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Michael Farmer

Publications and source records attributed to Michael Farmer.

6 recordsLinked to original sources

Abduction Without a Body? Representational Grounding and the Abduction Loop for Scientific Hypothesis Generation

Can scientific abduction occur without continuous sensorimotor embodiment? Recent arguments in AI and philosophy of science hold that genuine hypothesis generation requires an agent continuously coupled to the physical world. We defend a narrower claim: online embodiment is not necessary for every abductive scientific act. Our focus is identity abduction: the inference that two independently developed structures are one object under an explicit correspondence, reached through representational grounding rather than bodily interaction. An agent may acquire new inferential affordances not through physical interaction but through transformations into representations that expose latent invariants. Scientific diagrams are a practical substrate because they embody independently evolved conventions that partially canonicalize symmetry, topology, and operator structure across disciplines - a property we develop as convention space, which answers a hard retrieval problem: finding mathematically related work when two fields share no discriminating vocabulary. We operationalize the mechanism as an architecture, the Abduction Loop: representation generation, motif extraction, convention-space canonicalization, cross-domain retrieval, identity-hypothesis generation, and adversarial verification, with abstention as the designed default. A documented episode, in which a multimodal model given a figure of a gravitational-memory transport model generated and then verified the hypothesis that its central differential complex is equivalent to the spherical Kaiser-Squires mass-mapping complex of weak-lensing cosmology, serves as a motivating possibility witness from which the architecture is abstracted, not as evidence of general capability. We close with a falsifiable evaluation program, the DAB-30 benchmark. The contribution is a mechanistic proposal, an architecture, and a test program.

cs.AI

Transient Acceleration and Cross-Dissipation Interference in Fisher-Regularized Wasserstein Gradient Flows

We study transient nonequilibrium dynamics in Fisher-regularized Wasserstein gradient flows and identify a sign-changing cross-dissipation mechanism generated by the coupling between transport dissipation and Fisher-information geometry. Using the Ornstein--Uhlenbeck Fokker--Planck system as an analytically tractable setting, we derive an exact reduced variance dynamics on the Gaussian manifold, \[ \dot{u}=2(1-u)+\frac{\varepsilon}{u}, \] where \(u(t)=\sigma^2(t)\) is the variance and \(\varepsilon>0\) is the Fisher regularization strength. The reduced dynamics reveal distinct transient regimes induced by the interaction between transport relaxation and information-geometric curvature. The associated cross-dissipation term changes sign at the critical scale \(\sigma=1\), separating cooperative acceleration for localized states with \(\sigma<1\) from transient interference at larger variance scales. In the subcritical regime, Fisher curvature accelerates the descent of the baseline free energy; beyond the critical transition, it partially opposes the Ornstein--Uhlenbeck pullback and generates transient overshoot toward a displaced Fisher-regularized equilibrium. We also establish a bounded transient-acceleration-window result, showing that the cooperative acceleration phase has finite duration with an upper bound depending only on the Fisher regularization strength. Finite-difference simulations support the analytical predictions and suggest that qualitatively similar sign-transition behavior may persist beyond Gaussian closure for non-Gaussian initial conditions, including bimodal and Laplace distributions. Overall, the results provide a transient dynamical perspective on Fisher-regularized dissipative systems and show how information-geometric curvature can reorganize intermediate-time Wasserstein relaxation while preserving the globally dissipative structure of the flow.

cond-mat.stat-mech

A converse theorem for degree 2 elements of the Selberg class with restricted gamma factor

We prove a converse theorem for a family of L functions of degree 2 with gamma factor coming from a holomorphic cuspform. We show these L functions coincide with either those coming from a newform or a product of L functions arising from Dirichlet characters. We require some analytic data on the Euler factors, but don't require anything on the shape. We also suppose that the twisted L functions satisfy expected functional equations. We allow the non-trivial twists to have arbitrary poles.

math.NT

Strong multiplicity one for the Selberg class

We study the problem of determining elements of the Selberg class by information on the coefficents of the Dirichlet series at the squares of primes, or information about the zeroes of the functions.

math.NT

Quantitative recurrence properties for self-conformal sets

In this paper we study the quantitative recurrence properties of self-conformal sets $X$ equipped with the map $T:X\to X$ induced by the left shift. In particular, given a function $φ:\mathbb{N}\to(0,\infty),$ we study the metric properties of the set $$R(T,φ)=\left\{x\in X:|T^nx-x|<φ(n)\textrm{ for infinitely many }n\in \mathbb{N}\right\}.$$ Our main result shows that for the natural measure supported on $X$, $R(T,φ)$ has zero measure if a natural volume sum converges, and under the open set condition $R(T,φ)$ has full measure if this volume sum diverges.

math.DS