WEBVTT

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This overview explains how D through D7 connect task routing,
proved rules, caches, revision handling, and normalization.

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An operation saving can disappear after proof, matching,
preparation, execution, and delivery costs are charged.

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For input one zero zero, A and B gives zero and C is zero, so the output is zero.

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This point query has supplied all three inputs and returns one bit.

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Fixing only C to zero leaves a function of A and B.

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The answer is a residual rule, not a scalar bit.

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It remains necessary to supply A and B or evaluate the remaining assignments.

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At one zero the residual returns zero; at one one it returns one.

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The two different outputs demonstrate why the residual cannot be replaced by the single

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point result from the earlier request.

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point result from the earlier request.

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D through D7 move from task routing to proved rules,

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versioned caches, profitability gates, natural
incidence, real revisions and bounded normalization.

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The requested output determines which work can help.

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A point query asks for one decision.

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A restriction asks for the function under fixed inputs.

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A repeated-vector session can reuse preparation.

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A fresh full-vector request still pays construction and delivery.

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For a conceptual rule, factor role AND region, OR role
AND resource into role AND the OR of region and resource;

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verify all inputs, then charge discovery, matching, proof and replay.

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The retained D-series results are mixed:

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restrictions and repeated work could benefit while
complete-vector tasks and some proof paths lost.

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More exact machinery did not reliably create profitable whole requests.

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The conceptual policy identity illustrates proof; it
is not evidence of an actual deployed policy gain.

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Return to F equals A and B, or C.

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Fix only C to one and leave A and B free.

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This is a partial binding, not a complete three-input assignment.

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The remaining inputs zero zero, zero one, one zero and one one will all return one.

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Fixing C to one makes the outer or true for every remaining A and B assignment.

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The residual function is therefore the constant one.

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This restriction is different from fixing C to zero, which left the nonconstant function A and B.

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Fixing C to one collapses this residual to constant one for all four assignments of A and B.

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A restriction returns a remaining function; a complete assignment supplies A, B and C and returns one bit.

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Keep the parent rule and the fixed binding attached to the residual.

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For each assignment with C one, the final or returns one.

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When C is zero, the result is A and B.

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Interleaving those cases in zero-first binary order gives the displayed eight outputs.

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Every requested output is present.

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A resident object can avoid repeated preparation, but the caller may still require the

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vector to be delivered on every read.

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Account for the work actually owed rather than assuming residency eliminates all cost.

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A revised source can invalidate a prepared artifact or proof attached to the old rule.

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Matching, verifying, updating, and executing the replacement all cost work.

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Whether that overhead is repaid depends on the request and reuse lifetime.

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Evaluate the complete required request.

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Evaluate the complete required request.

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Keep task-specific gains and losses separate rather than
treating more exact machinery as a universal speedup.