ASSUMPTION_REVIEW_BLOCK10.md
Machine Native Reasoning
ASSUMPTION_REVIEW_BLOCK10.md
1 # Block10 assumption review
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3 **Source result:** Core6.4, `r:prefix`, printed page24 and continuation page25. The source book and all41 predecessor substantive modules remain unchanged.
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5 | Component | Premises actually used | Not inferred |
6 |---|---|---|
7 | Completion iff | Nonnegative counts, partial count at most m, total m at most2C | Realizability of further queries |
8 | Literal scan equality | Fixed total report function, same list/order/capacity | Correctness of an empirically fitted predicate |
9 | Ordered preservation | Identical terminal checks, permissions, menus, child order and horizon | Equality after changing query order or scope |
10 | Controller interpretation | Inherited immutable/singleton binary scope, nodup rows | Initial-case identification after destructive reset |
11 | Finite failure | Complete menus and actually terminated search | Infeasibility from a timeout or scope rejection |
12 | Read advantage | Named report-table calls in the same recursive algorithm | Lower predicate work or universal runtime gain |
13 | Scope guard | Finite supplied data and checked actual model fields | Physical fidelity or free scope verification |
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15 The integer theorem explicitly retains all printed premises, although some are unnecessary for its algebraic proof. The source range is not enlarged silently. The actual controller representation, validity and update semantics are imported unchanged. Query/repair labels need not be unique in their menus, but every available label must occur for completeness. Row uniqueness is needed to identify list counts with numbers of distinct cases.
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17 Probability, statistical confidence and learning performance do not enter these exact deterministic proofs. Scope depends on the actual next-state and success functions, not just names. The two compared procedures use the same held-fixed model and orders. Their concrete instance counters are not a host-instruction model. The ordinary compiler may be exponentially expensive and the guard can inspect all supports.
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19 The finite learned-expression example uses previously supplied primitives, contexts and teacher. Its universal pruning interpretation is separately proved here. No discovery of its proof rules, independent semantic oracle, or unrestricted learner is claimed.