Deterministic ACID Engine
Replay-deterministic serializable transactions with Calvin-style epoch ordering, WAL-backed LSNs, optional PITR, and timeline-x event publishing on commit — stronger than conventional serializable because commit order reproduces from the log alone.
Business Metric Tensor DDL
CREATE KAOS METRIC TENSOR composes cost, time, risk, engagement, and custom component metrics with enforced non-negative weights. Cholesky sampling rejects indefinite geometry before it reaches production queries.
Riemannian Geodesic Compute
Shortest paths on tenant-configured business manifolds via kaos.geodesic.compute — SQL, CLI, REST, gRPC, and MOIRA action kaos.geodesic.compute_path with self-approved query class.
Tri-Modal Solver Dispatch
Automatic selection among A*, Fast Marching Method, and Hamilton-Jacobi-Bellman based on dimensionality, grid discretizability, and optimal-control flags — override logged when suboptimal.
Riemannian A* with Closed-Set Reopening
Gershgorin admissible heuristic avoids O(d³) eigendecomposition per expansion; GA* wave frontier on GPU with mandatory reopening when λ_min varies spatially — optimality proved, not hoped.
Anisotropic FMM / FIM
Jeong-Whitaker fast iterative method on Riemannian eikonal equations with OUM/Mirebeau stencil escalation when anisotropy ratio κ exceeds 4 — refuses degraded accuracy when you have not opted in.
Four-Tier HJB Stack
Semi-Lagrangian through sparse-grid, tensor-train, and deep BSDE/MPPI tiers for optimal control — tier crossover at documented dimension walls, not engineer folklore.
ACID-Consistent Geodesic Cache
BLAKE3-keyed LRU per tenant with metric LSN binding, same-host invalidation broadcast, optional PostgreSQL persistence validated on reload.
Tucker / CP / PARAFAC2 Tensor Algebra
HOOI with randomized-SVD initialization, ALS for CP, distributed MPI decomposition for retail-scale inventory cubes — factor matrix mutations participate in ACID write sets.
Fellegi-Sunter Reconciliation
Prior-art matching inside live ACID boundaries: LSH blocking, Jaro-Winkler and phonetic comparators, clerical review queues, CRDT conflict resolution, and dual-approved snapshot rollback.
State-Space Trajectory Store
Tenant-scoped trajectory insert and query with optional HMM transitions, KD-tree/LSH indexing, DTW/Fréchet similarity, and isolation-forest anomaly ensemble when fullSET integration is enabled.
Path Integral Processor
Trajectory probability estimation via bootstrap particle filters, reconcile-potential coupling, and tensor reduction for high-dimensional forecasting workloads.
CRTL Runtime Integration
Product runtime manifest, seven deployment-class matrices, admission bridge, namespace grammar tenant_<id>__kaos__<engine>, and lifecycle hooks for health, endpoints, activation, cache usage, and accelerator requirements.
ARGUS Authorization Gating
Three-tier approval vocabulary aligned to CRTL Part 10: self-approved queries, dual-approved metric tensor and reconcile mutations, recovery-critical replay and PITR restore.
GPU Accelerator Claims
Per-engine CRTL Part 17 claims with VRAM estimation, compute-share co-scheduling against tensor workloads, and CPU fallback that actually returns identical paths within floating-point tolerance.
MOIRA Action Provider
Thirteen registered kaos.* actions from transaction begin through distributed tensor decompose — MOIRA chains invoke KAOS; KAOS emits timeline-x events back for reactive composition.
Cross-Product Manifest Discipline
Machine-readable KAOS_MANIFEST.toml per consumer with KEEP/MODIFY/DISCARD engine subsets, feature flag requirements, and spec-linter enforcement — no silent capability creep across DXP, XRP, Lugh-E, MUKR, Prometheus, or Hephaestus.
Observability Namespace
kaos.geodesic.*, kaos.acid.*, kaos.tensor.*, kaos.reconcile.*, kaos.statespace.*, kaos.pathint.* metrics, traces, and error flags — solver selection rationale logged on every query.
