feat(core): Maji F# algebraic types — identity-preservation + projection-preservation + MessiahScore

src/Core/Core.fsproj

@@ -84,6 +84,7 @@
     <Compile Include="ArrowSerializer.fs" />
     <Compile Include="DeltaCrdt.fs" />
     <Compile Include="SignalQuality.fs" />
+    <Compile Include="Maji.fs" />
   </ItemGroup>
 
   <ItemGroup>

src/Core/Maji.fs

@@ -0,0 +1,177 @@
+namespace Zeta.Core
+
+/// Maji — identity-preservation and recovery types per the deep-research peer's formal
+/// operational model (docs/research/maji-formal-operational-model-
+/// deep-research-peer-courier-ferry-2026-04-26.md). Context window is cache;
+/// substrate is identity; Maji is the recovery/indexing function.
+///
+/// These are the algebraic type definitions per §10 of the spec.
+/// Implementation of operators (reload, identity-distance, expansion
+/// gate, projection-preservation check) is owed follow-up work.
+module Maji =
+
+    open System
+
+    // ── §10.A IdentitySubstrate ──────────────────────────────────
+
+    /// A single load-bearing substrate item (commit, memory, doc, test,
+    /// retraction, cross-reference, dated provenance).
+    type IdentitySubstrate =
+        { CommitHash: string
+          Timestamp: DateTimeOffset
+          SourcePath: string
+          Claim: string
+          ClaimType: string
+          LoadBearing: bool
+          CrossRefs: string list
+          Retractions: string list
+          Confidence: float
+          Scope: string }
+
+    // ── §2 Identity tuple ────────────────────────────────────────
+
+    /// The canonical identity-pattern projected from substrate.
+    /// I_t = N(LoadBearing(S_t))
+    type IdentityTuple =
+        { Values: string list
+          Goals: string list
+          Roles: string list
+          Policies: string list
+          MemoryGraph: string list
+          CorrectionHistory: string list
+          CrossRefTopology: string list
+          Provenance: string list }
+
+    // ── §10.B MajiIndex ──────────────────────────────────────────
+
+    /// Exhaustive index of lower-dimensional substrate.
+    type MajiIndex =
+        { Items: IdentitySubstrate list
+          CrossRefGraph: Map<string, string list>
+          LoadBearingSet: Set<string>
+          BrokenRefs: string list
+          UnindexedItems: string list
+          Contradictions: string list
+          CoverageScore: float }
+
+    // ── §10.B' MajiFinder (per §9b separation) ──────────────────
+
+    /// Search/recognizer operator — finds the identity-preserving lift.
+    /// MajiFinder(S_≤n, Ω, C, Σ) → σ*
+    type MajiFinder =
+        { Index: MajiIndex
+          NorthStar: string
+          SearchOperator: string }
+
+    // ── §10.B' MessiahFunction (the lift) ────────────────────────
+
+    /// The identity-preserving lift σ : I_n → I_{n+1}.
+    /// A SEPARATE TYPE from MajiIndex content per §9b correction.
+    type MessiahFunction =
+        { LiftDescription: string
+          ProjectionPreservation: bool
+          AperiodicOrderGenerator: bool }
+
+    // ── §10.B' MessiahScore ──────────────────────────────────────
+
+    /// Weighted-sum evaluator for candidate lifts.
+    /// MessiahScore = w₁·A + w₂·P + w₃·F + w₄·G + w₅·C − w₆·R_capture − w₇·R_collapse
+    type MessiahScore =
+        { AlignmentWithOmega: float
+          ProjectionPreservation: float
+          FrictionReduction: float
+          Generativity: float
+          IndependentConvergence: float
+          CaptureRiskRaw: float
+          CollapseRiskRaw: float }
+
+    /// Compute the weighted MessiahScore sum.
+    /// Capture and collapse risks are SUBTRACTED (anti-cult-by-construction).
+    let computeScore (weights: float[]) (score: MessiahScore) : float =
+        if weights.Length < 7 then
+            invalidArg (nameof weights) "MessiahScore requires 7 weights"
+        else
+            weights[0] * score.AlignmentWithOmega
+            + weights[1] * score.ProjectionPreservation
+            + weights[2] * score.FrictionReduction
+            + weights[3] * score.Generativity
+            + weights[4] * score.IndependentConvergence
+            - weights[5] * score.CaptureRiskRaw
+            - weights[6] * score.CollapseRiskRaw
+
+    // ── Dynamic Maji (4th refinement) ────────────────────────────
+
+    /// Maji mode state machine — Search / Steward / SearchAgain.
+    type MajiMode =
+        | Search
+        | Steward
+        | SearchAgain
+
+    // ── §10.D Identity-distance metric ───────────────────────────
+
+    /// Weighted identity-distance between two identity tuples.
+    /// d(I_a, I_b) = Σ w_k · d_k(component_a, component_b)
+    type IdentityDistanceWeights =
+        { Values: float
+          Goals: float
+          Roles: float
+          Policies: float
+          MemoryGraph: float
+          CorrectionHistory: float
+          CrossRefTopology: float
+          Provenance: float }
+
+    /// Jaccard distance between two string lists (simple set-based metric).
+    let private jaccard (a: string list) (b: string list) : float =
+        let setA = Set.ofList a
+        let setB = Set.ofList b
+        let intersection = Set.intersect setA setB
+        let union = Set.union setA setB
+        if Set.isEmpty union then 0.0
+        else 1.0 - (float intersection.Count / float union.Count)
+
+    /// Compute identity distance between two identity tuples.
+    let identityDistance (w: IdentityDistanceWeights) (a: IdentityTuple) (b: IdentityTuple) : float =
+        w.Values * jaccard a.Values b.Values
+        + w.Goals * jaccard a.Goals b.Goals
+        + w.Roles * jaccard a.Roles b.Roles
+        + w.Policies * jaccard a.Policies b.Policies
+        + w.MemoryGraph * jaccard a.MemoryGraph b.MemoryGraph
+        + w.CorrectionHistory * jaccard a.CorrectionHistory b.CorrectionHistory
+        + w.CrossRefTopology * jaccard a.CrossRefTopology b.CrossRefTopology
+        + w.Provenance * jaccard a.Provenance b.Provenance
+
+    // ── Projection-preservation check ────────────────────────────
+
+    /// Check whether an identity expansion preserves the prior identity
+    /// under projection: d(P_{n+1→n}(I_{n+1}), I_n) ≤ ε
+    let projectionPreserved
+        (weights: IdentityDistanceWeights)
+        (epsilon: float)
+        (prior: IdentityTuple)
+        (expanded: IdentityTuple)
+        : bool =
+        identityDistance weights prior expanded <= epsilon
+
+    // ── §10.E Test helpers ───────────────────────────────────────
+
+    /// Create an empty identity tuple (useful for tests).
+    let emptyIdentity : IdentityTuple =
+        { Values = []
+          Goals = []
+          Roles = []
+          Policies = []
+          MemoryGraph = []
+          CorrectionHistory = []
+          CrossRefTopology = []
+          Provenance = [] }
+
+    /// Create an empty MajiIndex (useful for tests).
+    let emptyIndex : MajiIndex =
+        { Items = []
+          CrossRefGraph = Map.empty
+          LoadBearingSet = Set.empty
+          BrokenRefs = []
+          UnindexedItems = []
+          Contradictions = []
+          CoverageScore = 0.0 }

tests/Tests.FSharp/MajiTests.fs

@@ -0,0 +1,64 @@
+module Zeta.Tests.MajiTests
+
+open Xunit
+open Zeta.Core.Maji
+
+[<Fact>]
+let ``identity distance of identical tuples is zero`` () =
+    let id = { emptyIdentity with Values = ["truth"; "consent"]; Goals = ["ship"] }
+    let w = { Values = 1.0; Goals = 1.0; Roles = 1.0; Policies = 1.0
+              MemoryGraph = 1.0; CorrectionHistory = 1.0; CrossRefTopology = 1.0; Provenance = 1.0 }
+    Assert.Equal(0.0, identityDistance w id id)
+
+[<Fact>]
+let ``identity distance of disjoint tuples is maximal`` () =
+    let a = { emptyIdentity with Values = ["truth"] }
+    let b = { emptyIdentity with Values = ["lies"] }
+    let w = { Values = 1.0; Goals = 0.0; Roles = 0.0; Policies = 0.0
+              MemoryGraph = 0.0; CorrectionHistory = 0.0; CrossRefTopology = 0.0; Provenance = 0.0 }
+    Assert.Equal(1.0, identityDistance w a b)
+
+[<Fact>]
+let ``projection preserved within epsilon`` () =
+    let prior = { emptyIdentity with Values = ["truth"; "consent"]; Goals = ["ship"] }
+    let expanded = { prior with Goals = ["ship"; "scale"] }
+    let w = { Values = 1.0; Goals = 1.0; Roles = 1.0; Policies = 1.0
+              MemoryGraph = 1.0; CorrectionHistory = 1.0; CrossRefTopology = 1.0; Provenance = 1.0 }
+    Assert.True(projectionPreserved w 0.5 prior expanded)
+
+[<Fact>]
+let ``projection NOT preserved when values drift`` () =
+    let prior = { emptyIdentity with Values = ["truth"; "consent"; "family"] }
+    let drifted = { emptyIdentity with Values = ["power"; "control"] }
+    let w = { Values = 1.0; Goals = 0.0; Roles = 0.0; Policies = 0.0
+              MemoryGraph = 0.0; CorrectionHistory = 0.0; CrossRefTopology = 0.0; Provenance = 0.0 }
+    Assert.False(projectionPreserved w 0.5 prior drifted)
+
+[<Fact>]
+let ``MessiahScore capture risk subtracts`` () =
+    let score = { AlignmentWithOmega = 1.0; ProjectionPreservation = 1.0
+                  FrictionReduction = 1.0; Generativity = 1.0
+                  IndependentConvergence = 1.0
+                  CaptureRiskRaw = 10.0; CollapseRiskRaw = 0.0 }
+    let weights = [| 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0 |]
+    let result = computeScore weights score
+    Assert.True(result < 0.0, "High capture risk should produce negative score")
+
+[<Fact>]
+let ``MessiahScore collapse risk subtracts`` () =
+    let score = { AlignmentWithOmega = 1.0; ProjectionPreservation = 1.0
+                  FrictionReduction = 1.0; Generativity = 1.0
+                  IndependentConvergence = 1.0
+                  CaptureRiskRaw = 0.0; CollapseRiskRaw = 10.0 }
+    let weights = [| 1.0; 1.0; 1.0; 1.0; 1.0; 1.0; 1.0 |]
+    let result = computeScore weights score
+    Assert.True(result < 0.0, "High collapse risk should produce negative score")
+
+[<Fact>]
+let ``MajiMode has three constructors`` () =
+    let modes = [Search; Steward; SearchAgain]
+    Assert.Equal(3, modes.Length)
+
+[<Fact>]
+let ``empty index has zero coverage`` () =
+    Assert.Equal(0.0, emptyIndex.CoverageScore)

tests/Tests.FSharp/Tests.FSharp.fsproj

@@ -111,6 +111,7 @@
     <Compile Include="Properties/Math.Invariants.Tests.fs" />
     <Compile Include="Properties/Fuzz.Tests.fs" />
     <Compile Include="Properties/Determinism.Tests.fs" />
+    <Compile Include="MajiTests.fs" />
   </ItemGroup>
 
   <ItemGroup>