This proof demonstrates the linking number's equivalence to the Hopf invariant in a field theory context, implying foundational insights into physics.
The Ouroboros system is a classical Lagrangian field theory of two coupled vector fields over Minkowski space, proposed as a candidate for the fundamental law of physics prior to gravity. The theory's central mathematical claim is that the mutual Chern–Simons linking number Q[A,J] is quantized and deformation-invariant. The main Ouroboros paper established these results in Lean 4 using Hopf-invariant axioms. This paper supplies the rigorous mathematical proof that those axioms are correct: the linking number exactly equals the Hopf invariant of a composite map S³ → S² constructed from the fields, and therefore Q[A,J] ∈ ℤ as a theorem of differential topology.
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