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← AMRAL · PROGRAM-UNIVERSAL-COVERING
Kakeya–Moser Bridge Theory · Semi-autonomous research (led by Neo)
A bridge theory unifying the Kakeya needle problem, Neo's proposed "center-generated bidirectional-offset
spiral" geometry, and Moser's worm problem. Core proposition: under "positive thickness + internal
non-overlap" conditions, the swept area of the bidirectional normal band of any admissible centerline is a
fixed invariant 2ρL, independent of the curve's shape — this seals off the degeneration channel
in the Kakeya needle problem that relies on overlap to drive the swept area toward zero, while simultaneously
translating the optimization problem into a Moser-type universal-containment problem. See the
methodology page for the methodology. For a direct attack on the
Moser problem itself, see the separate Moser's Worm Problem (Chinese) case.
Every round's README states on its own that it "does not constitute a new bound for the Kakeya or Moser problem" — this is exploratory numerical research and a propositional theory draft, not a formal proof. The original packages are unmodified, with a full round-by-round trail, including verification and hashes.
Three original papers, unrewritten. The first two establish the bridge theory itself; the third is an independent formalization of a pure geometric proposition, the shared foundational proposition for the first two.
A positive-thickness bridge theory for center-generated bidirectional-offset spirals — establishes the first unified interface among Kakeya, spirals, and Moser.
v0.2 · 2026-07-27Measure-conserving skew-line fibers, the information-faithful kernel, and universal covering tension — a unified extended version, proving the fiber's first moment can invertibly reconstruct curvature.
v0.1 · 2026-07-27Formalized geometry of full turning, positive thickness, non-overlap, and spiral annuli — the shared foundational proposition for the first two papers, holding independently of the Kakeya/Moser framework.
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