Machine-Native ReasoningStatements and proofs
Statements and proofs
Find a statement anywhere in this work by title, printed number, type or source label. Entries follow the chapter order. Each proof link opens the written proof passage.
Statements by chapter
Chapter 1. From evidence to a reusable state
Chapter 2. Operations must survive their representations
- Proposition 2.1: Exact accounting of the discarded excursion Read proof
- Counterexample 2.2: A discarded coordinate returns
- Theorem 2.3: Forward transport of a reusable method Read proof
- Theorem 2.4: A common observable quotient Read proof
- Proposition 2.5: When complete packets are genuine probability components Read proof
- Counterexample 2.6: An exact detail component has negative probability mass
Chapter 3. Memory that remains open to correction
- Theorem 3.1: Minimal exact memory for a correction contract Read proof
- Corollary 3.2: The size of partition correction memory Read proof
- Counterexample 3.3: A new evidence event changes the required memory
- Theorem 3.4: When a report preserves every Bayesian correction Read proof
- Theorem 3.5: Least refinement closed under prediction and correction Read proof
- Theorem 3.6: One quotient for reports, posteriors, and feedback Read proof
- Counterexample 3.7: Correct marginals with an incorrect correction
- Proposition 3.8: A whole-history bound with an explicit conditioning cost Read proof
- Counterexample 3.9: A rare report carries the entire discrepancy
Chapter 4. From corrected records to decisions and explanations
Chapter 5. One investigation, one resource budget
- Theorem 5.1: Exact joint feasibility for explicit controllers Read proof
- Counterexample 5.2: Two separate optima do not form one controller
- Theorem 5.3: A candidate attaining both lower bounds is optimal Read proof
- Theorem 5.4: The same compressed belief supports the same inquiry Read proof
- Counterexample 5.5: A correct probability quotient can hide a forbidden action
- Proposition 5.6: Uniform model error controls a changed policy Read proof
Chapter 6. Improving discovery without changing its meaning
- Proposition 6.1: What finite counterexamples establish Read proof
- Theorem 6.2: Ordered semantic compression preserves the teacher trace Read proof
- Counterexample 6.3: A probe-equivalent equation is not a general identity
- Proposition 6.4: A sound prefix exclusion Read proof
- Counterexample 6.5: A changed repair defeats the old premise