LogicNat

"We connect partition logic with Generative Logic by translating finite partition logics into Prolog-based Simple Generative Logic Grammars... the grammar GL constructed from Eqs.(17)–(19) preserves the incidence relation between atoms and two-valued states."

"For the higher fibers r≥1, we prove a coefficient-level theorem consisting of a global digit-weight lower bound, a leading monomial theorem on divisible non-pure classes, a lag-e pure-power recursion, and subadditivity of the induced digit weight. This yields the pure-power branch word (B^{e-1}A)^{⌈r/e⌉}B^∞ and the radius formula ρ(f_{r,e})=p^{-θ_{r,e}}"

"μ(t) = μ_c + μ_A tanh[3 sin(2πt/Tω)] … local maxima … at approximately integer multiples of the modulation timescale"

"Drawing on cognitive theories of discourse comprehension... Construction-Integration model (Kintsch, 1988)"

"Theorem 2: Rk(ε,δ) expressed as mixture δ̃ R(0,1) + (1-δ̃) ∑ binom(k,i) (1-α)^i α^{k-i} C_{i,k-i}(ε)"

"Theorem 2 (Reverse Rescaling and Bijectivity)... Λ∗ : R+ → R+ is a C1 bijection with C1 inverse"

"Inspired by the Nelson–Narens theory from cognitive psychology, we propose a metacognitive harness that separates monitoring from reasoning"

"an LLM classifies each turn into one of 8 update operations drawn from four formalisms (dynamic epistemic logic, abductive reasoning, awareness logic, argumentation)"

"Gram-based recursion ... tree graph ... local tensors"

"explicit per-shot entity schedules tracking characters, objects, and locations simultaneously across easy / medium / hard tiers of up to 50 shots, 13 cross-shot characters, 8 cross-shot locations, 22 cross-shot objects, and recurrence gaps spanning up to 48 shots"

"We prove that termination of one-variable linear-constraint loops is decidable in polynomial time, provided a long-standing conjecture about generalized Collatz sequences holds. ... Minkowski–Weyl decomposition ... heightp(T) ... Reachability Conjecture"

"The support of any DL Laurent series p is M-convex (Lemma 3.4)."

"BitModEq that leverages range lemmas and case analysis to produce verified translations from finite fields to bitvectors"

"the extended process ζ^{λ,z} = (I_{t<σ_z^λ}, ξ_t^{λ,z}) is a Feller process. We compute its infinitesimal generator"

"the entire quasienergy spectrum of UF is ordered into triplets {ε, ε+2π/3, ε-2π/3}"

"Observe-Plan-Track mechanism for global observation, adaptive region inspection, and evidence tracking"

"Theorem 1 (Weak convergence for KDE process). Suppose 0 < hn ≤ C n^−δ ... Then P(Pn ⇀ P) = 1 ... supported on a (random) compact set V"

"Theorem B. The map C where C(G)=C(G) and C(ϕ)=Cϕ is a functor from Groups_crh to CentLattices."

"EG-GRPO ... aligns generative recall with downstream ranking signals under sparse reward conditions"

"The transport of chemical elements and angular momentum by rotationally induced instabilities is treated within the diffusive approximation."

"LIP is parameterized as πk=σ(αk) ... conditional logit with outside option p(km|Sm)=e^αkm / (e^α0 + Σj∈Sm e^αj)"

"Theorem 3.1 (Deep representer theorem). ... ϕ(l)_jk(t) = sum c(l)_ijk K(x(l-1)_ik, t)"

"the multimodal rate-distortion-perception function is given by R(D,P) = inf I(S_E; Ŝ) s.t. per-modality distortion and perception constraints"

"Theorem 1.1: G^T_∅(K)_C ≅ F^C_n / [r_i^{-1} γ(r_i), r_j] … for r_i ∈ (F^C_n)^{Γ_{v_i-n}}"

"WOODELF models this game as a PB function F... linearity property"

"The world model uses discrete representations... vector of several categorical variables... sparse binary vector of length 1024 with 32 active bits."

"binomial parameter analysis... 38.9% (7/18) ... P=0.0034"

"episodic memory buffer queue... sliding-window... capacity K=10"

"Theorem 1: unique k such that cycle lengths of Phi^{-1} on left/right subsequences are even; watershed defined thereby"

"The (2+1)-dimensional Hamiltonian SU(2) lattice gauge theory on a linear plaquette chain... mapped onto an Ising model with next-to-nearest neighbor transverse field coupling"