound from first principles, no mechanism for the constant's appearance across domains, and no connection to a physical theory not developed in it; the structural reading organizes what the observation invites, and a reader may adopt the observation without it (§14.6). A Verification Companion (a separate file in the same OSF project, shared DOI) carries the line-by-line mpmath verification of the algebraic identities at dps = 80–1000, including the re-verification at dps = 1000 (2026-05-28). Verified across seven independent AI architectures, including a twelve-agent, 1071-source reference-link check of the §16 citation block. Update — September 2026 (reprint with the reading-update block): every paper of the framework is re-issued with one short block under its title — "How the corpus is now read: One coordinate up — DOI 10.17605/OSF.IO/UJWC7 (https://osf.io/ujwc7)" — and is classed as a NOTE on the Documents page's Observational Record shelf under its short title "The η Corridor". The framework now writes the ratio p = GM/L_log and its complement G = 1 − p; K_AUD is this paper's own symbol for p and stays as printed. The fresh-print controls corrected six things in place: §5.1's SAW row 2G − η 0.008441 → 0.008440; the circumradius label in §13, bracketed; the §9.11 erratum written in place (the bridge sentence drops the factor (2^(2n) − 1); the theorems are unaffected); and in the Verification Companion five printed strings that carried digits beyond their computation's depth (2G's 100th–101st decimals; the last digit of M[g](2) and M[g](5); sinh and cosh of ln 2/2 from the 46th decimal) — corrected and noted in the reprint note. The prior version remains on OSF as an OLD- archived file. The framework Main OSF project (every paper, reading order, version history): https://osf.io/zx4g7 (DOI: 10.17605/OSF.IO/ZX4G7) The signpost — four doors: the framework, the instruments, the source, the deposits: https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/about.html The Documents page (current PDF and text of every paper, each with its DOI): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/direct-documents.html AI Readers (raw links and the verification block, for machine readers): https://gap-geometry.github.io/sqrt2-ln2-geometric-constants-/ai-readers.html GitHub: https://github.com/Gap-geometry
This document presents the formal mathematical axiomization of Relational Field Theory (RFT), establishing a single ontological primitive— the bounded scalar coherence field —and deriving the self-referential domain constraint .The Axiom Sheet (A1–A9) formalizes the Kernel identity, coherence evolution equation, domain threshold conditions, Genesis principle, and measurement-as-locking interpretation. A second section provides representative derived theorems showing how known physical laws emerge as limiting behaviors of and , including: Schrödinger equation as phase-locked Kernel dynamics Newtonian mechanics as low-curvature Rc trajectories General relativity as effective curvature geometry of Rc Maxwell/gauge structure as coherence-preserving invariants Thermodynamics as entropy of coherence loss Absence of physical singularities from Rc-threshold constraints This document serves as the foundational formal layer for the full RFT corpus, establishing the axiomatic base from which all subsequent proofs and derivations follow.
Preprint: This work is a preprint, has not undergone peer review, and is made publicly available to establish a public scientific record. This work presents a strictly structural analysis of directional Twin-Sign outcomes reported in Dynamical Information Geometry (DIG) Part VII. It derives minimal response-space implications from categorical PASS/FAIL classifications under fixed audit logic, without introducing new experiments, protocols, observables, or interpretive rules. Dynamical Information Geometry assigns an effective, state-dependent information geometry to quantum many-body dynamics via the curvature of coarse-grained mutual-information profiles. Earlier work introduced the theoretical framework (Part I), provided numerical evidence for sign-sensitive refraction effects (Part II), validated a minimal operational consequence on quantum hardware (Part III), established regime structure and operational necessity (Part IV), and formulated the intrinsic multidimensional (tensorial) nature of information geometry (Part V). Subsequent work reported experimental two-dimensional Twin-Sign validation under fixed audit and regime constraints (Part VII). The present work occupies a strictly consolidating and structural position within the DIG series. It does not perform new experiments, reanalyze raw measurement data, or extend the intervention space. Instead, it analyzes what minimal response-space structure is logically implied by the directional Twin-Sign outcome patterns already reported in DIG Part VII. Specifically, the work shows that simultaneous Twin-Sign PASS outcomes along two non-collinear projection directions necessitate the existence of a multidimensional response subspace. One-dimensional Twin-Sign behavior is identified as a degenerate projection of this structure. The analysis relies solely on linear independence and audit-fixed PASS/FAIL classifications and halts explicitly prior to any geometrical, dynamical, or ontological interpretation. No claim is made regarding the full dimensionality, geometry, dynamics, or reconstructability of the underlying response space. The structural necessity identified here is consistent with the DIG No-Derivation Claim: it does not enable reconstruction, dynamical inference, or ontological identification of internal response structures. All conclusions reported in this work are fully reproducible from the categorical Twin-Sign outcomes documented in DIG Part VII, using the publicly available dataset and analysis scripts provided therein, without additional assumptions. For reference and context, related DIG manuscripts include: DIG Part I (theoretical framework):https://doi.org/10.5281/zenodo.17983399 DIG Part II (“Positive Information Curvature and Acceleration of Operator Fronts”):https://doi.org/10.5281/zenodo.17982058 DIG Part III (“Hardware Validation of an Operational Consequence”):https://doi.org/10.5281/zenodo.18100057 DIG Part IV (regime structure and operational necessity):https://doi.org/10.5281/zenodo.18202656 DIG Part V (multidimensional formulation of the framework):https://doi.org/10.5281/zenodo.18210315 DIG Part VI (scaling 1D hardware validation):https://doi.org/10.5281/zenodo.18226369 DIG Part VII (“Two-Dimensional Twin-Sign Validation under Fixed Audit and Regime Constraints”):https://doi.org/10.5281/zenodo.18313460 A companion definitions and scope document (DIG — N1) is available at:https://doi.org/10.5281/zenodo.18001179This document fixes terminology, scope, and explicit non-equivalences of the Dynamical Information Geometry framework and serves as a definitional anchor for the present work. Normative interpretation rules for the Twin Test are fixed in DIG — N2:https://doi.org/10.5281/zenodo.18380514 The DIG No-Derivation Claim and scope delimitation are documented in:https://doi.org/10.5281/zenodo.18392928 Correspondence regarding this work may be directed to:kaya@cab-film.com