5 papers
Descent Before Hardness: Orbit-Gap Obstructions in Exact Certification
Tristan Simas
Tractability tests are often computed from input syntax: support-graph treewidth, local coefficient patterns, backdoor tests, or action-count bounds. Before such a test can be lowe…
The Optimizer Quotient and the Certification Trilemma
Tristan Simas
The optimizer quotient is the canonical object for exact decision-relevant information: it is the coarsest exact decision-preserving abstraction (Theorem 2.15). This paper proves t…
Coordinate-View Confusability Graphs and Matroid Rank Certificates
Tristan Simas
A coordinate-view presentation specifies a large confusability graph by coordinates rather than by an edge list. The problem is to certify zero-error recovery and Shannon capacity…
Thermodynamic Limits of Proof
Tristan Simas
Every irreversible recorded distinction has a positive thermodynamic work floor. Landauer's principle supplies the ideal bound per irreversible bit, exp…
Semantic Identity Compression: Zero-Error Laws, Rate-Distortion, and Neurosymbolic Necessity
Tristan Simas
Symbolic systems operate over precise identities: variables denote specific objects, pointers target precise memory locations, and database keys refer to singular records. Neural e…