E.4.PFR:3.6 - Optional high-cost basis analysis

Open a basis analysis only for a named automated candidate comparison, reproducible cross-edition replay, same-subject conflict whose resolution can change the exact cell disposition or named receiver action, or bounded reliance/assurance receiver. One analysis is one C.2.1 episteme identified by <AnalysisClaimGraph, BasisAnalysisQuestion@QGroup, effective ReferenceScheme>. The question includes every independently current discriminator: S, U, derive/evaluate mode, bounded receiving use, exact actual-use claim identities, the receiving edition whenever changing it can change candidate applicability, the exact cell disposition, or the named receiver action, effective scheme, optional exact ClaimScope, and exact temporal-policy branch.

The analysis ClaimGraph carries a finite candidate universe containing only bases whose inclusion or exclusion can change the exact cell disposition or named receiver action. It carries a closure claim only when the enumeration rule, source boundary, completeness evidence, qualification window, and exclusion argument are exact. Each candidate is a finite nonempty set of semantic-base subgraphs used conjunctively. Each CandidateEvaluation keeps exactness, applicability, acceptance, witness, sufficiency and minimality independent, with supporting claim refs and a reconsideration condition for every unresolved or negative axis. Establishment follows RuleContentBasisFamilyAlgebra@R8 in A.6.0 §4.6b: exactness, applicability and sufficiency are required; acceptance and witness are required only by the receiving contract. All required axes true establishes the candidate; any false required axis defeats it even if another is unknown; otherwise establishment is unresolved. Optional minimality is a separate answer and never filters a sufficient candidate. Duplicate graphs under one scheme collapse to one semantic atom while retaining source qualifications. Independently sufficient bases remain separate alternatives; jointly necessary bases remain one conjunctive alternative.

Derive-mode sufficiency requires derivation of the exact proposition under the named inference rules without undeclared premises. Evaluate-mode sufficiency requires the criteria and facts needed to obtain the bounded result under the named evaluation rule, including a negative result. These candidate tests establish neither R7 actual-premise use nor actual criterion selection. A minimal-family request adds a separately qualified minimality answer.

Compatibility is pairwise, not a candidate property. Every overlapping established pair whose resolution can change the exact cell disposition or named receiver action receives an exact result naming both alternatives, overlap, supporting claims, and, when conflicting, incompatible consequences plus a bounded E.9 decision. Candidate axes, pairs, conflicts, and receiving-edition distinctions enter the analysis only under that same effect test. The temporal partition is maximal and non-overlapping under the selected policy and this candidate set. A no-time-dependence policy yields one atemporal cell. Changes to scope, temporal policy, candidate inclusion, or applicability reopen only the assertions and cells whose disposition or named receiver action can change.

Apply conflict precedence, then exactly one disposition in each cell:

An unknown axis on a defeated candidate does not make establishment unresolved. Unknown optional minimality does not open the family disposition. With no required pair, all required pairs are compatible vacuously. The closed-empty branches differ in the supported need claim, not in how many candidates were found.

The basis answer is non-permissive. A downstream A.10 bounded-reliance claim or B.3 assurance result cites the exact analysis edition or cell-answer subgraph and supplies its own evidence, freshness, rival explanation, attempted use, and disposition. Neither grants permission, gate passage, decision, Work, actual use, publication, or authority. A reverse consumer lookup is derived rather than inserted into the upstream ClaimGraph.