# Furey source-provenance matrix

**Prepared:** 24 October 2026  
**Status:** attribution control for the foundational review; bibliographic locator, not independent reproduction  
**Controls:** [Furey comprehensive review](../../claims/0000-0099/02_furey_comprehensive_research_review.md) · [technical guide](../../claims/0000-0099/03_furey_technical_algebraic_guide.md) · [foundational acceptance audit](spin23_foundational_document_acceptance_20261021.md)

## Purpose

This matrix prevents three layers from being blended:

1. what Furey's cited publications explicitly construct or claim;
2. what the foundational review infers or uses as physical interpretation; and
3. what the later Spin(2,3)/admissibility corpus independently derives, tests or rules out.

The links below identify the primary source and the corresponding review section. They do not certify every displayed derivation in the source. Equation-, proposition- and page-level reproduction remains a specialist verification task wherever the final column says **reproduce**.

## Primary-source map

| Source | Primary object/result used by the review | Review location | Attribution boundary | Verification state |
|---|---|---|---|---|
| Furey, [*Towards a unified theory of ideals*](https://arxiv.org/abs/1002.1497) | Generalised ideals in complex quaternionic and octonionic settings; Lorentz-spinor and particle-representation motivation | [§3.1](../../claims/0000-0099/02_furey_comprehensive_research_review.md#31-towards-a-unified-theory-of-ideals-20102012) | Representation behaviour does not supply a local action, quantisation or empirical particle identification. | Source identified; reproduce transformation conventions. |
| Furey, [*Generations: Three Prints, in Colour*](https://arxiv.org/abs/1405.4601) | Three generation-like copies from the complex Clifford/octonionic construction | [§6.1](../../claims/0000-0099/02_furey_comprehensive_research_review.md#61-generations-three-prints-in-colour) | Algebraic multiplicity is not yet three complete chiral Standard-Model families with observed dynamics. | Source identified; reproduce module decomposition. |
| Furey, [*Charge quantization from a number operator*](https://arxiv.org/abs/1603.04078) | Ladder operators, minimal left ideals and number-operator charge assignments | [§4.1](../../claims/0000-0099/02_furey_comprehensive_research_review.md#41-charge-quantization-from-a-number-operator-and-the-2016-thesis) | Charge-like eigenvalues require physical normalization, gauging and anomaly-compatible embedding. | Source identified; core algebra summarized. |
| Furey, [*Standard model physics from an algebra?*](https://arxiv.org/abs/1611.09182) | Unified technical presentation of ideals, Clifford actions, charge, colour and Lorentz constructions | [§4](../../claims/0000-0099/02_furey_comprehensive_research_review.md#4-phase-ii-one-generation-from-complex-octonions) and [technical guide](../../claims/0000-0099/03_furey_technical_algebraic_guide.md) | Thesis-level programme and representation results must not be cited as a completed Standard-Model QFT. | Principal technical source; reproduce convention-sensitive identities as used. |
| Furey, [*A demonstration that electroweak theory can violate parity automatically*](https://doi.org/10.1142/S0217751X18300053) | Algebraic asymmetry between left- and right-handed leptonic sectors | [§5](../../claims/0000-0099/02_furey_comprehensive_research_review.md#5-phase-iii-electroweak-chirality) | Leptonic parity structure is not by itself the full quark-lepton chiral theory or an anomaly analysis. | Source identified; reproduce action of the stated algebra. |
| Furey, [*SU(3)×SU(2)×U(1)(×U(1))*](https://arxiv.org/abs/1806.00612) | Symmetries preserving division-algebraic ladder-operator structure | [§5](../../claims/0000-0099/02_furey_comprehensive_research_review.md#5-phase-iii-electroweak-chirality) | A stabiliser/symmetry algebra is not yet a dynamical gauge field with a selected vacuum. | Source identified; reproduce stabiliser intersection. |
| Furey, [*Three generations, two unbroken gauge symmetries, and one eight-dimensional algebra*](https://arxiv.org/abs/1910.08395) | Generation structure and simultaneous unbroken symmetry actions in one algebraic setting | [§6.2](../../claims/0000-0099/02_furey_comprehensive_research_review.md#62-three-generations-two-unbroken-gauge-symmetries-and-one-eight-dimensional-algebra) | The result concerns algebraic representations; family masses, mixing, locality and dynamics remain external. | Source identified; reproduce multiplicity and symmetry action. |
| Furey & Hughes, [*Division algebraic symmetry breaking*](https://arxiv.org/abs/2210.10126) | Nested compatible complex structures and a symmetry-breaking cascade | [§7](../../claims/0000-0099/02_furey_comprehensive_research_review.md#7-phase-v-division-algebraic-symmetry-breaking) | Selection of algebraic compatibility data is not a derived potential, phase transition or cosmological history. | Source identified; reproduce common-stabiliser chain. |
| Furey, [*Algebraic Roadmap I*](https://arxiv.org/abs/2312.12377) | General construction language for particle-theory algebras and their actions | [§8](../../claims/0000-0099/02_furey_comprehensive_research_review.md#8-phase-vi-the-algebraic-roadmap-and-intersections) | Roadmap structure organizes candidates; it does not itself choose the physical carrier or action. | Source identified; terminology cross-checked in review. |
| Furey, [*Algebraic Roadmap II*](https://arxiv.org/abs/2312.12799) | Checkpoints and constraints on candidate algebraic particle constructions | [§8](../../claims/0000-0099/02_furey_comprehensive_research_review.md#8-phase-vi-the-algebraic-roadmap-and-intersections) | Checkpoints are algebraic admissibility conditions, not empirical confirmation. | Source identified; reproduce checkpoints used by later comparisons. |
| Furey, [*Algebraic Roadmap III*](https://arxiv.org/abs/2312.14207) | Intersections of symmetry-preserving structures used to isolate Standard-Model-like algebra | [§8](../../claims/0000-0099/02_furey_comprehensive_research_review.md#8-phase-vi-the-algebraic-roadmap-and-intersections) | An intersection result does not derive gauge kinetics, Higgs dynamics or fermion masses. | Principal intersection source; reproduce exact common stabiliser. |
| Furey & Hughes, [*Three Generations and a Trio of Trialities*](https://arxiv.org/abs/2409.17948) | Three triality slots and generation-like representation structure | [§9](../../claims/0000-0099/02_furey_comprehensive_research_review.md#9-phase-vii-three-generations-and-three-triality-slots) | Triality slots must not be identified with observed families until complete chiral content and interactions are matched. | Source identified; reproduction and anomaly comparison open. |
| Furey, [*A Superalgebra Within*](https://arxiv.org/abs/2505.07923) | Light-particle representations assembled into a \(\mathbb Z_2^5\)-graded algebraic structure | [§10](../../claims/0000-0099/02_furey_comprehensive_research_review.md#10-phase-viii-a-mathbb-z_25-graded-jordan-superalgebra) | Graded closure is an algebraic organization, not a supersymmetric field theory or measured new symmetry. | Source identified; reproduce grading and product conventions. |
| Furey, [*Standard Model Symmetries and the Nested Embeddings*](https://arxiv.org/abs/2607.18450) | Compatibility conditions arising from \(\mathbb R\subset\mathbb C\subset\mathbb H\subset\mathbb O\) and associated endomorphism algebra | [§11](../../claims/0000-0099/02_furey_comprehensive_research_review.md#11-phase-ix-nested-embeddings-july-2026) | Nested algebra labels do not provide a spacetime carrier, dynamics or a Spin(2,3) identification. | Current source horizon; detailed equation audit open. |

## Later corpus results that must not be back-attributed

The following belong to this corpus unless and until independent prior art is attached directly to the relevant claim:

- the typed Furey-shaped channel generator's participation in full \(\mathfrak{sp}(4,\mathbb R)\) closure;
- the charge-minus-two phase-reference reopening criterion;
- the specific ternary-operator/module, anomaly and CP classification programme;
- the Kantor, structurable and Freudenthal extension tests;
- the magic-square, triple-bond, Golay/Leech and modular frontier crosswalks; and
- the admissibility-zone interpretation joining state cones, dynamics, detectors and frontier bounds.

These may be motivated by Furey's work or adjacent mathematics, but motivation is not provenance.

## Maintenance rule

When a document makes a Furey-related claim, it should cite either a primary source row above or a numbered corpus claim that explicitly owns the later deduction. If neither exists, label the statement as a question or analogy. A future page-level audit should add exact equation, proposition or page locators without strengthening the source's physical claims.