arXiv:2604.04069v1 Announce Type: new Abstract: Information flow is central to contemporary accounts of cognition, yet its physical basis in living neural matter remains poorly specified. Here, we develop a multiscale resource-theoretical framework motivated by the \textit{thermocoherent effect}, where heat flow is reciprocally coupled to a delocalized information flow carried by shared coherence and not reducible to local subsystem variables. Extending this line of work in light of recent results on correlation-enabled Mpemba-type thermal relaxation, we argue that the operational relevance of correlations depends less on their taxonomy than on their dynamical accessibility under the underlying interaction geometry. Relational structure encoded in the state of a single composite system -- including quantum entanglement, quantum discord, and classical correlations -- may therefore act as a usable physical resource that remains hidden from local subsystem descriptions. We propose that electrical, chemical, ionic, and thermal transport processes in neural matter may, under suitable microscopic conditions, generate or transduce partially hidden relational resources whose mutual coupling can progressively build larger-scale thermocoherent organization across spatial or spatiotemporal partitions in neural tissue. Ion-channel interfaces, hydrogen-bonded proton networks, aromatic $\pi$-electron architectures, and phosphate-rich motifs emerge as plausible substrate classes in which such resources may arise, become transiently accessible under environmental coupling, and leave coarse-grained signatures in neural dynamics. The resulting picture is neither a claim of macroscopic quantum cognition nor a reduction of cognition to abstract coding, but a falsifiable framework in which microscopic relational resources can bias transport, relaxation, signaling, and cross-scale neural coordination.

arXiv:2604.04786v1 Announce Type: cross Abstract: This paper presents a quantum search approach to combinatorial constraint satisfaction problems, demonstrated through the generation of magic squares. We reformulate magic square construction as a quantum search problem in which a reversible, constraint-sensitive oracle marks valid configurations for amplitude amplification via Grover's algorithm. Classical pre-processing using the Siamese construction and partial constraint checks generates a compact candidate domain before quantum encoding. Rather than integrating classical and quantum solvers in an iterative loop, this work uses the classical component for structured initialisation and the quantum component for search, and benchmarks the quantum approach against classical brute-force enumeration and backtracking. Our Qiskit implementation demonstrates the design of multi-register modular arithmetic circuits, oracle logic, and diffusion operators. Experiments are conducted on small grid instances, as larger grids are intractable on classical statevector simulators due to exponential memory growth. The results validate the correctness of the proposed quantum search pipeline and confirm the theoretical quadratic query advantage over classical search.

arXiv:2510.20728v3 Announce Type: replace-cross Abstract: Exact scientific discovery requires more than heuristic search: candidate constructions must be turned into exact objects and checked independently. We address this gap by extending TeXRA with an independent Lean 4 verification layer, turning it into a human-guided multi-agent platform for exact scientific discovery. The platform couples symbolic synthesis, combinatorial and linear-programming search, exact reconstruction of numerical candidates, and formal verification in Lean. We apply this platform to nonadditive quantum error-correcting codes with prescribed transversal diagonal gates within the subset-sum linear-programming (SSLP) framework. In the distance-2 regime where logical states occupy distinct residue classes, the platform yields a Lean-certified catalogue of 14,116 codes for $K\in\{2,3,4\}$ and up to six physical qubits, realizing cyclic logical orders 2 through 18, from which we extract closed-form infinite families. We also construct a residue-degenerate $((6,4,2))$ code implementing the logical controlled-phase gate $\mathrm{diag}(1,1,1,i)$. At distance 3, we resolve the transversal-$T$ problem for $((7,2,3))$ codes within the complementary binary-dihedral $\mathrm{BD}_{16}$ setting: among the 12 candidates surviving the SSLP filters, 10 admit exact realizations and 2 are excluded by no-go proofs. All accepted constructions, families, and no-go results are formalized and checked in Lean, illustrating how AI-assisted workflows can bridge search, exact reconstruction, and formal proof in the physical sciences.

arXiv:2601.00860v2 Announce Type: replace-cross Abstract: Can purely mechanical systems generate intelligent language? We prove that dissipative quantum dynamics with analytically tractable non-local context aggregation produce coherent text generation, while conservation laws cause fundamental failure. Employing Koopman operators with closed-form path integral propagators, we show irreversible computation fundamentally requires both controlled information dissipation and causal context aggregation. Spectral analysis reveals emergent eigenvalue structure, separating into decay modes (forgetting), growth modes (amplification), and neutral modes (preservation) -- the essential ingredients for directed information flow. Hamiltonian constraints force the elimination of these dissipative modes and degrading performance despite unchanged model capacity. This establishes language generation as dissipative quantum field theory, proving mechanical systems acquire intelligence through the combination of dissipation and non-locality, not through conservation.

arXiv:2603.26718v2 Announce Type: replace-cross Abstract: We analyze the challenges of benchmarking scientific (multi)-agentic systems, including the difficulty of distinguishing reasoning from retrieval, the risks of data/model contamination, the lack of reliable ground truth for novel research problems, the complications introduced by tool use, and the replication challenges due to the continuously changing/updating knowledge base. We discuss strategies for constructing contamination-resistant problems, generating scalable families of tasks, and the need for evaluating systems through multi-turn interactions that better reflect real scientific practice. As an early feasibility test, we demonstrate how to construct a dataset of novel research ideas to test the out-of-sample performance of our system. We also discuss the results of interviews with several researchers and engineers working in quantum science. Through those interviews, we examine how scientists expect to interact with AI systems and how these expectations should shape evaluation methods.