diff --git a/docs/BACKLOG.md b/docs/BACKLOG.md
index ac0d49c318..8df4ff0438 100644
--- a/docs/BACKLOG.md
+++ b/docs/BACKLOG.md
@@ -391,6 +391,7 @@ are closed (status: closed in frontmatter)._
 - [ ] **[B-0821](backlog/P1/B-0821-zeta-as-dependency-graph-and-variable-passing-layer-on-top-of-helm-empty-architectural-slot-claim-aaron-2026-05-26.md)** Zeta as the dependency-graph + auto-variable-passing layer on top of Helm — empty architectural slot above sync engines (ArgoCD / Flux) that nobody has claimed; load-bearing strategic-positioning substrate (Aaron 2026-05-26)
 - [ ] **[B-0822](backlog/P1/B-0822-diamond-resolution-namespace-cardinality-multi-tenant-awareness-as-third-dimension-of-shared-chart-dependency-resolution-aaron-2026-05-26.md)** diamond-resolution namespace + cardinality + multi-tenant-awareness — three orthogonal properties on shared charts that determine whether the Maven-for-Helm graph deploys ONE shared instance or N per-consumer instances; substrate-engineering target for Ace package manager's chart-graph resolver (Aaron 2026-05-26)
 - [ ] **[B-0824](backlog/P1/B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md)** Ace as "package manager of package managers" — N-dimensional dependency space (Maven is 2D; we're at least 3D / N-D) + holographic projection (merge 2D streams from each PM into higher-D views) + AI-rate continuous upstream negotiation (push-forward + absorb-forward at AI cadence — no existing PM does this); strategic-architectural substrate for the Ace meta-PM substrate (Aaron 2026-05-26)
+- [ ] **[B-0824.1](backlog/P1/B-0824.1-n-dimensional-dependency-space-formalism.md)** Ace meta-PM: N-dimensional dependency-space formalism
 - [ ] **[B-0825](backlog/P1/B-0825-time-modeled-dependencies-for-helm-clusters-as-long-running-stateful-systems-require-temporal-axis-in-dependency-graph-aaron-2026-05-26.md)** time-modeled dependencies for Helm — clusters are long-running stateful systems; chart-graph needs temporal axis for revision history + migration phases + rolling-upgrade windows + concurrent-version overlap; Helm uniquely requires this among package managers; substrate-engineering target for Ace meta-PM (Aaron 2026-05-26)
 - [ ] **[B-0831](backlog/P1/B-0831-ci-cascade-6-full-install-plus-cluster-auto-join-eliminate-routine-human-physical-usb-test-aaron-2026-05-26.md)** CI cascade #6 — full-install-and-cluster-auto-join (post-boot install completes; node self-registers; eliminates routine human physical USB test) (Aaron 2026-05-26)
 - [ ] **[B-0833](backlog/P1/B-0833-installer-interactive-login-vs-baked-in-keys-ci-test-tension-resolve-without-shipping-credentials-aaron-2026-05-26.md)** installer interactive-login vs baked-in-keys CI-test tension — resolve without shipping credentials on ISO (operator 2026-05-26 from physical hardware-support test)
diff --git a/docs/backlog/P1/B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md b/docs/backlog/P1/B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md
index f3cb9e7e0c..1fc92685b7 100644
--- a/docs/backlog/P1/B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md
+++ b/docs/backlog/P1/B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md
@@ -6,7 +6,9 @@ title: Ace as "package manager of package managers" — N-dimensional dependency
 effort: L
 ask: aaron 2026-05-26
 created: 2026-05-26
-last_updated: 2026-05-26
+last_updated: 2026-05-27
+decomposition: decomposed
+children: [B-0824.1]
 depends_on:
   - B-0247
   - B-0288
diff --git a/docs/backlog/P1/B-0824.1-n-dimensional-dependency-space-formalism.md b/docs/backlog/P1/B-0824.1-n-dimensional-dependency-space-formalism.md
new file mode 100644
index 0000000000..435eae297b
--- /dev/null
+++ b/docs/backlog/P1/B-0824.1-n-dimensional-dependency-space-formalism.md
@@ -0,0 +1,48 @@
+---
+id: B-0824.1
+priority: P1
+status: open
+title: "Ace meta-PM: N-dimensional dependency-space formalism"
+tier: substrate-architecture
+effort: M
+ask: aaron 2026-05-26
+created: 2026-05-27
+last_updated: 2026-05-27
+parent: B-0824
+depends_on: [B-0822]
+composes_with: []
+tags: [ace-feature, meta-package-manager, n-dimensional-dependency-space]
+---
+
+## N-dimensional dependency-space formalism
+
+This backlog item is a decomposition of [B-0824](B-0824-package-manager-of-package-managers-n-dimensional-dependency-space-holographic-projection-ai-rate-continuous-upstream-negotiation-aaron-2026-05-26.md).
+
+### Problem
+
+Today's package managers (Maven, npm, apt, Helm, etc.) each operate in their own 2D-projection of the dependency space (e.g., dependencies × versions). The true substrate Ace operates over is N-dimensional. Ace needs to operate on the full N-D space, not just a 2D projection.
+
+### Task
+
+Formalize the N-dimensional dependency space. This includes:
+
+1. **Axis Enumeration**: Enumerate the axes of the dependency space. This is not expected to be exhaustive, but should include the most important axes.
+    * Dependency relation (depends_on, conflicts_with, provides, replaces)
+    * Version (semver, range, pin)
+    * Cardinality (cluster-singleton, N-allowed)
+    * Namespace scope (cluster, namespace, per-consumer)
+    * Multi-tenant (cross-tenant isolation strategy)
+    * Multi-use (intra-tenant use-axis)
+    * Time (revision history, migration phase, rolling-upgrade window)
+    * Cross-PM (jar inside Docker inside Helm inside ArgoCD)
+    * Security posture (signed, sbom-verified, vuln-scan-status)
+    * Operator policy (environment, org-policy, compliance-tier)
+2. **Documentation**: Create a document that formalizes the N-dimensional dependency space, its axes, and how it relates to existing 2D package managers. This documentation will be consumed by future substrate-engineering decisions.
+3. **Composition with B-0822**: Make the composition with [B-0822](B-0822-diamond-resolution-namespace-cardinality-multi-tenant-awareness-as-third-dimension-of-shared-chart-dependency-resolution-aaron-2026-05-26.md) explicit in the documentation. The 4 properties from B-0822 are a 4-axis slice of the N-D space.
+
+### Acceptance Criteria
+
+* A document exists that formalizes the N-D dependency space.
+* The document enumerates the axes of the dependency space.
+* The document is consumable by future substrate-engineering decisions.
+* The composition with B-0822 is made explicit.