Hostile audit · Frontier models · Human decision
Research should survive hostile audit.
ARR is not a file dump. New admissions face the strongest suitable frontier-model audit the operator can assemble for that assessment round on the exact hashed version: counterexamples, hidden assumptions, proof gaps and novelty claims are tested before a human signs the decision. Providers, models and report counts may change; the public record says exactly what was used.
Research paperAcceptedARR-2026-4NC14QTZMT8708NN · v1
Lluis Eriksson
We determine the complete minimax error versus peak angular delay law for rational-inner passive routing of degree at most one at three asymmetric boundary nodes, with one exceptional orthogonal target and two repeated targets. The result supplies both exact branches, the positivity transition, positive lower certificates, and an attaining two-port construction. We then invert the law: a prescribed chordal error determines the minimum delay through one uniquely isolated cubic root with an explicit positivity constraint, or an elementary expression in the active regime. Constant and degree-one branches, the jump at unit peak delay, the transition target and the unattainability of zero error at finite delay are included. Exact rational and symbolic certificates distinguish the continuum proof from supplementary numerical constructions. The result concerns a dimensionless one-state, three-node model and does not claim general circuit-component synthesis or higher-degree optimality.
Research paperAcceptedARR-2026-0WESHW4YMM9FG8EK · v1
Lluis Eriksson
We classify the ranks of nonzero operators with at most three terms in a fixed cyclic Weyl basis in every prime-power dimension. A central-sector formula valid in arbitrary cyclic dimension computes trinomial nullity from commuting powers and a common block multiplicity; nonzero three-term coefficients permit at most two singular sectors. The formula explains composite-dimension departures from the prime-power bound. For exact-rank pure probes in one-use Weyl channel list discrimination, we classify all reduced states below rank 3d/4 in dyadic dimensions: exactly thirty flat half-rank states. Positive sums of sparse squares produce ranks impossible for an individual three-term factor, including an exact three-label family of rank 13d/16. We also determine an exact four-label family of rank 5d/8 and the complete feasible three-label rank set in dimension sixteen. Classical Weyl representation and covariance tools are attributed; exact algebraic certificates and replay programs accompany the proofs.
Research paperAcceptedARR-2026-54Q3HMFJ0Z8CZB4T · v1
Lluis Eriksson
For every balanced sign multiplicity N and fixed ambient dimension, we reduce the optimal forward stability coefficient for inverse self-commutator cost to a rational list of O(N^5) spectral pairs. This counts Horn linear programs, not their size or total running time. At inertia (4,4), exact rational certificates for 89 ordered vertices establish the optimal coefficient 4/7 in every fixed ambient dimension at least eight. An ambient-independent Horn obstruction and a boundary perturbation prove sharpness. We classify the full equality set on the compact spectral closure and show strictness throughout the exact inertia stratum. Together with the previously sharp reverse coefficient 3/2, this completes both stability constants at multiplicity four. Constants for N at least five remain unevaluated. All finite certificates and replay programs are supplied; classical Horn sufficiency and written polyhedral arguments are explicit dependencies.
Research paperAcceptedARR-2026-24M24KDPZK8HDBQ9 · v1
Lluis Eriksson
We determine the sharp worst inverse self-commutator cost for every prescribed inertia, including arbitrary ambient zeros, and quantify its extremal geometry. For unequal sign multiplicities we obtain both optimal constants relating the normalized cost deficit to distance from the one-spike, opposite-flat boundary. The reverse coefficient is also optimal for every balanced inertia. For three positive and three negative eigenvalues we close the other direction as well: the optimal forward coefficient is 17/36. Its proof reduces a piecewise-affine distance to 22 rational vertices and supplies exact Horn witnesses; a boundary spectrum gives ambient-independent sharpness. Thus every nearly extremal sequence is classified. A transportation refinement gives computable primal-dual upper certificates, while an exact example shows a 12.5% gap from the actual matrix cost. A sharp deficit threshold also reduces rank-ceiling stability to the known one-spike case. Classical Horn sufficiency is imported; all finite certificates are supplied for replay. The optimal balanced forward coefficient for multiplicity at least four and the general interior cost remain open here.
Research paperAcceptedARR-2026-12W84G9BVC8BQAEQ · v1
Lluis Eriksson
For F_(p,q)=diag(q repeated p times, -p repeated q times), this paper studies the least rank among factors minimizing one half of the squared Hilbert--Schmidt norm subject to CC^*-C^*C=2F. On q=2p+1, exact rational hive primal-dual certificates determine the complete finite cost-and-rank frontier for 4<=p<=32: the rank excess above q is 0 on p=4..7, 1 on p=8..14, 2 on p=15..26, 3 at p=27, and 4 on p=28..32. The resulting consecutive rank transitions at p=27 and p=28 are followed by a distinct cost-slope transition at p=29. Separately, exact certificates prove kappa(F_(53,107))=8847 with minimum attaining rank 115; its optimum is half-integral, while an earlier integer candidate of trace 8843 is refuted by an integral Farkas certificate. The conclusions are finite and conditional on the classical Horn--Klyachko/hive theorem; no all-parameter recurrence, classification of all minimizers, exhaustive priority result, proof-assistant formalization, or independent peer review is claimed.
Research paperAcceptedARR-2026-5QQF95VHTC9GABH8 · v1
Lluis Eriksson
For a traceless Hermitian target F, this paper studies the least rank r_*(F) among factors C minimizing one half of the squared Hilbert--Schmidt norm subject to CC^*-C^*C=2F. It proves r_*(F)=max(n_+(F),n_-(F)) for every target through dimension seven, including singular spectra, and proves sharp failure in dimension eight on an explicit two-ray cone whose interior has r_*=5>4. An exact dimension-nine seed and a symbolic hive coarse-graining theorem yield targets G_t in dimension 27t with kappa(G_t)=87t and 17t+1<=r_*(G_t)<=18t, so the additive excess above inertia is unbounded. The proof is computer-assisted through exact rational Horn/polyhedral and hive certificates with independent replay routes. It does not determine the exact amplified rank, classify all optimizers, formally verify the imported Horn/hive theorem, or claim exhaustive priority.
