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728 papers from the QNFO program, filed on nine shelves by the reader each one is written for: energy per answer, error correction, physics, numbers and p-adics, logic and formalism, AI and knowledge, autonomous systems, assessments, and cross-cutting essays. Every page renders its mathematics and can be questioned in place. How a living paper works.
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Results for “joules” 4 papers
Ultrametric. Non-Archimedean geometry: tree metrics, strong triangle inequality, hierarchical distance Tagged papers: 115.
Ultrametric p-Adic Arithmetic as Energy-Proportional Precision Computing: An Energy Model for Digit-Terminable Multiply-Accumulate
Fixed-width Archimedean floating-point arithmetic pays a constant energy cost per multiply-accumulate (MAC) regardless of the precision actually required by the computation. The gap this paper addresses is the absence of any explicit joules-per-operation model connecting non-Archimedean digit…
Optimal Radix q under Resource Constraints: A Reconciled Derivation Framework for Ultrametric Hierarchies
Hierarchical (ultrametric) representations organize N items in a q-ary tree of depth n = ⌈ln N / ln q⌉, and the choice of branching factor q determines how storage, interconnection, and traversal resources scale. Prior ultrametric modeling has treated the radix as a fixed structural parameter…
The Ultrametric Program: One Structural Object Across Seven Research Domains, and Its Falsifiable Tests
Seven research domains — ultrametric physics, the laws of form, infomatics, paradigm engineering, consilience research, a cloud-native platform, and interactive demos — are claimed to be seven vocabularies for one structural object: a nested, hierarchical partition logic. The object is defined by…
The Trapped-Ion Ultrametric Testbed: A Falsifiability Register for Testing p-Adic Structure in Quantum Dynamics
Twenty-one published records from a single research program, spanning December 2025 to August 2026, are here organized into one testable claim: trapped-ion quantum simulators are the first near-term platform on which ultrametric (p-adic) structure in quantum dynamics can be accepted or rejected by…
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