arXiv:2608.11211v1 Announce Type: new
Abstract: Conway’s 99-graph problem asks whether a strongly regular graph with parameters $mathrm{srg}(99,14,1,2)$ exists. We report a systematic, fully reproducible attack by an autonomous AI research agent, scored under the track’s partial-credit metric. Our verifiable contributions are: (1) an exhaustive proof that no circulant graph on $mathbb{Z}/99$ satisfies more than $3366/4950=68.0%$ of the constraints ($33$ of $49$ difference-classes), with the same ceiling for the other abelian group of order $99$; (2) a forced-structure reduction: $lambda=1$ makes each neighbourhood a perfect matching and $mu=2$ puts the outer vertices in bijection with non-matched neighbour-pairs, collapsing existence to a $12$-regular graph on $84$ vertices, encoded for CP-SAT and validated by recovering the unique $mathrm{srg}(9,4,1,2)$; (3) a validated prescribed-automorphism orbit-existence framework (fixed-point-free and single-fixed-point actions, checked on $mathrm{srg}(9,4,1,2)$ and the Paley graph $mathrm{srg}(13,6,2,3)$), and (4) a best verified artifact at $69.43%$, with evidence that this is a robust frontier (fourteen distinct methods, none exceeding it) entangled with the open question, since any provable bound below $4950$ is a non-existence proof.

arXiv:2608.11212v1 Announce Type: new
Abstract: Top-k Mixture-of-Experts (MoE) routing is discontinuous, so a deployment-motivated numerical disturbance — simulated 4-bit KV-cache quantization read by a protected BF16 gate — pushes tokens across decision boundaries and flips which experts fire. This paper proposes no new mitigation; it supplies a causal apparatus, empirical findings, and a detection-limit result. A four-run apparatus prices the route-mediated fraction (RMF) of quantization damage, a token-level attribution decomposes it by mechanism, and pre-registered probes carry the findings across three architectures. On OLMoE-1B-7B at 4-bit KV (pilot), about a third of the damage is routing-mediated: RMF ~ 0.31 (discovery 0.31 [0.20, 0.41]; process-replicated mean 0.313 +/- 0.020; pre-registered re-execution 0.231). The deployable router margin detects that a flip occurred (AUC 0.772) but cannot tell a harmful flip from a helpful one (at chance): among the tested local, inference-observable router statistics we find no predictor of a flip’s loss sign above chance — an empirical benefit-detection barrier bounding selective repair restricted to this feature family. The signed-flip tax and sign-inseparability carry cross-model; the clean-reference remedy’s payout is architecture-modulated; a controlled same-checkpoint flag-swap re-scopes the gate’s normalization convention to a damage-magnitude moderator, not a route-recoverability mechanism. A real int4 KV kernel yields a fraction compatible with the fake-quant dose curve but underpowered (95% CI [-0.111, 0.394] includes zero) — ruling out gross disagreement, not an independent replication. Hypotheses, thresholds, and evaluations were pre-registered before measurement, with misses reported; a pre-registered held-out read replicates the partition and the near-cancelling tax out of sample, while the strict impossibility exclusion narrowly misses.

arXiv:2608.11215v1 Announce Type: new
Abstract: Simulating societies of many large language model (LLM) agents is expensive, yet the questions asked of such simulations are usually macroscopic: phase behaviour, stylised facts, and scaling with the number of agents $N$, not the cognition of any single agent. We turn a statistical-physics observation into a method: replace each LLM agent by a low-parameter model fitted from a few hundred to a few thousand cheap queries, then run the society at any $N$ on a laptop. Whether this works is decided before the simulation runs, chiefly by what each agent perceives. We introduce an [interaction order x memory] taxonomy that maps perception and memory to an effective theory and a predicted $N$-trend of the surrogate error. We validate it on a faithful reimplementation of the LLM macroeconomy EconAgent and seven further named LLM simulations, with agent decisions cloned from genuine LLM elicitations (primarily DeepSeek) for a few dollars; the predicted error trends hold cell by cell, and the two refuted predictions, both on a strongly saturating response and traced to its curvature, are themselves matched quantitatively by the theory with no free parameters.

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