arXiv:2512.05765v2 Announce Type: replace Abstract: In this paper we argue that influential critiques dismissing Large Language Models (LLMs) as a dead end for AGI misidentify the bottleneck: they confuse the ocean with the net. Pattern repositories are the necessary System-1 substrate; the missing component is a System-2 coordination layer that recruits relevant patterns, verifies their use, preserves state, and governs convergence. We separate two uses of control that are often conflated. Semantic anchoring, formalized by UCCT (Unified Contextual Control Theory), binds labels and task intent to learned pattern regions through a phase transition governed by effective support (rho_d), representational mismatch (d_r), and an adaptive anchoring budget (gamma log k). Trace-answer verification, implemented by Recursive Causal Audit (RCA), tests whether a final causal judgment is warranted by its own reasoning trace under pressure. We translate these ideas into MACI, a multi-agent coordination stack that integrates diversity and control via baiting (PID-modulated debate), filtering (Socratic and causal audit), and persistence (transactional memory). Empirical validation on causal judgment and the sycophancy-paranoia trade-off demonstrates that static prompting fails where adaptive control succeeds. By reframing common objections as testable coordination failures, we argue that the path to AGI runs through LLMs, not around them. Capability is not coordination.

arXiv:2603.11066v5 Announce Type: replace-cross Abstract: We develop a structural framework for the Collatz map based on odd-to-odd dynamics, modular return structure, and burst-gap decomposition. We prove exact results for fiber-57 return dynamics, including a uniform affine channel for q = 7 (mod 8), minimum return gap five for q = 3 (mod 8), and that the chain map on the invariant core is a permutation at every depth. These yield a depth-2 partial return kernel with Perron root 129/1024. A conditional reduction via phantom-cycle gain analysis and a weak-mixing hierarchy establishes an exact geometric block law, an exponential almost-all crossing bound, and per-orbit phantom gain within a 4.65x contraction margin, reducing convergence to a single orbitwise regularity statement. New in v5: the Carry Contamination Theorem proves that at every Sturmian depth D, n_D mod 8 is exactly equidistributed over {1,3,5,7}, yielding an exact (3/4)^D survivor law. The reduction terminates at the Carry Independence Conjecture (CIC): no n_0 > 1 avoids class 5 at every depth. CIC implies Collatz via a proved Dichotomy theorem. This extends via a seven-block cross-core alphabet with spectral radius rho = 2+sqrt(2). The safe Collatz map is a 2-adic expander with measure shrinkage mu_2(T_j) = 5 non-descending rounds for large K. Cycle impossibility is verified through period 13 (238,811 words). Anti-correlation is bounded (constant ~0.635, not exponential in K). This is not a proof of the Collatz conjecture but a sharpened structural reduction along two routes, each terminating at a distributional-to-pointwise gap.