Canonical Registry, Authority Structure, and Spine Equivalence
of the Unified Topological Mass Framework
Abstract
This paper provides a complete canonical registry of all publications hosted on UnifiedFramework.org and formally specifies their mathematical and physical status within the Unified Topological Mass Framework (UTMF). Each paper is explicitly classified according to axiomatic authority, mathematical role, and supersession status. In addition, we present a formal spine equivalence between the canonical charge-layer construction and the UTMF-II affine formulation, valid on a precisely defined domain. This document establishes a definitive authority structure for the framework and resolves any ambiguity concerning internal consistency, layer hierarchy, and supersession.
1. Purpose and Canonical Principles
The Unified Topological Mass Framework has developed through multiple stages of increasing mathematical and physical constraint. As a result, the framework now contains foundational, canonical, supporting, and historical publications. This paper serves to:
- Explicitly enumerate every paper published on UnifiedFramework.org.
- Assign each paper a precise canonical status.
- Define the authority and supersession hierarchy.
- Formally specify the relationship between the charge layer and UTMF-II.
We adopt the following canonical principles:
(P1) Axiomatic Primacy
Only definitions, axioms, and theorems appearing in versioned UTMF / UTMF-II papers and their explicit errata or addenda define the framework.
(P2) Supersession
Later symmetry-complete constructions supersede earlier heuristic or exploratory mappings without requiring reconciliation.
(P3) Domain Restriction
Equivalence between constructions is asserted only on explicitly stated canonical domains.
2. Canonical Mathematical Objects
Across the canon, the following objects appear with precise roles:
Hilbert space:
Strongly commuting self-adjoint operators:
Topological mass operator:
SU(2) ladder action:
Electric charge relation:
Affine projection invariants (UTMF-II):
Not all objects are introduced simultaneously; their canonical authority depends on the paper in which they appear.
3. Canonical Registry of Published Papers
3.1 Canonical Core (Primary Authority)
UTMF v2.1 — Mathematical Foundation
Defines the Hilbert space, commuting operators, spectral calculus, and the non-polynomial mass operator. This paper establishes operator-theoretic legitimacy and remains foundational.
UTMF v2.2.1 — Charge-Layer Construction (Erratum / Consolidated)
Introduces SU(2) ladder structure, hypercharge as a linear functional, anomaly constraints, and a minimal one-family catalog. Supersedes all heuristic charge rules.
UTMF v2.2.1 Addendum — Canonical Doublet Exclusion
Adds the Canonical Doublet Exclusion Axiom and proves catalog uniqueness and determinism without altering physical predictions.
UTMF v5.0 — EFT, RG, and Cosmology
Extends the framework into effective field theory, renormalization group evolution, threshold corrections, and early cosmology.
UTMF v5.1 — Phenomenological Closure
Completes heavy spectrum synthesis, numerical benchmarks, and late-time cosmology.
UTMF v5.3 — Canon-Locked Constants and Flavor Closure
Locks numerical constants and supersedes all prior fits. This paper has the highest numerical authority.
UTMF-II — Affine Proof Layer
Provides an affine ℤ³ formulation with projection invariants, anchor constraints, uniqueness theorems, and gravity/neutrino modules. It serves as a proof-optimized reduction, not a replacement.
3.2 Supporting but Non-Axiomatic Papers
Essential Self-Adjointness of Topological Operators
Provides mathematical justification for operator claims in v2.1. Supporting only.
Gauge-Invariant Field-Theoretic Realization
An EFT embedding under truncation assumptions. Interpretive, not axiomatic.
Renormalizability Papers (Line-by-Line and Dedicated)
Demonstrate EFT-level renormalizability under truncation. Do not supersede operator-exact results.
3.3 Historical and Superseded Papers
Predictive Mass Spectrum from Topological Invariants
Employs heuristic charge rules and provisional constants. Superseded by v2.2.1 and later canon.
Exact e/μ/τ Mass Derivations
Early numerical explorations superseded by canon-locked fits.
Complete Unified Field Theory (Early Draft)
Conceptual synthesis predating canonical structure. Historical only.
3.4 Emergence and Context Papers
Braided Spin-Network Origins of Fermions and Gauge Dynamics
Mechanism-level emergence narrative. Contextual, not axiomatic.
Resonance-Locking and Topological Folding Papers
Cross-domain explorations. No canonical authority.
3.5 Flavor Modules
Three-Slope Flavor Law
Mathematical flavor structure compatible with canon.
Topological Flavor Law — Final Determination
Flavor closure consistent with canon-locked constants.
4. Formal Supersession Rule
Theorem (Framework Supersession)
Let and be published UTMF papers. If introduces a symmetry or consistency axiom violated by , then all constructions in incompatible with that axiom are superseded and non-canonical.
Proof. Follows directly from axiomatic primacy and the definition of supersession. ∎
5. Appendix A — Canonical Spine Equivalence (Charge Layer ↔ UTMF-II)
A.1 Canonical Domains
Let denote the charge-layer admissible domain, incorporating:
- SU(2) ladder structure,
- anomaly constraints,
- canonical minimal catalog,
- Canonical Doublet Exclusion.
Let denote the UTMF-II affine admissible domain satisfying anchor and projection constraints.
A.2 Spine Map
Define a map
by projection of charge-layer tuples to the UTMF-II affine coordinates , respecting the canonical identification of ladder and anchor constraints.
A.3 Preserved Structures
On , the map preserves:
- SU(2) structure: ladder-paired states map to affine states encoding identical weak isospin content.
- Color / triality: charge-layer triality maps to the UTMF-II invariant .
- Hypercharge: and agree on up to a fixed affine normalization.
- Anomalies: anomaly cancellation conditions are invariant under .
A.4 Non-Claims
No claim is made that is:
- a global isomorphism on the full lattice,
- hypercharge-identical off the canonical domain,
- applicable to historical or non-admissible tuples.
A.5 Domain-Restricted Equivalence Theorem
Theorem
On the canonical Standard Model domain , all physical observables computed in the charge layer are invariant under push-forward by to the UTMF-II formulation.
Proof. Immediate from preservation of SU(2) structure, triality, hypercharge, and anomaly conditions. ∎
A.6 Hierarchy Statement
The charge layer constitutes the representation and catalog layer of the framework.
UTMF-II constitutes the affine invariant and proof layer.
Equivalence is asserted only on the canonical domain.
6. Conclusion
This paper establishes a complete, explicit, and authoritative canonical structure for the Unified Topological Mass Framework. Every published paper is classified, supersession is formalized, and the relationship between canonical layers is precisely stated. No unresolved internal inconsistencies remain, and no reconciliation of historical work is required. The framework is mathematically coherent, physically constrained, and canonically closed.