This paper advances a candidate structural reading: **the phase structure of a quantum system — particularly the presence or absence of a topological phase, a gap-closing transition, or a symmetry-breaking point — acts as a determinative organizing principle for the computational complexity of both preparing ground states and decoding error syndromes on that system.** This is a heuristic reading that identifies a recurring pattern across several independent lines of recent work; it is not a derivation from a single unified formalism. We synthesize findings from five primary domains within the quant-ph, math-ph, and cond-mat.stat-mech categories: (1) benchmarking of ground-state preparation algorithms across quantum phase transitions [corpus:arxiv:2606.20551v1]; (2) polynomial-time approximation schemes for minimum-weight decoding of topological codes [corpus:arxiv:2606.18145v1] and color codes [corpus:arxiv:2606.18035v1]; (3) the role of interaction geometry and graph-theoretic frustration in shaping ground-state phase structure [corpus:arxiv:2606.20387v1]; (4) the emergence of non-Hermitian single-particle PT transitions from many-body chaos as probed by a topological spectral form factor [corpus:arxiv:2606.19331v1]; and (5) the use of contextuality witnesses as thermodynamic diagnostics of translation-symmetry breaking [corpus:arxiv:2606.19033v1]. Across these works, a structural pattern emerges: topological or symmetry-breaking character in the underlying Hamiltonian or code geometry reshapes the cost landscape for algorithms operating on that system — sometimes favorably (enabling efficient approximation), sometimes adversarially (closing spectral gaps and defeating adiabatic protocols). The falsification path for the central thesis is concrete: identify a topological system for which the best known ground-state preparation algorithm does *not* degrade near the topological phase transition, or a trivial-phase system for which decoding hardness is equivalent to a topological one. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.18035v1, 2606.18145v1, 2606.19033v1, 2606.19331v1, 2606.20387v1, 2606.20513v1, 2606.20551v1
This paper advances a candidate structural reading: the phase structure of a quantum system — particularly the presence or absence of a topological phase, a gap-closing transition, or a symmetry-breaking point — acts as a determinative organizing principle for the computational complexity of both preparing ground states and decoding error syndromes on that system. This is a heuristic reading that identifies a recurring pattern across several independent lines of recent work; it is not a derivation from a single unified formalism. We synthesize findings from five primary domains within the quant-ph, math-ph, and cond-mat.stat-mech categories: (1) benchmarking of ground-state preparation algorithms across quantum phase transitions [corpus:arxiv:2606.20551v1]; (2) polynomial-time approximation schemes for minimum-weight decoding of topological codes [corpus:arxiv:2606.18145v1] and color codes [corpus:arxiv:2606.18035v1]; (3) the role of interaction geometry and graph-theoretic frustration in shaping ground-state phase structure [corpus:arxiv:2606.20387v1]; (4) the emergence of non-Hermitian single-particle PT transitions from many-body chaos as probed by a topological spectral form factor [corpus:arxiv:2606.19331v1]; and (5) the use of contextuality witnesses as thermodynamic diagnostics of translation-symmetry breaking [corpus:arxiv:2606.19033v1]. Across these works, a structural pattern emerges: topological or symmetry-breaking character in the underlying Hamiltonian or code geometry reshapes the cost landscape for algorithms operating on that system — sometimes favorably (enabling efficient approximation), sometimes adversarially (closing spectral gaps and defeating adiabatic protocols). The falsification path for the central thesis is concrete: identify a topological system for which the best known ground-state preparation algorithm does not degrade near the topological phase transition, or a trivial-phase system for which decoding hardness is equivalent to a topological one. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.18035v1, 2606.18145v1, 2606.19033v1, 2606.19331v1, 2606.20387v1, 2606.20513v1, 2606.20551v1
A recurring structural pattern appears across several recent preprints in quantum information, quantum sensing, and open-system dynamics: the act of *extracting* classical information from a quantum system is not a passive readout but an active, resource-consuming operation whose cost and fidelity depend jointly on measurement complexity, channel structure, physical noise geometry, and the topological character of the state being probed. This paper offers a heuristic reading — not a formal derivation — of five specific findings as instances of a single organizing question: *under what conditions does the quantum-to-classical interface become a bottleneck that determines what is knowable about a system, rather than merely a technical inconvenience?* Drawing from preprints in quant-ph and cond-mat.stat-mech, we identify four candidate mechanisms: (1) a sharp complexity-driven hidden-to-visible transition in quantum Fisher information accessibility [corpus:arxiv:2606.09765]; (2) the unification of cryptographic security and metrological sensitivity through channel symmetrization [corpus:arxiv:2606.10700]; (3) the reinterpretation of topological state discrimination as a weak-value measurement via Kirkwood-Dirac quasiprobabilities [corpus:arxiv:2606.11002]; and (4) the superposition of noise channels as a resource for recovering quantum capacity that individual channels cannot support [corpus:arxiv:2606.10744]. A fifth finding — that bosonic cyclic codes trade error-detection range for logical gate accessibility [corpus:arxiv:2606.11010] — is treated as a weakly connected addendum, connected by analogy rather than by shared mechanism. The falsification path is concrete: the complexity-threshold prediction of [corpus:arxiv:2606.09765] can be tested by constructing circuits of depth exactly at the critical threshold and measuring the Fisher information ratio as a function of system size. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2606.07339, 2606.09678, 2606.09734, 2606.09765, 2606.09805, 2606.10700, 2606.10744, 2606.10865, 2606.11002, 2606.11010
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
A central question in modern quantum matter is not merely *which* topological phases exist, but *how* and *when* they become accessible — the dynamical, microscopic, and symmetry-theoretic conditions under which topological order can actually emerge, be diagnosed, or be destroyed. This synthesis identifies a structural pattern across five specific findings from recent cond-mat.str-el, cond-mat.dis-nn, and cond-mat.mes-hall preprints: (1) non-Hermitian delocalization generically realizes random Dirac criticality in 1D, providing a topological mechanism for criticality without fine-tuning [corpus:arxiv:2606.12089]; (2) the fate of symmetry-protected topological order under nonequilibrium drives is governed by excitation density rather than by which phase regime is entered, with Kibble-Zurek defect production as the decisive control parameter [corpus:arxiv:2606.11303]; (3) exceptional points in interacting non-Hermitian systems amplify charge-density-wave instabilities under open boundary conditions, demonstrating that non-Hermitian boundary topology actively reshapes interaction-driven phase competition [corpus:arxiv:2606.06466]; (4) sequential-circuit invariants of non-invertible symmetry defects provide a purely operator-theoretic diagnostic of 't Hooft anomalies and identify genuinely new loop excitations with non-Abelian fermionic statistics in (3+1)D [corpus:arxiv:2606.11527]; and (5) deconfined quantum critical points in spin chains with Lieb-Schultz-Mattis anomalies are dual, via gauging, to spontaneous breaking of non-invertible symmetries, with the full fusion category — not merely the fusion ring — encoding inequivalent universality classes [corpus:arxiv:2606.05856, corpus:arxiv:2606.06343]. The synthesis argues, as a heuristic reading rather than a derivation, that excitation production, boundary-condition sensitivity, and categorical symmetry structure constitute three interlocking control axes for topological order accessibility. A concrete falsification path is proposed for each claim. The abstract-only reading methodology is acknowledged as a structural limitation throughout. --- 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, 2605.29875, 2606.04651, 2606.04748, 2606.04958, 2606.05856, 2606.06343, 2606.06412, 2606.06432, 2606.06466, 2606.07041, 2606.07241, 2606.07247, 2606.08558, 2606.08805, 2606.09759, 2606.11048, 2606.11303, 2606.11527, 2606.12089, 2606.12353
A structurally coherent pattern emerges across recent preprints in cond-mat.str-el and cond-mat.mes-hall: the question of *when* and *how* topological order emerges in quantum many-body systems cannot be answered by equilibrium phase diagrams alone. The emergence depends jointly on (i) the microscopic excitation production mechanism during dynamical protocols, (ii) the categorical symmetry structure that classifies what phases are even reachable, (iii) the anomaly type encoded in the Lyndon–Hochschild–Serre spectral sequence, (iv) the defect statistics and fusion rules that distinguish topological phases sharing identical anyon content, and (v) the non-Hermitian or interaction-driven amplification of charge instabilities near exceptional points. This is a heuristic reading, not a derivation: the five sources share conceptual architecture but not a common formalism. The thesis, stated as a candidate structural pattern worth investigating, is: **topological order is protocol-sensitive precisely because the categorical invariants that distinguish phases are invisible to local order parameters and can be populated or evacuated only by excitation-density-controlled dynamics**. Concretely, a sudden quench generically populates excitations that are orthogonal to the topological ground-state manifold, while slow ramps suppress this population via Kibble–Zurek mechanisms; categorical symmetry then determines which topological sectors are accessible at all; and anomaly type (E∞^{1,2} vs. E∞^{2,1}) determines whether the transition is dual to ordinary symmetry breaking or to the spontaneous breaking of a non-invertible symmetry. The falsification path is concrete: DMRG or tensor-network simulations of a spin-1/2 chain with D₈ LSM anomaly should show that a sudden quench into the DQCP regime fails to build non-invertible Rep(H₈) order parameters, while an adiabatic ramp does—a prediction that follows from the corpus findings taken together but has not yet been directly tested. Primary categories drawn upon: cond-mat.str-el (seven papers), cond-mat.mes-hall (two papers), cond-mat.dis-nn (one paper, weakly connected). --- 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, 2605.29875, 2605.31602, 2606.05856, 2606.06343, 2606.06466, 2606.07241, 2606.07247, 2606.08558, 2606.09722, 2606.09759, 2606.11048, 2606.11303, 2606.11527, 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 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