Constructive sources and readers
Certified Target-Sufficient Readout Design and Exact Finite-Model Reduction
Exact collision witnesses and constrained synthesis turn target sufficiency into minimum-cost finite readout design.
Jeremy Rodgers · Independent Researcher · 2026-10-27
The question and the results
Given a finite source, target and feasible sensor menu, can a solver exhibit the missing distinction and certify the least costly sufficient readout?
- An exact circuit compiler turns failure of target descent into an explicit pair of source states with the same readout and different target answers. Counterexample-guided synthesis returns a globally minimum-cost sufficient feasible selection, or a sound impossibility result within the declared menu.
- Rational branch-and-bound certificates preserve valid lower and upper costs when interrupted, including feasibility families that are not upward closed. A candidate becomes a sufficient upper certificate only after its source collision check passes.
- A nonlinear autonomous register has sharp predictive-completion and full-source reconstruction formulas. Under unit port costs these are b and 2b − 1, making the difference between target sufficiency and complete reconstruction explicit. The implemented backends are conventional exact solvers; external asymptotic complexity corollaries retain their stated dependencies.
Connections to the programme
The complete argument.
Read every section on site, including the mathematics, proofs, examples and references. Each section has its own address for citation and navigation.
- 01Orientation and abstract
- 02Question, contribution and prior scope
- 03Constructive obstruction and minimum-cost predictive completion
- 04Scalable completion design with checkable interrupted bounds
- 05External-theorem dependency and reproducibility
- 06Limitations and relation to source–readout research
- 07Computational assistance
- 08Exact rational weighted contraction and target-dependent precision
- 09Target-sensitive summary preprocessing and a completed restricted improvement
- 10Context-relative crossing compilation and explicit integer pieces
- 11References
Publication and computational material.
Original PDFComplete searchable textOriginal verification supplement ZIPReading inventoryThe supplied publication is a PDF. Prose reflows as HTML where its notation permits; complex mathematical passages retain their exact source-vector layout with searchable transcriptions. The transcription preserves extracted symbols rather than fraction or matrix structure.