This document provides an index and navigation layer for a set of four related records forming a single logical unit within the Tuckwell corpus: (1) a theoretical condition for torus topology, (2) a spectral discriminator (D3), (3) a boundary case demonstrating non-equivalence (Lohmiller–Slotine), (4) a testable experimental protocol (optical probe v0.1). Together these define a complete structure: theory → discrimination → boundary → experiment The theoretical result establishes a minimal algebraic condition for torus topology via two independent commuting S1 actions, yielding Z x Z winding-index organisation. The D3 discriminator reads this structure from spectral organisation. The related signal note demonstrates a negative case: a classical multipath density formulation that reproduces quantum wave functions but does not satisfy the D3 condition. The experimental protocol defines a minimal optical test using two phase variables (theta_1, theta_2) in S1 x S1, including local commutation testing and Z x Z mode detection. No new claims are introduced. This document serves only to map relationships, define entry points, and identify open questions. Open questions include: - Whether a physical optical system can be constrained to satisfy D3 conditions - Whether measurable mode lattices emerge under commuting phase flows - The quantitative behaviour of non-commutation (C_max) This index enables the corpus to be cited and reviewed as a unified structure rather than as separate records. Keywords: corpus index torus topology spectral geometry D3 discriminator commuting circle actions quantum optics phase space topology experimental protocol constraint systems
This document provides an index and navigation layer for a set of four related records forming a single logical unit within the Tuckwell corpus: (1) a theoretical condition for torus topology, (2) a spectral discriminator (D3), (3) a boundary case demonstrating non-equivalence (Lohmiller–Slotine), (4) a testable experimental protocol (optical probe v0.1). Together these define a complete structure: theory → discrimination → boundary → experiment The theoretical result establishes a minimal algebraic condition for torus topology via two independent commuting S1 actions, yielding Z x Z winding-index organisation. The D3 discriminator reads this structure from spectral organisation. The related signal note demonstrates a negative case: a classical multipath density formulation that reproduces quantum wave functions but does not satisfy the D3 condition. The experimental protocol defines a minimal optical test using two phase variables (theta_1, theta_2) in S1 x S1, including local commutation testing and Z x Z mode detection. No new claims are introduced. This document serves only to map relationships, define entry points, and identify open questions. Open questions include: - Whether a physical optical system can be constrained to satisfy D3 conditions - Whether measurable mode lattices emerge under commuting phase flows - The quantitative behaviour of non-commutation (C_max) This index enables the corpus to be cited and reviewed as a unified structure rather than as separate records. Keywords: corpus index torus topology spectral geometry D3 discriminator commuting circle actions quantum optics phase space topology experimental protocol constraint systems
This document defines a minimal experimental protocol for testing whether a photonic quantum-link platform can be constrained so that its output modes are organised by two independent commuting winding indices, rather than by externally programmed phase parameters. The protocol is designed for application to optical systems such as electro-optic transducer networks and programmable Mach–Zehnder interferometer meshes. It isolates two phase variables (θ1, θ2) ∈ S1 × S1 and applies three tests: (1) periodic closure on S1, (2) local commutation of infinitesimal phase flows, (3) spectral organisation as a Z x Z mode lattice with non-zero cross modes. The central condition is Test 2 v1.1, which measures the commutation residual C(θ1_0, θ2_0, δ) = ||Output_A − Output_B|| across the phase space. The maximum deviation C_max(δ) provides a quantitative measure of non-commutation. The protocol does not claim that existing optical link systems exhibit torus topology. It defines a testable constraint under which such topology would be detectable via the D3 spectral discriminator framework (Tuckwell, 2026). No experiment has been performed. C_max(δ) is unmeasured. The document is presented as an initial experimental design (v0.1) and is open to revision upon implementation. Structural analogy: PASS. D3 equivalence: FAIL. Experimental platform relevance: VERY HIGH. Keywords: torus topology spectral geometry quantum optics optical interferometry Mach-Zehnder interferometer phase space topology commuting generators winding indices D3 spectral discriminator experimental protocol electro-optic transduction quantum communication
Lohmiller and Slotine (Proc. Royal Society A, 2026) show that classical constrained systems can reproduce quantum wave functions via multivalued action and density, establishing a computational equivalence between the Hamilton–Jacobi equation and the Schrödinger equation under appropriate density construction. This note evaluates that result against the D3 spectral discriminator (Tuckwell, 2026), which requires two independent commuting S1 actions and Z x Z winding-index organisation as the minimal algebraic condition for torus topology T2 = S1 x S1. The Lohmiller–Slotine construction does not satisfy the D3 condition: no independent cyclic generators, no commutativity requirement, and no Z x Z mode indexing are present. The constraint mechanism is analytic (density weighting over least-action paths) rather than topological (fundamental group condition on the manifold). However, the result reinforces the broader constraint-selection principle and identifies a testable bridge: whether the density-action formulation, applied within a toroidal confinement geometry, produces modes organised by commuting winding indices (m, n) in Z x Z. This document is filed as a standalone related signal note within the Tuckwell corpus. Structural analogy: PASS. D3 equivalence: FAIL. Corpus relevance: HIGH.
Overview This Zenodo record gathers the connected mathematical, computational and methodological corpus developed by Thierry Origas under the title Riemann Strong Origas. The corpus is organised as a three-level scientific programme: the local level — World A, represented by Galilean and Einsteinian local frames, experimentally accessible measurements, spectral outputs, operators and predictive results; the exchange and reconstruction level — the Cabine 1/2, represented by Point 0, the structural bridge Kstr, the finite arithmetic prototype KX, the global history parameter T and the differentiated local branches t+ and t−; the frozen non-local level — World B, represented by an independent EPR-type observational question asking whether the proposed Double RingCross Origas structure is physically real. The central reconstruction problem The central mathematical question is whether a common local observation, a spectrum, a determinant or a predictive output is sufficient to reconstruct the complete structure that produced it. The corpus studies situations in which two differentiated sectors A and B may project onto the same observable Point 0 while retaining different order, projector, phase, orientation, holonomy, gluing and history data. In such a case, a representation that depends only on the common projected output is not conservative. The Cabine 1/2 is therefore introduced as an over-arching reconstruction framework rather than as an additional local measurement device. In its consolidated mathematical formulation, it is represented by a third object connecting two local sectors through a common observation space. The corpus makes a strict distinction between: Kstr: the structural gluing datum required to preserve the fibre, order, phases, projectors, holonomy and history; KX: a finite, prime-generated arithmetic prototype proposed as a candidate realisation of this bridge; T: a global parameter of history, provenance and ordering; t+ and t−: two differentiated local branches associated respectively with predictive or spectral information and with differential, historical or geometric information. Mathematical and computational programme The successive manuscripts develop two-sector chiral operators, spectral-blindness and non-reconstruction theorems, four graded roots around Point 0, B-completeness criteria, oriented holonomy, topos-conservative reconstruction, prime-power-generated phases, sealed out-of-sample predictions, Null tests, Bridge-OFF controls and criteria for temporal and conservative completeness. A recurring result of the programme is that identical spectral outputs do not necessarily determine identical projectors, indices, orientations, histories or hidden geometries. The ordinary spectrum may describe a common visible channel while leaving a differentiated wing undetermined. The finite arithmetic bridge KX is constructed from declared prime and prime-power data and frozen parameters. Its numerical performance, phases, wing labels and sealed predictions are computational results. KX is not identified with the final infinite Riemann operator unless convergence toward the completed Riemann function, determinant identification, self-adjointness and complete conservative reconstruction are independently established. Relationship to the Wang–Kakeya publication This corpus is directly related to the previously published Zenodo record DOI 10.5281/zenodo.21535840, which applies a corresponding conservative A+B methodology to Kakeya geometry. The Wang–Kakeya record constitutes a specific application of the broader reconstruction question developed here: a projected spatial support or a correct theoretical result may remain insufficient to reconstruct incidence histories, non-commutative order, multiscale structure, oriented holonomy or all the information carried by the complete A+B object. The purpose of the A+B lift is not to invalidate or replace the original Kakeya result. It is to investigate whether a richer conservative representation can preserve additional operational information while leaving the established result intact. Relationship to Aspect, Connes and contemporary programmes The published works of Alain Aspect, Alain Connes, Hong Wang and the other researchers cited in the manuscripts are used as scientific references, comparison points and boundary cases. Their presence in this record does not imply collaboration, endorsement or agreement with the author’s interpretations. The corpus does not claim that their established experimental or mathematical results are invalid. It asks a different and stronger reconstruction question: in addition to producing a correct observable or spectral output, does a model preserve the order, projectors, phases, holonomy, gluing data and history required to reconstruct the complete differentiated structure? Non-commutativity is treated not merely as an algebraic complication but as a possible carrier of order and meaning. Commutativisation may be legitimate for a declared output while remaining non-conservative for the complete history from which that output was derived. The frozen non-local EPR question A separate series of prior Zenodo deposits contains frozen, dated and publicly traceable predictions associated with an EPR-type question posed to Nature: is the proposed Double RingCross Origas structure real? This question is not presented in the present record as already answered. The Double RingCross, its proposed role as an external clock or space-time structure, the non-local interpretation of World B and the physical interpretation of T remain hypotheses awaiting independent observational adjudication. Within the author’s methodology, Nature is treated as the final empirical adjudicator. This means that the outcome must be determined by observations made under declared coordinates, tolerances, instruments and protocols, without post-hoc modification of the frozen question or predictions. If the independent observations answer negatively, the corresponding non-local interpretation must be rejected or revised. If they answer positively under the frozen conditions, the result would provide an external empirical anchor for the relationship between the local sector, the Cabine 1/2 exchange level and the proposed non-local sector. In neither case may the mathematical requirements of the Riemann programme be replaced by a physical interpretation. Scientific status This record does not claim: a completed proof of the Riemann Hypothesis; the established non-existence of Planet Nine; the present observational validation of the Double RingCross; the experimental establishment of a universal absolute physical reference frame; the physical identification of Kstr, KX or T without an independent test. The corpus contains several distinct levels of result: exact mathematical statements under explicitly declared assumptions; finite and reproducible computational constructions; numerical audits and sealed predictions; methodological interpretations and proposed reconstruction criteria; local physical analogies and protocols; open non-local hypotheses awaiting independent observational adjudication. These levels must be evaluated separately. A result established at one level is not automatically promoted to a stronger mathematical, physical or ontological status. Corpus organisation Strong Origas XI is the consolidated mathematical entry point. Earlier manuscripts preserve the chronological development of the programme, including corrections, negative results, intermediate constructions, proof-status distinctions and computational stages. The principal international editions are provided in English. Two French-language source manuscripts are retained in their original language where exact authorial formulation is considered important. Their language does not alter their scientific status.
A recurring pattern across several recent preprints in condensed-matter physics is that the *density of excitations above the ground state* functions as a decisive control parameter for whether topological order can emerge, persist, or be characterized — and that this density is shaped not only by equilibrium phase boundaries but by the microscopic dynamics of how a system is driven, the boundary conditions imposed, the non-Hermitian structure of the effective Hamiltonian, and the algebraic framework used to classify order parameters. This synthesis draws on six papers from cond-mat.str-el and cond-mat.dis-nn (plus one connecting result from cond-mat.mes-hall) to develop a candidate reading — explicitly heuristic, not a derivation — of how these mechanisms compose. The central thesis is: topological order is not merely a property of a ground-state wave function but a *dynamically conditional* object whose emergence requires simultaneous suppression of excitation density (controlled by ramp protocol [corpus:arxiv:2606.11303]), non-Hermitian boundary-condition sensitivity [corpus:arxiv:2606.06466], and categorical symmetry structure [corpus:arxiv:2605.27672; corpus:arxiv:2606.05856; corpus:arxiv:2606.06343; corpus:arxiv:2605.31601]. The microscopic universal theory of symmetry-enriched topological quantum spin liquids [corpus:arxiv:2606.08558] provides the overarching framework within which these conditions can, in principle, be stated precisely. The falsification path is concrete: DMRG or tensor-network simulation of an interacting non-Hermitian SSH chain under controlled ramp protocols should reveal whether the exceptional-point amplification of charge-density-wave order [corpus:arxiv:2606.06466] suppresses or merely delays SPT order buildup in a manner quantitatively consistent with Kibble-Zurek defect counting. The synthesis is limited by abstract-only reading and by the fact that the papers do not share a common formalism; bridges between them are argued by mechanism, not derived. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166, 2605.27672, 2605.29745, 2605.29875, 2605.31540, 2605.31601, 2606.02512, 2606.04651, 2606.04748, 2606.04958, 2606.05856, 2606.06343, 2606.06412, 2606.06432, 2606.06466, 2606.06490, 2606.07241, 2606.08558, 2606.08805, 2606.09722, 2606.09759, 2606.11048, 2606.11060, 2606.11303, 2606.12089, 2606.12180, 2606.12353
A recurring obstacle in quantum many-body physics is the identification of phase boundaries from microscopic, experimentally accessible quantities rather than from effective field-theoretic arguments applied post hoc. This synthesis examines five specific findings from recent cond-mat.str-el, cond-mat.dis-nn, cond-mat.mes-hall, and physics.atom-ph preprints and argues — as a heuristic reading, not a derivation — that they converge on a shared structural pattern: phase boundaries are most sharply located when excitation production, spectral topology, or symmetry-defect statistics can be directly controlled or measured at the microscopic level. The sources span (i) non-Hermitian delocalization realizing random Dirac criticality in 1D via spectral winding [corpus:arxiv:2606.12089], (ii) protocol-dependent SPT order emergence governed by Kibble-Zurek defect suppression [corpus:arxiv:2606.11303], (iii) categorical symmetry structure encoding deconfined quantum critical points beyond the Landau paradigm [corpus:arxiv:2606.05856], (iv) a constrained Rydberg spin chain whose phase diagram is fully resolved by DMRG and exact factorization lines [corpus:arxiv:2605.27166], and (v) strain-tunable bandgap and doping in carbon nanotube quantum dots as a direct mechanical handle on transport phase boundaries [corpus:arxiv:2606.12180]. Two additional sources serve supporting roles: the non-Hermitian interacting SSH model demonstrating that exceptional-point proximity amplifies charge-density-wave instabilities [corpus:arxiv:2606.06466], and the Localization Landscape Theory analysis on the Bethe lattice distinguishing percolation from Anderson-transition criticality [corpus:arxiv:2605.29745]. The central falsification path is concrete: if SPT order can be produced by sudden quench protocols in systems where excitation density is independently controlled (e.g., via post-selection or feedback cooling), the excitation-suppression mechanism claimed in [corpus:arxiv:2606.11303] would require revision. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166, 2605.29745, 2606.04958, 2606.05856, 2606.06343, 2606.06432, 2606.06466, 2606.09759, 2606.11048, 2606.11060, 2606.11303, 2606.12089, 2606.12180
A recurring structural question across quantum foundations, many-body physics, and quantum information is deceptively simple: under what conditions does quantum dynamics produce outcomes that look classical? This paper synthesizes five to seven specific findings from the recent arXiv corpus — drawn primarily from quant-ph and cond-mat.stat-mech preprints — to argue for a candidate heuristic reading (explicitly not a derivation) in which classicality emergence, spectral phase transitions, and non-Hermitian dynamics are linked by a shared mechanism: the selective destruction of coherence across competing symmetry sectors. We identify three structural primitives that recur across these works — (1) symmetry-sector selection as a driver of effective classicality, (2) topological and spectral defect insertions as probes of dynamical phase structure, and (3) non-Hermitian exceptional-point physics as a boundary marker between coherent and incoherent regimes — and argue that these primitives appear, with different surface languages but analogous roles, in the random-matrix projective quantum mechanics framework [corpus:arxiv:2606.19272], the topological spectral form factor analysis [corpus:arxiv:2606.19331], the isolated-system classicality derivation [corpus:arxiv:2606.19188], the contextuality-as-thermodynamics result [corpus:arxiv:2606.19033], and the non-Hermitian phase diagram work [corpus:arxiv:2606.18916]. A weakly connected addendum discusses the quantum magic / wormhole teleportation result [corpus:arxiv:2606.19180] as an analogy rather than a mechanistic contributor. The primary falsification path for the central claim is concrete: if classicality in isolated systems can be demonstrated in systems where no symmetry sector dominates the long-time equilibrated state, the sector-selection mechanism is insufficient and the heuristic reading fails. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.16785, 2606.17771, 2606.17908, 2606.18145, 2606.18240, 2606.18635, 2606.18871, 2606.18916, 2606.19033, 2606.19180, 2606.19188, 2606.19239, 2606.19272, 2606.19273, 2606.19331