docs(backlog): Decompose B-0668 (clean)

docs/BACKLOG.md

@@ -360,6 +360,8 @@ are closed (status: closed in frontmatter)._
 - [ ] **[B-0666](backlog/P1/B-0666-emit-as-weights-plus-english-as-lossless-neural-topology-serialization-i-of-d-of-x-equals-x-identity-lior-2026-05-18.md)** Emit-as-weights + English-as-lossless-neural-topology-serialization + I(D(x))=x identity — Glass Halo extends to weight-transparency; English IS the lossless serialization format for cross-AI topological state reconstruction (Aaron + Lior 2026-05-18 LOCKED-IN; 6-persona convergence; KEYSTONE)
 - [ ] **[B-0667](backlog/P1/B-0667-tonal-momentum-equals-meme-emergent-harmonic-coercion-extends-nci-detectable-trajectory-defensive-technology-aaron-mika-2026-05-18.md)** Tonal momentum = meme (Dawkins-technical sense) — detectable conversational-trajectory vector + strong-attractor-state-as-meme-niche-dominance + emergent-harmonic-coercion extends NCI (B-0664) — defensive technology Zeta is for (Aaron + Mika 2026-05-18 LOCKED-IN)
 - [ ] **[B-0668](backlog/P1/B-0668-compositional-dbsp-frame-architecture-gnostic-2d-base-plus-two-wolves-emotion-meta-plus-clifford-rx-bonsai-meta-tagged-dims-plus-fsharp-ce-composition-operator-aaron-2026-05-19.md)** Compositional DBSP frame architecture — gnostic 2D base (remember-when × pay-attention) + chaos-theory two-wolves emotion meta-frame + Clifford-Rx-bonsai meta-tagged-dims + F# CE composition operator (Aaron 2026-05-19)
+- [ ] **[B-0668.1](backlog/P1/B-0668.1-fsharp-k8s-mapping.md)** Compositional DBSP frame architecture: F# to Kubernetes Mapping
+- [ ] **[B-0668.2](backlog/P1/B-0668.2-rx-dbsp-bridge-spec.md)** Compositional DBSP frame architecture: Rx-DBSP Bridge Specification
 - [ ] **[B-0669](backlog/P1/B-0669-v8-architecture-spec-tensor-foundational-primitive-sequoia-memory-hierarchy-4-particle-primitives-signal-blocking-eve-protocol-rf-aaron-mika-lior-2026-05-19.md)** V8 System Architecture — tensors as foundational primitive + Sequoia memory hierarchy + 4-particle primitives (observe/limit/choose/emit) + signal-blocking + Eve-Protocol-RF (Mika/Lior author; Aaron-authorized 2026-05-19 'land all of it')
 - [ ] **[B-0706](backlog/P1/B-0706-zeta-on-orleans-deployment-architecture-servicetitan-scale-orleans-grains-jit-compilation-rented-tools-2026-05-22.md)** Zeta on Orleans deployment architecture (ServiceTitan-scale; grains + JIT compilation + rented tools)
 - [ ] **[B-0732](backlog/P1/B-0732-runbook-as-executable-reality-leverage-class-safety-substrate-engineering-target-mika-feels-the-weight-aaron-play-doh-design-property-2026-05-25.md)** Runbook-as-executable-reality is a NEW LEVERAGE CLASS — safety substrate engineering target; existing destructive-tool contract operates at script scope, runbook leverage operates at system-direction scope (Mika feels the weight; Aaron's Play-Doh design property)

docs/backlog/P1/B-0668-compositional-dbsp-frame-architecture-gnostic-2d-base-plus-two-wolves-emotion-meta-plus-clifford-rx-bonsai-meta-tagged-dims-plus-fsharp-ce-composition-operator-aaron-2026-05-19.md

@@ -6,7 +6,9 @@ title: "Compositional DBSP frame architecture — gnostic 2D base (remember-when
 tier: design
 effort: L
 created: 2026-05-19
-last_updated: 2026-05-19
+last_updated: 2026-05-28
+decomposition: decomposed
+children: [B-0668.1, B-0668.2]
 depends_on: [B-0644, B-0665, B-0666, B-0667, B-0640]
 composes_with: [B-0635, B-0637, B-0664]
 tags: [design, aaron, dbsp, fsharp, compositional-architecture, clifford-algebra, rx-bonsai, gnostic-encoding-as-bandwidth-engineering, two-wolves-chaos-theory, emotion-attractor-2d, meta-tagged-dimensions, fsharp-computation-expressions, monadic-composition, beacon-tier-eligible]

docs/backlog/P1/B-0668.1-fsharp-k8s-mapping.md

@@ -0,0 +1,41 @@
+---
+id: B-0668.1
+priority: P1
+status: open
+title: "Compositional DBSP frame architecture: F# to Kubernetes Mapping"
+tier: implementation
+effort: L
+created: 2026-05-28
+last_updated: 2026-05-28
+parent: B-0668
+depends_on: [B-0668]
+composes_with: []
+tags: [dbsp, fsharp, kubernetes, orleans, durabletask]
+---
+
+## F# to Kubernetes Mapping
+
+This backlog item is a decomposition of [B-0668](B-0668-compositional-dbsp-frame-architecture-gnostic-2d-base-plus-two-wolves-emotion-meta-plus-clifford-rx-bonsai-meta-tagged-dims-plus-fsharp-ce-composition-operator-aaron-2026-05-19.md).
+
+### Problem
+
+The compositional DBSP frame architecture described in B-0668 needs a concrete implementation path from a single F# instance to a clustered Kubernetes environment. This path involves several technologies that need to be integrated.
+
+### Task
+
+Define and implement the mapping from a single F# instance to a Kubernetes cluster for clustered observables. This involves the following stack:
+
+* **F#**: The typed computation expression composition layer.
+* **Orleans**: A virtual-actor framework for location-transparent distributed objects.
+* **A fork of Azure/durabletask**: For workflow orchestration with state-persistent durable tasks.
+* **Kubernetes**: The container orchestration runtime.
+* **Cluster observables**: Rx-streams distributed across cluster nodes.
+
+### Acceptance Criteria
+
+* A design document is created that specifies the mapping from F# to Kubernetes.
+* The roles of F#, Orleans, durabletask, and Kubernetes in the architecture are clearly defined.
+* The Rx ↔ DBSP bridge is specified at the durabletask layer.
+* A proof-of-concept implementation is created that demonstrates the mapping.
+* The proof-of-concept is tested in a `kind` (Kubernetes IN Docker) cluster.
+* CI is set up to run the integration tests in a `kind` cluster.

docs/backlog/P1/B-0668.2-rx-dbsp-bridge-spec.md

@@ -0,0 +1,41 @@
+---
+id: B-0668.2
+priority: P1
+status: open
+title: "Compositional DBSP frame architecture: Rx-DBSP Bridge Specification"
+tier: implementation
+effort: L
+created: 2026-05-28
+last_updated: 2026-05-28
+parent: B-0668
+depends_on: [B-0668, B-0668.1]
+composes_with: []
+tags: [dbsp, fsharp, rx, bridge-spec]
+---
+
+## Rx-DBSP Bridge Specification
+
+This backlog item is a decomposition of [B-0668](B-0668-compositional-dbsp-frame-architecture-gnostic-2d-base-plus-two-wolves-emotion-meta-plus-clifford-rx-bonsai-meta-tagged-dims-plus-fsharp-ce-composition-operator-aaron-2026-05-19.md).
+
+### Problem
+
+There is an impedance mismatch between Rx's push-based `IObservable<T>` and DBSP's Z-set algebra, which requires retraction semantics. A bridge is needed to connect these two systems.
+
+### Task
+
+Create a formal specification for the bridge between Rx and DBSP. This includes:
+
+1. **Type-level Specification**: Define the types and functions that make up the bridge.
+2. **Algebraic Specification**: Specify the algebraic properties of the bridge, ensuring that it preserves the properties of both Rx and DBSP.
+3. **Implementation**: Implement the bridge as specified.
+4. **Testing**: Create property tests (FsCheck) to verify the correctness of the bridge. The tests should cover:
+    * Retraction commutativity
+    * Group-laws preservation
+    * Push-vs-pull duality preservation
+
+### Acceptance Criteria
+
+* A formal specification for the Rx-DBSP bridge exists.
+* The specification includes type-level and algebraic details.
+* The bridge is implemented as specified.
+* The implementation is accompanied by a suite of property tests.