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Results for “topological” 9 papers
Adelic. Adeles, restricted products and adelic constructions Tagged papers: 45.
Zitterbewegung as Archimedean–2-adic Channel Mixing: A Conjectural Adelic Framework and Its Testable Consequences
Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale, first identified by Breit and Schrödinger — is conventionally explained as interference between positive- and negative-energy branches on the real line. We develop a conjecture, motivated by the adelic physics…
The Harmonic Paradigm Under Ostrowski’s Theorem: A p-Adic/Adélic Re-Evaluation with Helical Compton Vortex Synthesis
The Harmonic Paradigm (V1.0–V4.0) proposed the harmonic oscillator as the universal IR attractor of quantum theory, spanning an 8-rung ladder from transmon anharmonicity to quantum gravity. Its bibliography cited Vladimirov-Volovich-Zelenov p-adic QFT (1994) and Ostrowski's theorem (1918), invoking…
Adelic Quantum Error Correction: A Synthesis Across All Primes v1.0.0
The $p$-adic quantum error correction program has developed three independent but connected strands: a mathematical theory of $p$-adic stabilizer codes (Phase A), an experimental protocol to test for ultrametric error structure (Phase B), and a hardware co-design proposal for tree-structured qubit…
The Adelic ZBW Programme: ZBW-Majorana Hypothesis, Ostrowski-QEC Synthesis, and Cross-Programme Consilience
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions at the hardware…
Fine-Structure Constant as a Cross-Ratio: A Geometric Reframing of α
The fine-structure constant $\alpha \approx 1/137.036$ is reframed as the cross-ratio of two measurable electron length scales (classical radius $r_e$ / Compton wavelength $\lambda_C$). This reveals projective invariance in $\alpha$, connects to integer-ratio precision experiments, and integrates…
Adelic Quantum Error Correction: Intrinsic Qubit Protection from Ostrowski
We formalize an adelic approach to quantum error correction (QEC) based on Ostrowski's theorem: the only non-trivial completions of the rational numbers are the Archimedean (real) completion $\mathbb{R}$ and the p-adic completions $\mathbb{Q}_p$, and these topologies are mutually singular. The…
The Adelic Physics Program: A Grand Synthesis
Six papers, one thesis: Physics is adelic. The Archimedean (real-number) description is the $\infty$-place readout of a richer ultrametric structure defined over the p-adic completions of $\mathbb{Q}$. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as…
Adelic Synthesis: The Pattern-Particle Correspondence and the Complete Arithmetic Theory of Anyons
The prior three phases of this program constructed p-adic anyon theories at individual finite places: p-adic braid groups on Bruhat-Tits buildings (Phase 1), the Temperley-Lieb parameter as p-adic cyclotomic units with the p-adic Jones polynomial (Phase 2), and anyon fusion and braiding via…
Ratio-Based Adelic Physics
The tension between continuous Archimedean spacetime paradigms and discrete, non-Archimedean topological realities constitutes the central mathematical bottleneck in modern complexity science, hindering the unification of quantum mechanics, spin glass phase dynamics, and cognitive psychophysics.…
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