#NQD‑CAL — Open‑Ended Search Calculus

C.18 · Cluster C.IV - Composite & Macro-Scale · Stable · Part C - Kernel Extension Specifications

#About this pattern

This is a generated FPF pattern page projected from the published FPF source. It is canonical FPF content for this ID; it is not a fpf-memory product feature page.

#How to use this pattern

Read the ID, status, type, and normativity first. Use the content for exact wording, the relations for adjacent concepts, and citations to keep active work grounded without pasting the whole specification.

Status. Calculus specification (CAL). Exports Γ_nqd.* operators for open‑ended, illumination‑style generation. ΔKernel = 0 (no kernel primitives added). Minting note: this CAL does not mint new U‑types; it defines CAL‑records that MAY alias to registered U‑types where present via E.10/UTS.

Depends on. A‑kernel (A.1–A.15), MM‑CHR (C.16) for measurements, KD‑CAL for similarity/corpora, Sys‑CAL for carriers, Decsn‑CAL (objectives; advisory), Compose‑CAL (set aggregation; advisory).

Coordinates with. B.5.2.1 (binding), C.17 Creativity‑CHR (characteristics & scales), C.19 E/E‑LOG (policies: emitter selection, explore/exploit).

Exports (CAL; no U‑type minting here).

• Records: NQD.DescriptorMap (alias of U.DescriptorMap if minted), NQD.NQDArchive (alias of U.NQDArchive), NQD.Niche, NQD.ArchiveCell, NQD.EmissionSeed?, U.EmitterPolicyRef, U.InsertionPolicyRef, U.IlluminationSummary, and NQD.CandidateSet (alias of Set<U.Hypothesis>).

Open‑ended search (NQD) equips FPF with illumination‑style generation and Pareto / selected-set selection in multi‑criteria, partially ordered spaces; it feeds G.5 without scalarising ordinal or mixed‑scale characteristics.

#Keywords

• NQD-CAL
• Γnqd.generate
• Γnqd.updateArchive
• Γnqd.illuminate
• Γnqd.selectFront
• DescriptorMapRef
• DistanceDefRef
• NQDArchive
• CandidateSet
• Front vs ExplorationArchive
• IlluminationSummary report-only telemetry
• EmitterPolicyRef
• InsertionPolicyRef
• provenance editions.

#Relations

#Content

#Problem frame

Open‑ended search (NQD) equips FPF with illumination‑style generation and Pareto / selected-set selection in multi‑criteria, partially ordered spaces; it feeds G.5 without scalarising ordinal or mixed‑scale characteristics.

#Problem

Without a disciplined NQD calculus, contexts (a) conflate illumination telemetry with dominance, (b) lose reproducibility due to undeclared DescriptorMap/DistanceDefRef.editions, and (c) perform illegal aggregations across scales.

#Forces

• Posets vs. scalarisation — selectors must return sets (Pareto/archive) rather than illegal weighted sums across mixed scales. • Exploration vs. exploitation — emitters must adapt while preserving provenance and editioning. • Telemetry metric vs. objective — Illumination (coverage/QD‑score) informs health but is not a dominance characteristic by default. • Reproducibility vs. adaptivity — budgets, ε, K, and InsertionPolicy must be edition‑tracked.

#Solution

Provide Γ_nqd.* operators and U.Types for DescriptorMap, Archive/Niche, policies, and illumination telemetry summaries; bind measurement legality to MM‑CHR and policy control to E/E‑LOG. (Exports/Type notes/Operator specs below are normative parts of this Solution.)

• Operators (Γ):
  • Γ_nqd.generate(seed?, EmitterPolicyRef, Budget, DescriptorMapRef, QualityMeasuresRef, NoveltyMetricRef, CoverageGrid, CellCapacity K=1, EpsilonDominance ε=0, DedupThreshold?, InsertionPolicyRef?) → CandidateSet<U.Hypothesis>
  • Γ_nqd.updateArchive(Archive, CandidateSet, InsertionPolicyRef?) → Archive'
  • Γ_nqd.illuminate(Archive) → IlluminationSummary{coverage, QD-score, occupancyEntropy, filledCells} (report‑only telemetry summary; not a dominance characteristic unless a policy explicitly promotes it).
  • Γ_nqd.selectFront(Archive|CandidateSet, characteristics={Q components, Novelty@context, ΔDiversity_P, …}) → ParetoFront

Type notes.

• U.DescriptorMap (Tech; twin‑labelled Plain) : Hypothesis → ℝ^d (declares encoder, invariances, version, CharacteristicSpaceRef). Publish Tech/Plain per E.10; declare DescriptorMapRef.edition and DistanceDefRef.edition. Dimensionality rule. Require d≥2 only when QD/illumination surfaces are active; for non‑QD contexts d≥1 is lawful.
• NQD.CandidateSet ≡ Set<U.Hypothesis> with attached per‑item vectors {Q_i, N_i, D_i:=ΔDiversity_P, S_i?, provenance_i}.
• U.NQDArchive holds per‑cell elites and genealogy refs; context‑local.
• U.Niche is a region in CharacteristicSpace (grid bucket / CVT centroid / cluster).
• U.EmitterPolicyRef points to a named policy in C.19 E/E‑LOG.
• U.InsertionPolicyRef — named archive‑update policy (e.g., replace_if_better | replace_worst | bounded_age | bounded_regret); versioned.
• U.IlluminationSummary is a telemetry summary over Diversity_P (see C.17), not a dominance characteristic.

Operator specs (normative).

• Γ_nqd.generate(… ) SHALL: (a) respect Budget,
  (b) compute {Q_i} (vector), N_i (Novelty@context), D_i := ΔDiversity_P(h_i | Pool) under the same CharacteristicSpace & TimeWindow as the Pool, and optional S_i (Surprise), (c) deduplicate by DedupThreshold in CharacteristicSpace,
  (d) record DescriptorMapRef.edition, DistanceDefRef.edition, EmitterPolicyRef, ε, K, Seeds, and genealogy references (parent/seed ids) to enable replay and selection auditing.
• Γ_nqd.updateArchive SHALL apply local competition per cell (keep up to K elites), preserve genealogy, and enact the declared InsertionPolicyRef; default is replace_if_better with deterministic tie‑breakers.
• Γ_nqd.illuminate SHALL return coverage and QD‑score computed against the declared grid and archive edition.
• Γ_nqd.selectFront SHALL compute the (ε‑)Pareto front over the declared characteristics; Illumination is excluded by default (report‑only).

Pipeline: apply Eligibility (ConstraintFit=pass) → Dominance over the declared DominanceSet → Tie‑breakers (Novelty@context, ΔDiversity_P, Surprise; Illumination telemetry metric). When the context relies on the ordinary default, consume DefaultId.DominanceRegime from G.Core/G.5 together with the active C.19 emitter/archive policy instead of restating one local dominance doctrine here. Ordinary default Q-front mode: When no narrower promotion policy is declared, dominance stays on the context-declared Q components while N/ΔD work through archive occupancy and tie-breakers. Any deviation SHALL be declared by policy id and recorded in provenance.

Reproducibility & editions. Each call SHALL emit provenance sufficient for replay: {DHCMethodRef.edition, DescriptorMapRef.edition, EmitterPolicyRef (params), **InsertionPolicyRef**, DedupThreshold?, ε, K, Seeds, TimeWindow}. Telemetry hook: whenever IlluminationSummary increases (Δcoverage>0 or ΔQD‑score>0), the Context SHALL emit a Telemetry(PathSlice) record that cites {EmitterPolicyRef, DescriptorMapRef.edition, DistanceDefRef.edition, InsertionPolicyRef?, TimeWindow}. (Aligns with G.6/G.7/G.11 PortfolioMode/edition constraints.)

Measurement alignment. Novelty@context, Use‑Value (ValueGain), Surprise, Diversity_P SHALL be measured per C.17 (MM‑CHR templates). IlluminationSummary is a telemetry summary over Diversity_P (coverage/QD‑score); when CharacteristicSpace includes domain‑family cells, publish grid id and FamilyCoverage, plus DescriptorMapRef.edition/DistanceDefRef.edition. .

#Front and archive are different returns

• Start from one declared EligibilitySet.
• Return the non-dominated Front over the declared DominanceSet.
• When archive mode is active, return the corresponding ExplorationArchive separately.
• Archive membership may use novelty, diversity, stepping-stone potential, or coverage policy and is not by itself evidence of membership in the current Q-Front.
• Keep TieBreakerSet and TelemetrySet explicit so diversity or illumination signals do not silently rewrite the front semantics.
• Use RetentionIntent=steppingStone when the point of retention is frontier expansion rather than current dominance.
• Here EligibilitySet, DominanceSet, TieBreakerSet, and TelemetrySet are comparison-bundle sets, while RetentionIntent=steppingStone is one archive-retention field value; none of them renames the returned Front or ExplorationArchive.
• If one line keeps both returns, say that the front answers current non-domination while the archive answers retained exploration value.
• When retained exploration value depends on future reachability or curriculum expansion across transitions, cite the declared reachability or transfer rule together with LearningProgressSignal, CompetenceModelRef, or GoalSpaceExpansionCue. That bridge stays archive/pool-policy-side unless one explicit policy promotes it; it does not require the heavier atlas layer and it does not rewrite front semantics.

#Conformance Checklist

• C18‑1 Declare DescriptorMap (encoder, invariances, corpus edition) before generation.
• C18‑1b When used in F/G triads, DescriptorMap SHALL declare a domain‑family coordinate (grid/cells) and reference an F1‑Card::DistanceDefRef & δ_family.
• C18‑1c When a domain‑family coordinate is declared, the Context SHALL compute and publish AliasRisk for each front / declared set-surface emission, together with the dSig collision rule and the policy id. AliasRisk is computed against U.DomainDiversitySignature (dSig); the DescriptorMap SHALL publish: (i) collisionRuleId (near‑duplicate threshold, e.g. “≥3 characteristics equal”), (ii) dSigSource pointers used for coding the five characteristics. The collision rule and formula MUST be part of DescriptorMap provenance (see Creativity‑CHR, Heterogeneity Characterisation).
• C18‑2 Record EmitterPolicyRef (policy id from C.19) and parameter set.
• C18‑3 Compute D = ΔDiversity_P(h | Pool) under the same DescriptorMap & TimeWindow as the Pool (see C.17).
• C18‑4 Exclude Illumination from dominance unless policy explicitly promotes it.
• C18‑5 Keep Use‑Value separate from assurance scores; do not alter F/G/R semantics (see B.3, C.17 §Use‑Value).
• C18‑6 Emit full provenance; thinning after front computation MUST be recorded.
• C18‑7 Before computing any front, apply ConstraintFit = pass as a hard eligibility filter.

Defaults. Default ownership is split on purpose: G.Core/G.5 own DefaultId.DominanceRegime and selector-facing default routing, while C.19 owns emitter, insertion, and pool-policy defaults. C.18 consumes those defaults and records the active refs instead of restating them locally. Minimum provenance remains: DescriptorMapRef.edition and DistanceDefRef.edition, DHCMethodRef.edition, EmitterPolicyRef, InsertionPolicyRef, TimeWindow, Seeds, DedupThreshold?; also record FamilyCoverage/MinInterFamilyDistance.

Didactic quickstart (Context).

1. Pick 2–4 Quality coordinates and a simple DescriptorMap (2–4 dims).
2. Set defaults: K=1, ε=0, a conservative EmitterPolicy.
3. Run Γ_nqd.generate to fixed Budget; inspect the front; log coverage (IlluminationSummary).
4. Apply abductive plausibility filters; promote prime hypothesis to L0.

#Archetypal Grounding

System. Legged‑robot gait exploration: Q = {forward speed, energy efficiency}; DescriptorMap/CharacteristicSpace = morphology/coordination descriptors (ℝ^d); D = ΔDiversity_P(h | Pool) computed over that declared descriptor space; Archive = CVT grid; illumination reports coverage without entering dominance. Episteme. SoTA palette synthesis: Q is one declared objective tuple for the current synthesis task, for example external-validity gain, reuse value, or Use-Value only when the Context explicitly declares it inside Q; DescriptorMap/CharacteristicSpace carries method-family or claim-graph descriptors; D = ΔDiversity_P(h | Pool) is computed over that declared descriptor space or niche grid. Publish DescriptorMapRef.edition and DistanceDefRef.edition so the front remains reproducible.

#Bias‑Annotation

Lexical firewall and notation independence apply; no vendor/tool tokens; ordinal characteristics never averaged; illumination treated as report‑only telemetry unless a policy promotes it. (E.5.1, E.5.2, C.16)

#Consequences

• Selected-set honesty (no forced scalarisation). • Reproducibility (editioned maps/policies). • Healthy diversity signals via telemetry metrics.

#Rationale

Post‑2015 Quality‑Diversity (MAP‑Elites & successors) demonstrates illumination efficacy; NQD‑CAL captures these ideas while preserving MM‑CHR legality and LOG governance.

#Relations

Builds on: C.16, C.2. Coordinates with: B.5.2.1 (binding), C.17, C.19, G.5, G.6, G.11.

#C.18:End

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