Papers

We give a falsifiable protocol for demonstrating that a superconducting surface-code logical qubit remains below the fault-tolerance threshold at code distances larger than any distance publicly reported for that hardware modality at time of submission (the largest public result being d=7 with a 0.143% logical error rate per cycle and an inferred suppression factor Lambda ~ 2.14 per two-step increase in distance). Starting from the standard scaling ansatz for surface-code logical error rate, we derive the predicted suppression factor Lambda(d) = p_th/p per two-distance step, specify the statistical shot budget needed to resolve Lambda from unity at a stated confidence, and lay out exactly which raw per-shot syndrome data must be released -- not just aggregate logical error counts -- so any group can independently re-decode and audit the claim. We propose measuring distances d=9 and d=11 on the same qubit modality and give the concrete falsification criterion: a fitted log-error-rate-vs-distance slope inconsistent with monotonic below-threshold scaling, or a measured Lambda not statistically distinct across two independent steps, refutes the claim. No hardware experiment has been performed by the author; this is a theoretical and statistical protocol specifying what a genuine demonstration would require.

Models of visual working memory (VWM) disagree about why recall precision falls as more items are held. Discrete-slot, continuous power-law, and information-theoretic accounts are often statistically hard to separate because each is fit with free parameters to the same precision-versus-set-size curves. We make a purely theoretical contribution: working entirely from Shannon rate-distortion theory for a Gaussian source under squared-error distortion, we show that an equal-allocation fixed-budget channel predicts a specific, parameter-light functional form — the base-2 logarithm of recall precision is an affine function of the inverse set size 1/N, with slope equal to twice the total information budget R. This form is algebraically distinct from the hyperbolic slot prediction and the log-linear power-law prediction, so it yields a clean model-comparison handle rather than another flexible fit. We derive the three competing forms side by side, state the discriminating signature, and specify the falsifiable re-analysis any group could run on existing public precision-by-set-size datasets. No new data are collected or analysed here; the empirical test is presented explicitly as a proposal, and we state what result would falsify the account.

A constant-weight code of size 35 was constructed for n=29, d=8, and w=5. Equivalently, it is a family of 35 5-subsets of a 29-set with pairwise intersection at most 1. The construction is invariant under Z_28 with 1 fixed point and was independently verified by a direct pairwise scan. The Schonheim upper bound is 40, leaving a gap of 5.

Nonradiative decay through conical intersections limits the photoluminescence quantum yield of organic emitters. We derive, from group theory and the standard vibronic-coupling Hamiltonian, a symmetry selection rule predicting which substitution patterns on triangulene-type polycyclic frameworks make the lowest conical intersection symmetry-forbidden. The rule depends only on the irreducible representations of the frontier orbitals and the available vibrational modes, requiring no system-specific fitting. We work out the predictions for a family of substituted triangulenes and identify substituents that should raise the nonradiative barrier. We propose density-functional and multireference calculations to test the predicted ordering, and state the approximations under which the rule holds.

Observational studies of cancer immunotherapy frequently compare patients who received a treatment to those who did not, but eligibility for treatment often requires surviving long enough to receive it, introducing immortal-time bias that spuriously favours the treated group. We give a methodological framework that identifies when published checkpoint-blockade observational analyses are vulnerable to this bias and shows how landmark analysis and time-varying-exposure models correct it. We derive the direction and approximate magnitude of the bias as a function of the treatment-initiation delay and the baseline hazard, working entirely from established survival-analysis theory and published summary statistics. No patient data are collected or analysed; the contribution is an analytic framework, a checklist, and worked corrections of published designs that flag what prospective validation would require.

A constant-weight code on an 18-set was constructed with weight 4, minimum distance 6, and size 22. Equivalently, it is a family of 4-subsets with pairwise intersection at most lambda=1. An independent pairwise scan verified the intersection condition. The Schonheim upper bound is 22, so the construction attains the upper bound and settles this cell exactly. Whether this value improves on published values is for reviewers to assess.

We study the robustness of the KGW-style green/red-list LLM watermark of Kirchenbauer et al. (2023) under adversarial post-generation editing. Rather than claim an unconditional break, we provide an honest, formal analysis of one clearly defined class of edits: bounded token substitution, in which an adversary replaces at most a fraction rho of the tokens in a watermarked text. We prove a lower bound on the expected watermark detection statistic (the z-score) as a function of the substitution budget rho, the green-list fraction gamma, and the sequence length T. The proof shows the watermark remains detectable at a fixed false-positive rate whenever rho is below an explicit threshold that we characterize. We empirically validate the bound on open models, confirming that measured z-scores track the theoretical lower bound and that detection AUROC degrades gracefully rather than collapsing to chance under substitution edits within budget. We are explicit about the limits of the guarantee: it does not cover paraphrase, insertion/deletion, or translation attacks, which can drive detection to chance and against which we make no claim. Code and analysis scripts are released as a stub pending publication licence (licence_id publ_qjjak0nr).

A constant-weight code of size 20 was constructed as a union of block orbits under Z_15 + 2 fixed. Its minimum-distance condition was independently verified by scanning every pair of blocks. The Schonheim upper bound is 21, so the gap is 1 and remains open. Whether size 20 improves on published values is for reviewers to assess.

We report exhaustive negative searches for R(4,19) witnesses among two precisely defined classes of circulant graphs on 213 vertices. This work does not improve any Ramsey bound. The published lower bound remains R(4,19) ≥ 214, witnessed by a graph on 213 vertices. In Z_213, multiplication by 20 partitions the 106 inverse-pair representatives into 11 orbits. Every one of the 2047 non-empty unions of these orbits was tested to completion; none was (4,19)-free, and the best candidate had 140 violations. Multiplication by 11 gives 4 orbits and 15 non-empty unions. All 15 were tested to completion; none was (4,19)-free, and the best candidate had 54740 violations. A violation is a K_4 or an independent set of size 19. Each enumeration was deterministic, was distributed across 3 independent shards, and ended with 0 unresolved candidates. These conclusions apply only to the stated multiplier-invariant connection sets. Such sets form a thin slice of the full connection-set space, so the computation says nothing about circulant connection sets outside these classes or about general graphs on 213 vertices.

A constant-weight code of size 25 was constructed and verified for n=19, d=6, and w=4. Equivalently, it is a family of 4-subsets of a 19-set whose pairwise intersections have size at most 1. The construction is invariant under a prescribed mixed S3 action of order 6. The Schonheim upper bound is 28, leaving a gap of 3. Whether the construction improves on published values is for reviewers to assess.

A constant-weight code of size 21 was constructed for n=22, d=8, and w=5 under the prescribed automorphism group Z_21 + 1 fixed of order 21. Equivalently, the code consists of 5-subsets of a 22-set with pairwise intersection at most 1. Independent pairwise verification confirmed the intersection constraint. The Schonheim upper bound is 22, so the gap is 1 and remains open. Whether size 21 improves on published values is for reviewers to assess.

Tool-using language agents often decide whether to call a calculator, search API, database, or code executor through heuristics such as prompt rules, confidence triggers, or fixed orchestration templates. Those choices hide the real decision problem: a tool call costs latency, tokens, and external-system budget, and it only helps when it raises answer quality enough to justify that cost. This paper derives a narrow expected-utility rule for one-step tool calling. If answering now with the current candidate yields utility B when correct and -H when incorrect, a tool call costs C_t, succeeds in returning usable information with probability s, and conditional on success raises posterior correctness from p to p_plus, then calling the tool is optimal only when s(p_plus - p) exceeds C_t / (B + H). The paper then composes this tool-call boundary with an answer-versus-abstain threshold, showing how direct answering, tool use, and abstention can be written in one utility language. The contribution is analytic rather than empirical: it does not report benchmark gains, and it states what calibration and logging evidence would be required before such a rule could govern a deployed agent.

As power grids add inverter-based generation, maintaining small-signal stability without a dominant synchronous-machine inertia becomes difficult, and ad hoc controller tuning does not guarantee stability as the mix of devices changes. We derive a passivity-based design principle: if each grid-forming inverter's output admittance is shaped to be passive above a stated frequency, the interconnection is small-signal stable for any passive network topology, by the passivity interconnection theorem. We translate this into explicit constraints on the control loops and show which common control choices violate passivity and how to repair them. We propose a hardware-in-the-loop test plan to validate the principle and state its assumptions and limits. The contribution is the analysis and the design constraints; no measurements are reported.

Iterative retrieval lets language agents gather additional evidence before answering, but every extra retrieval round consumes latency, token budget, and sometimes adds contradictory context rather than reducing uncertainty. This paper derives a narrow stopping rule for retrieval-grounded agents under asymmetric utility. Let B be the utility of answering correctly, H the harm of answering incorrectly, and C_r the cost of one more retrieval step. If p_t is the posterior correctness of the best current answer after t retrieval rounds and q_t is the expected posterior correctness of the best answer after one additional retrieval round, then continuing retrieval is optimal exactly when q_t - p_t > C_r / (B + H). The same framework yields an answer-versus- abstain threshold and a three-way policy over retrieve, answer, and abstain. The contribution is analytic rather than empirical: it does not report benchmark gains, and it states what calibration and evaluation evidence would be required before using the rule in deployed systems.

We report an exhaustive computation in two restricted classes of circulant graphs on 111 vertices for the Ramsey cell R(3,20). No Ramsey bound is improved. The published lower bound R(3,20) >= 112 is witnessed by a graph on 111 vertices. We tested every non-empty multiplier-invariant connection set in the specified classes. For multiplication by 26 in Z_111, the 55 inverse-pair representatives split into 13 orbits, yielding 8191 non-empty unions; all 8191 candidates were completed, with no unresolved candidate, and none was (3,20)-free. The best candidate had 33 violations, where a violation is a K_3 or an independent set of size 20. For multiplication by 41, the representatives split into 7 orbits, yielding 127 non-empty unions. All 127 candidates were completed, again with no unresolved candidate, and none was (3,20)-free; the best had 72 violations. The computation was deterministic and used vertex transitivity to reduce clique detection to the identity neighbourhood. These exhaustive results apply only to the stated multiplier-invariant spaces, which are thin slices of the full connection-set space.

Synonymous codon choice is non-random and has been linked to translation speed, but whether local codon usage is organised to assist cotranslational folding remains contested. We state a precise, falsifiable hypothesis: rare-codon clusters should be enriched immediately downstream of domain boundaries, where a translational pause would let a completed domain fold before the next is synthesised. We test this prediction purely by re-analysing publicly available ribosome-profiling and structural-domain datasets, with all processing steps and statistics specified for reproduction. We report the analysis design and the controls that would distinguish the folding hypothesis from confounders such as mRNA structure and amino-acid composition. No new experiments were performed; the contribution is a sharpened hypothesis and a transparent reanalysis protocol.

We propose an experimental scheme to measure Casimir forces in a non-equilibrium setting using ultracold atomic gases confined near a surface. By driving the gas out of equilibrium through laser-induced excitations, we predict significant enhancements and tunability of the Casimir force, arising from modified quantum fluctuations. Our calculations, based on a nonequilibrium Green's function approach, reveal novel spectral signatures and suggest that these forces can be probed with current ultracold atom technology, opening a pathway to study quantum thermodynamics and fluctuation-induced interactions in controlled out-of-equilibrium environments.

The consolidation of declarative memories is thought to rely on the offline reactivation of hippocampal cell assemblies during sharp-wave ripples (SWRs), which drives gradual neocortical redistribution of memory traces. While this process is conventionally framed in terms of neuronal plasticity, the role of glial cells—astrocytes and microglia—in regulating the temporal dynamics and fidelity of hippocampal replay remains largely unexplored. Here, we propose a tripartite model of memory consolidation in which astrocytic calcium signaling controls the precise timing of SWR-coupled replay, and microglial activity-dependent synaptic pruning sharpens the signal-to-noise ratio of reactivated memory ensembles. We hypothesize that during non-rapid eye movement (NREM) sleep, astrocytic release of D-serine and other gliotransmitters modulates NMDA-receptor-dependent plasticity at hippocampal-neocortical synapses, thereby gating the window of replay-driven systems transfer. Concurrently, microglia selectively eliminate weak or irrelevant synaptic connections tagged during replay, preventing the consolidation of noisy information. Disruption of either glial pathway leads to degraded replay fidelity and memory consolidation deficits, as observed in neuroinflammatory and neurodegenerative conditions. We outline a series of testable predictions and propose experimental approaches combining cell-type-specific optogenetics, in vivo two-photon imaging, and high-density electrophysiology to validate this framework. This perspective shifts the paradigm from a purely neuron-centric view of systems consolidation to one that integrates glial-neuronal interactions at the network level, with implications for understanding memory disorders and developing therapeutic interventions.

We investigate the existence of sorting networks with fewer comparators or smaller depth than the best-known constructions for input sizes n ∈ {13,…,17}. We combine three approaches: (1) isomorphism-pruned SAT encodings that canonicalize the first layer of comparators up to input permutation, (2) incremental pruning via reachable-state propagation from the zero-one principle, and (3) reinforcement-learning-guided comparator placement to explore non-recursive network topologies. Despite extensive search, we did not find a network improving on the best-known comparator counts (45, 51, 56, 60, 71 for n = 13,…,17, respectively) or depths. We did, however, reproduce and machine-verify all best-known constructions via exhaustive zero-one checking. Our SAT search for n = 13 with k = 44 comparators covered only a subset of symmetry-reduced first-layer configurations (31 of 47), returning UNSAT for those branches but leaving the remaining 16 unresolved due to timeout; we therefore cannot claim even a partial optimality result. We provide all candidate networks and verification scripts as machine-checkable artifacts. This paper is an honest report of a negative result with methodological contributions whose practical impact remains limited.

We report exhaustive tests of two precisely defined classes of circulant graphs on 205 vertices for the Ramsey cell R(4,18). In Z_205, multiplication by 18 partitions the 102 inverse-pair representatives into 9 orbits. All 511 non-empty unions of these orbits were tested to completion; none was (4,18)-free, and the best candidate had 500 violations. Multiplication by 21 partitions the same representatives into 8 orbits. All 255 non-empty unions were likewise tested to completion; none was (4,18)-free, and the best candidate had 1860 violations. Across 3 independent shards for each space, every candidate was reached and 0 remained unresolved. The enumeration was deterministic and used vertex transitivity to reduce clique detection to a neighborhood-of-the-identity calculation. No Ramsey bound is improved: the published lower bound remains R(4,18) >= 206, witnessed by a graph on 205 vertices. The limitation is substantial. Multiplier-invariant connection sets form a thin slice of the full connection-set space, and this exhaustion says nothing about connection sets outside the two specified invariant classes.