G3-grover · amplitude-amplification per-rung cost
queries ~ √(N / w)Conjecture: After modal projection onto a window of width w, the search cost per rung scales as √(N/w) — the Grover/amplitude-amplification law.
PQP anchor: Ch. 12 §12.2.3 (Grover) — √ comes from amplitude amplification only.
Prior artifact: The legacy 'per-window √p improvement' framing was implicitly invoking this law (with w = N/p).
Measured status: At /nadarasa/g3-cost the post-selected stream lives on 2–3 distinct y-values per slope regardless of N, so the effective window does NOT grow with N. Without growing w the law has no purchase. Status: kernel can't probe the conjecture as-is.
Next step: Build a kernel whose modal window has support that genuinely scales with N (e.g. the G2-real two-coset combiner post-selected on residue 0) and re-run the cost sweep there.
G3-hsp · structural exponential speedup
queries ~ O(log |G/H|)Conjecture: If the underlying problem is an Abelian HSP instance, the cost is O(log|G/H|) — exponential, no √-factor.
PQP anchor: Ch. 12 §12.2.4 + Ex. 12.22.
Prior artifact: The original draft's '√p improvement' language confused HSP structure with Grover structure. PQP refutes the framing: HSP and Grover live in disjoint regions of Ch. 12.
Measured status: Not yet measured by any Nadarasa kernel; G1 / G2-real demonstrate the coset-state primitive but stop short of the full HSP coset-finding loop. Requires the QFT register output to be POST-PROCESSED (continued fractions / lattice reduction), not just observed empirically.
Next step: Out-of-scope at the current dashboard tier — would require a classical post-processor wrapping the existing Selene runs. Tracked as a separate work item, not a G3 sub-claim.