Rewrites across complete tasks

This overview explains how D through D7 connect task routing, proved rules, caches, revision handling, and normalization. An operation saving can disappear after proof, matching, preparation, execution, and delivery costs are charged. For input one zero zero, A and B gives zero and C is zero, so the output is zero. This point query has supplied all three inputs and returns one bit. Fixing only C to zero leaves a function of A and B. The answer is a residual rule, not a scalar bit. It remains necessary to supply A and B or evaluate the remaining assignments. At one zero the residual returns zero; at one one it returns one. The two different outputs demonstrate why the residual cannot be replaced by the single point result from the earlier request. D through D7 move from task routing to proved rules, versioned caches, profitability gates, natural incidence, real revisions and bounded normalization. The requested output determines which work can help. A point query asks for one decision. A restriction asks for the function under fixed inputs. A repeated-vector session can reuse preparation. A fresh full-vector request still pays construction and delivery. For a conceptual rule, factor role AND region, OR role AND resource into role AND the OR of region and resource; verify all inputs, then charge discovery, matching, proof and replay. The retained D-series results are mixed: restrictions and repeated work could benefit while complete-vector tasks and some proof paths lost. More exact machinery did not reliably create profitable whole requests. The conceptual policy identity illustrates proof; it is not evidence of an actual deployed policy gain. Return to F equals A and B, or C. Fix only C to one and leave A and B free. This is a partial binding, not a complete three-input assignment. The remaining inputs zero zero, zero one, one zero and one one will all return one. Fixing C to one makes the outer or true for every remaining A and B assignment. The residual function is therefore the constant one. This restriction is different from fixing C to zero, which left the nonconstant function A and B. Fixing C to one collapses this residual to constant one for all four assignments of A and B. A restriction returns a remaining function; a complete assignment supplies A, B and C and returns one bit. Keep the parent rule and the fixed binding attached to the residual. For each assignment with C one, the final or returns one. When C is zero, the result is A and B. Interleaving those cases in zero-first binary order gives the displayed eight outputs. Every requested output is present. A resident object can avoid repeated preparation, but the caller may still require the vector to be delivered on every read. Account for the work actually owed rather than assuming residency eliminates all cost. A revised source can invalidate a prepared artifact or proof attached to the old rule. Matching, verifying, updating, and executing the replacement all cost work. Whether that overhead is repaid depends on the request and reuse lifetime. Evaluate the complete required request. Keep task-specific gains and losses separate rather than treating more exact machinery as a universal speedup.