Toward Evidence That Travels in P vs NP: A Hypothesis-Driven, Verifiable Kernel Architecture (K) for 3-SAT

We step outside the P = NP vs. P ≠ NP dichotomy and, following a co-evolutionary, hypothesis-first program, we frame evidence by the accounting constraint P (L, t) + NP (L, t) = 1, where t indexes registered time windows and L indexes structural layers of analysis. The credit assigned to constructive computation P (L, t) versus certificate-based reasoning NP (L, t) may shift across windows and layers, but their sum is conserved by design. Within this multilayer, time-indexed lens, we propose a test object for proof in 3-SAT: a small, auditable branching set K. Our operational hypothesis is that, within controlled experimental windows, there exists K ⊆ V (F) with |K| ≤ c·log n such that, for every partial assignment α: K → 0, 1, the restricted formula F ∣ α terminates in polynomial time and emits a publicly verifiable certificate (a satisfying assignment or a DRAT/DRUP-style unsatisfiability proof). Because 2^|K| = nO (1), exhaustive branching over K is polynomial inside the window, enabling artifact-backed constructive behavior without asserting a universal algorithm. We (i) define auditable objects and falsifiable hypotheses, (ii) sketch a π-rounds normalization pipeline that contracts structure while logging transformations, (iii) posit a finite catalog of local obstructions with radius-2 witnesses, (iv) outline a greedy hitting-set routine to assemble K, and (v) introduce protection mechanisms against recovery of K by an adversary (commitments and zero-knowledge). Evidence will be supplied via reproducible artifacts (DRAT logs, commitments, run ledgers) and transport tests across registered windows and layers, and will be interpreted under the constraint P (L, t) + NP (L, t) = 1, in a manner consistent with kernelization barriers and sparsification limits.