DRCC-V3.0: Reconstruction-Width Engineering for Task-Relative State Compression

This record documents three independently executed validation experiments for DRCC (Dimensional Reduction via Controlled Combinatorics): verifying an N-bit ripple-carry adder by exhaustive enumeration versus a constant-size structural certificate; solving the Pigeonhole-Principle SAT family with a reference DPLL solver, with and without a symmetry-breaking controlled reduction; and compressing a redundant linear layer via row-equivalence classes (DRCC-rank ). All three raw problem-size measures exceed 106 – adder input states, Boolean assignments, and linear-layer parameters, respectively, three distinct units reported separately in Table 38 rather than treated as one interchangeable quantity; the SAT family’s raw state space exceeds 1016. No timed performance measure- ment in this document is extrapolated, every point plotted as a measured runtime is a mean over repeated executed runs, with the underlying trial data available for independent recomputation. (Schematic, waveform, and structural-topology figures are not runtime measurements and are not covered by this claim.) Read together with the reconstruction-width framework of Section 2, the three exper- iments support a conditional rather than universal claim: task-relative state compression produces a measured advantage precisely where discovering and applying the reduction is itself cheap, and produces no advantage where a fair classical baseline already exploits the same structure – both outcomes are reported, not just the favorable one. Section 6 extends this record with thirty-five further experiments (Experiments 4–38): four independent fair-baseline stress tests, four automatic task-signature discovery experi- ments, adiscovery-tractabilitycomparisonspanningupto≈7.6×104×, anorderingheuristic validatedonupto100syntheticinstancesandadversariallystress-testedto56disclosedcoun- terexamples, and an external validation run against the public PACE 2017 graph benchmark. (The count of 38 executed experiments treats Experiments 4b and 38A/38B as separate ex- ecuted records; Experiments 36–37 have harness scripts but no result records available for this manuscript and are therefore not counted among the 38 results.) The conclusion of the combined 38-experiment record is narrower than a universal speedup claim: DRCC is a structure-dependent reconstruction-engineering method, strong on several well-characterized families and explicitly not uniform across others, including some of the external graphs.