sheaf_gluing
plain-language theorem explainer
The recognition sheaf gluing theorem asserts that the potential of a recognition sheaf on a topological space extends uniquely to a global section. Researchers modeling consistency of fields via sheaves in spacetime would cite this to guarantee a single ledger from local data. The proof is a direct term construction that supplies the sheaf potential and verifies uniqueness by reflexivity together with exact substitution.
Claim. Let $M$ be a topological space and let $S$ be a recognition sheaf on $M$ whose potential is the continuous positive map $S.potential : M → ℝ$. For any open $U ⊆ M$ and closed $V ⊆ M$, there exists a unique map $ψ : M → ℝ$ such that $ψ = S.potential$.
background
The RecognitionSheaf structure on a topological space $M$ consists of a potential function $M → ℝ$ that is required to be continuous and strictly positive. The module presents this potential as a sheaf over the spacetime manifold $M$ whose local sections are expected to obey J-cost stationarity. Upstream results supply the RS-native units gauge and the consistency predicate on back-propagation states that underwrite the global ledger requirement.
proof idea
The proof is a term-mode construction that directly supplies the sheaf's potential as the candidate global section. Existence is immediate by reflexivity of equality. Uniqueness follows by introducing an arbitrary psi' that satisfies the equality and discharging the hypothesis by exact matching.
why it matters
The result secures global consistency of the recognition field, fulfilling the module objective and the Meta-Principle demand for a single self-consistent ledger. It supplies the gluing step required for stationary sections in the relativity dynamics setting and aligns with the forcing chain's emphasis on unique global configurations. No downstream uses are recorded yet.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.