feat(pist): port minimal PIST classifier surface to SilverSight

- Add SilverSight.PIST.Spectral with isqrt, powerIteration, SpectralProfile,
  and computeSpectral (pure Int + Q16_16; no Float, no photonic extras).
- Add SilverSight.PIST.Classify with Matrix8, hashMatrix, classifyProxy,
  classifyExact, spectral-radius color gate, and blend rules.
- Add SilverSight.PIST.Matrices250 auto-generated from Research Stack
  rrc_pist_predictions_250_v1.json (250 entries).
- Add python/build_pist_matrices_250.py generator with deterministic ordering
  and content-hash comment.
- Register PIST modules under SilverSightRRC in lakefile.lean.
- Regenerate PROJECT_MAP.md/json.

Build: 2981 jobs, 0 errors (lake build); SilverSightRRC: 2994 jobs, 0 errors.

docs/PROJECT_MAP.json

@@ -1,13 +1,13 @@
 {
   "schema": "silversight_project_map_v1",
-  "generated_at": "2026-06-21T14:16:47.617133+00:00",
+  "generated_at": "2026-06-21T14:45:59.149164+00:00",
   "repo": "https://github.com/allaunthefox/SilverSight",
   "local_path": "/tmp/SilverSight",
   "summary": {
-    "total_files": 97,
+    "total_files": 101,
-    "lean_files": 48,
+    "lean_files": 51,
-    "python_files": 20,
+    "python_files": 21,
-    "active": 96,
+    "active": 100,
     "quarantined": 1,
     "archived": 0,
     "receipt_boundary_files": 4
@@ -78,10 +78,10 @@
       "name": "PythonShims",
       "path": "python",
       "description": "I/O and feature extraction; no admissibility logic.",
-      "file_count": 7,
+      "file_count": 8,
       "lean_files": 0,
-      "python_files": 7,
+      "python_files": 8,
-      "active": 7,
+      "active": 8,
       "quarantined": 0,
       "archived": 0
     },
@@ -375,7 +375,7 @@
       "research_stack_source": null,
       "role": "",
       "receipt_boundary": false,
-      "line_count": 74
+      "line_count": 89
     },
     {
       "path": "docs/LIBRARY_MANIFEST.md",
@@ -1386,6 +1386,53 @@
       "receipt_boundary": false,
       "line_count": 34
     },
+    {
+      "path": "formal/SilverSight/PIST/Classify.lean",
+      "layer": "other",
+      "language": "lean",
+      "kind": "formal",
+      "module": "SilverSight.PIST.Classify",
+      "build_target": "SilverSightFormal",
+      "status": "active",
+      "imports": [
+        "SilverSight.PIST.Spectral",
+        "SilverSight.FixedPoint"
+      ],
+      "research_stack_source": null,
+      "role": "",
+      "receipt_boundary": false,
+      "line_count": 229
+    },
+    {
+      "path": "formal/SilverSight/PIST/Matrices250.lean",
+      "layer": "other",
+      "language": "lean",
+      "kind": "formal",
+      "module": "SilverSight.PIST.Matrices250",
+      "build_target": "SilverSightFormal",
+      "status": "active",
+      "imports": [],
+      "research_stack_source": null,
+      "role": "",
+      "receipt_boundary": false,
+      "line_count": 2526
+    },
+    {
+      "path": "formal/SilverSight/PIST/Spectral.lean",
+      "layer": "other",
+      "language": "lean",
+      "kind": "formal",
+      "module": "SilverSight.PIST.Spectral",
+      "build_target": "SilverSightFormal",
+      "status": "active",
+      "imports": [
+        "SilverSight.FixedPoint"
+      ],
+      "research_stack_source": null,
+      "role": "",
+      "receipt_boundary": false,
+      "line_count": 213
+    },
     {
       "path": "formal/SilverSight/RRC/Emit.lean",
       "layer": "other",
@@ -1497,7 +1544,7 @@
       "research_stack_source": null,
       "role": "",
       "receipt_boundary": false,
-      "line_count": 56
+      "line_count": 59
     },
     {
       "path": "lean-toolchain",
@@ -1527,6 +1574,24 @@
       "receipt_boundary": false,
       "line_count": 6
     },
+    {
+      "path": "python/build_pist_matrices_250.py",
+      "layer": "python_shim",
+      "language": "python",
+      "kind": "python_shim",
+      "module": null,
+      "build_target": null,
+      "status": "active",
+      "imports": [
+        "__future__",
+        "argparse",
+        "pathlib"
+      ],
+      "research_stack_source": null,
+      "role": "",
+      "receipt_boundary": false,
+      "line_count": 123
+    },
     {
       "path": "python/chaos_game.py",
       "layer": "python_shim",
@@ -2046,6 +2111,21 @@
       "to": "Core/SilverSight/FixedPoint.lean",
       "relation": "imports"
     },
+    {
+      "from": "formal/SilverSight/PIST/Classify.lean",
+      "to": "formal/SilverSight/PIST/Spectral.lean",
+      "relation": "imports"
+    },
+    {
+      "from": "formal/SilverSight/PIST/Classify.lean",
+      "to": "Core/SilverSight/FixedPoint.lean",
+      "relation": "imports"
+    },
+    {
+      "from": "formal/SilverSight/PIST/Spectral.lean",
+      "to": "Core/SilverSight/FixedPoint.lean",
+      "relation": "imports"
+    },
     {
       "from": "formal/SilverSight/RRC/Emit.lean",
       "to": "formal/SilverSight/RRCLogogramProjection.lean",

docs/PROJECT_MAP.md

@@ -1,6 +1,6 @@
 # SilverSight Project Map
 
-**Generated:** 2026-06-21T14:16:47.617133+00:00
+**Generated:** 2026-06-21T14:45:59.149164+00:00
 
 **Source repo:** https://github.com/allaunthefox/SilverSight
 
@@ -8,10 +8,10 @@
 
 ## 1. Project Overview
 
-- **Total tracked files:** 97
+- **Total tracked files:** 101
-- **Lean files:** 48
+- **Lean files:** 51
-- **Python files:** 20
+- **Python files:** 21
-- **Active:** 96 | **Quarantined:** 1 | **Archived:** 0
+- **Active:** 100 | **Quarantined:** 1 | **Archived:** 0
 - **Receipt-boundary files:** 4
 
 ## 2. Layer Summary
@@ -23,7 +23,7 @@
 | PVGS_DQ_Bridge | `formal/PVGS_DQ_Bridge` | 9 | 8 | 1 | 9 | 0 | 0 | Photon-varied Gaussian state dual-quaternion bridge. |
 | UniversalEncoding | `formal/UniversalEncoding` | 2 | 2 | 0 | 2 | 0 | 0 | Universal math address space and chirality. |
 | BindingSite | `formal/BindingSite` | 3 | 3 | 0 | 3 | 0 | 0 | Amino-acid / protein binding sketches. |
-| PythonShims | `python` | 7 | 0 | 7 | 7 | 0 | 0 | I/O and feature extraction; no admissibility logic. |
+| PythonShims | `python` | 8 | 0 | 8 | 8 | 0 | 0 | I/O and feature extraction; no admissibility logic. |
 | QUBOShims | `qubo` | 5 | 0 | 5 | 5 | 0 | 0 | QUBO/QAOA/Finsler optimization shims. |
 | Tests | `tests` | 2 | 0 | 2 | 1 | 1 | 0 | Verification fixtures. |
 | Infrastructure | `.github` | 6 | 0 | 2 | 6 | 0 | 0 | CI workflows and repo scripts. |
@@ -94,6 +94,7 @@
 
 | File | Module | Build Target | Status | Receipt Boundary | Research-Stack Source | Role |
 |------|--------|--------------|--------|------------------|----------------------|------|
+| `python/build_pist_matrices_250.py` | — | — | active | — | — | — |
 | `python/chaos_game.py` | — | — | active | — | `4-Infrastructure/shim/chaos_game_16d.py` | 16D chaos-game basin sampler. |
 | `python/pist_matrix_builder.py` | — | — | active | — | — | — |
 | `python/q16_canonical.py` | — | — | active | — | — | Canonical Q16_16 Python reference implementation. |

formal/SilverSight/PIST/Classify.lean

@@ -0,0 +1,229 @@
+-- SilverSight.PIST.Classify — minimal RRC shape classifier over 8×8 matrices
+--
+-- Ports only the classifier surface needed for Corpus250:
+--   • 8×8 braid adjacency matrix type
+--   • spectral-radius → RGB color → shape-name gate
+--   • matrix-hash lookup table (proxy classifier)
+--   • spectral-radius exact classifier
+--   • deterministic blending rules for shared equation_ids
+--
+-- Photonic/Kubelka-Munk/Quandela extensions from Research Stack are omitted.
+
+import SilverSight.PIST.Spectral
+import SilverSight.FixedPoint
+
+namespace SilverSight.PIST.Classify
+
+open SilverSight.FixedPoint
+open SilverSight.FixedPoint.Q16_16
+open SilverSight.PIST.Spectral
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §1  Matrix type
+-- ─────────────────────────────────────────────────────────────────────────────
+
+abbrev Matrix8 : Type := Array (Array Int)
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §2  Spectral-radius thresholds
+-- ─────────────────────────────────────────────────────────────────────────────
+
+/-- High amplification threshold: λ ≥ 4.0 (Q16.16 raw). -/
+def oberthHighThreshold : Int := 262144
+
+/-- Moderate amplification threshold: λ ≥ 2.0 (Q16.16 raw). -/
+def signalThreshold : Int := 131072
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §3  Spectral color gate
+-- ─────────────────────────────────────────────────────────────────────────────
+
+structure SpectralColor where
+  red   : Q16_16
+  green : Q16_16
+  blue  : Q16_16
+  deriving Repr
+
+/-- Convert a raw spectral radius (Int) to an RGB SpectralColor. -/
+def spectralRadiusToColor (lam : Int) : SpectralColor :=
+  let max_raw := oberthHighThreshold
+  let r := if lam ≥ max_raw then one else zero
+  let g := if lam ≥ signalThreshold then
+    ofRawInt ((lam - signalThreshold) * 65536 / (max_raw - signalThreshold))
+    else zero
+  let b := if lam < signalThreshold then
+    ofRawInt (lam * 65536 / signalThreshold)
+    else zero
+  { red := r, green := g, blue := b }
+
+/-- Extract the shape-name string from a SpectralColor. -/
+def colorToShapeName (c : SpectralColor) : Option String :=
+  if c.red.toInt > 0 then some "CognitiveLoadField"
+  else if c.green.toInt > 0 then some "SignalShapedRouteCompiler"
+  else none
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §4  Blending rules for shared equation_ids
+-- ─────────────────────────────────────────────────────────────────────────────
+
+inductive BlendType where
+  | additive
+  | rms
+  | vortex
+  deriving Repr
+
+def blend_additive (lam1 lam2 : Int) : Int :=
+  max lam1 lam2
+
+def blend_rms (lam1 lam2 : Int) : Int :=
+  Int.ofNat (Nat.sqrt (((lam1 * lam1 + lam2 * lam2) / 2).toNat))
+
+def blend_vortex (lam1 lam2 : Int) : Int :=
+  (lam1 * lam2) / (lam1 + lam2 + 1)
+
+/-- Blend a list of spectral radii under a given topology. -/
+def blendRadii (blendType : BlendType) (lams : List Int) : Int :=
+  match lams with
+  | [] => 0
+  | lam :: rest =>
+    rest.foldl (fun acc lam2 =>
+      match blendType with
+      | .additive => if acc ≥ lam2 then acc else lam2
+      | .rms => isqrt ((acc * acc + lam2 * lam2) / 2)
+      | .vortex => (acc * lam2) / (acc + lam2 + 1)
+    ) lam
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §5  Classifier surface
+-- ─────────────────────────────────────────────────────────────────────────────
+
+def hashMatrix (m : Matrix8) : Int :=
+  let rec loop (i j : Nat) (pow_5 : Int) (acc : Int) : Int :=
+    if i ≥ 8 then acc
+    else if j ≥ 8 then loop (i + 1) 0 pow_5 acc
+    else
+      let val := m.getD i #[] |>.getD j 0
+      loop i (j + 1) (pow_5 * 5) (acc + val * pow_5)
+  loop 0 0 1 0
+
+/-- Advisory shape proxy via matrix-hash lookup. -/
+def classifyProxy (m : Matrix8) : Option String :=
+  match hashMatrix m with
+  | 0 => some "CognitiveLoadField"
+  | 25 => some "CognitiveLoadField"
+  | 125 => some "CognitiveLoadField"
+  | 625 => some "CognitiveLoadField"
+  | 78125 => some "SignalShapedRouteCompiler"
+  | 390625 => some "CognitiveLoadField"
+  | 1953125 => some "SignalShapedRouteCompiler"
+  | 9765625 => some "ProjectableGeometryTopology"
+  | 48828125 => some "ProjectableGeometryTopology"
+  | 244140625 => some "SignalShapedRouteCompiler"
+  | 30517578125 => some "ProjectableGeometryTopology"
+  | 152587890625 => some "ProjectableGeometryTopology"
+  | 152587968750 => some "ProjectableGeometryTopology"
+  | 3814697265625 => some "SignalShapedRouteCompiler"
+  | 19073496093750 => some "CognitiveLoadField"
+  | 476837158203150 => some "CadForceProbeReceipt"
+  | 2384185791015625 => some "ProjectableGeometryTopology"
+  | 11920928955078125 => some "ProjectableGeometryTopology"
+  | 59604644775390626 => some "ProjectableGeometryTopology"
+  | 59604644824218750 => some "CognitiveLoadField"
+  | 298023223876953125 => some "ProjectableGeometryTopology"
+  | 1490116119384765625 => some "ProjectableGeometryTopology"
+  | 1490211486816406250 => some "ProjectableGeometryTopology"
+  | 1502037048339843750 => some "CognitiveLoadField"
+  | 7450580596923828125 => some "ProjectableGeometryTopology"
+  | 7510185241699218875 => some "ProjectableGeometryTopology"
+  | 37252902984619140625 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 186264514923095703125 => some "ProjectableGeometryTopology"
+  | 931322574615478515625 => some "ProjectableGeometryTopology"
+  | 4656612873077392578125 => some "CognitiveLoadField"
+  | 4656612873077441406250 => some "CognitiveLoadField"
+  | 23283064365386962890625 => some "ProjectableGeometryTopology"
+  | 23283064365386962890626 => some "ProjectableGeometryTopology"
+  | 23283064365386962890630 => some "CognitiveLoadField"
+  | 23283064365386962890750 => some "SignalShapedRouteCompiler"
+  | 23320317268371582031250 => some "SignalShapedRouteCompiler"
+  | 116415321826934814453125 => some "SignalShapedRouteCompiler"
+  | 116415321826965576171875 => some "SignalShapedRouteCompiler"
+  | 582076609135443115234375 => some "CognitiveLoadField"
+  | 582076621055603027343750 => some "CognitiveLoadField"
+  | 2910383343696594482421875 => some "CognitiveLoadField"
+  | 2910420298576354980468750 => some "CognitiveLoadField"
+  | 14575198292732238769531250 => some "SignalShapedRouteCompiler"
+  | 17462298274040222167968750 => some "SignalShapedRouteCompiler"
+  | 72759576141929626464843750 => some "CognitiveLoadField"
+  | 363797917962074279785156250 => some "CognitiveLoadField"
+  | 9094947017729282379150390625 => some "CognitiveLoadField"
+  | 9094947017729759216308593750 => some "ProjectableGeometryTopology"
+  | 9094947203993797302246093750 => some "SignalShapedRouteCompiler"
+  | 45474735088646411895751953125 => some "ProjectableGeometryTopology"
+  | 45474735088646412048339846876 => some "CognitiveLoadField"
+  | 45547494664788246155029687500 => some "CognitiveLoadField"
+  | 227373675443232059478759765625 => some "SignalShapedRouteCompiler"
+  | 227373675443232060241699609375 => some "ProjectableGeometryTopology"
+  | 227373675443232063293457031250 => some "ProjectableGeometryTopology"
+  | 227373675443234443664550781250 => some "CognitiveLoadField"
+  | 227446435019376277923828125000 => some "CognitiveLoadField"
+  | 5684341886080801486968994140625 => some "ProjectableGeometryTopology"
+  | 5684414668940007686615234375000 => some "CognitiveLoadField"
+  | 28421709430404007911682128906250 => some "CognitiveLoadField"
+  | 28421709430405498027801513671875 => some "CognitiveLoadField"
+  | 56843418860808014869689941406250 => some "CognitiveLoadField"
+  | 56843491620384156703949218750000 => some "CognitiveLoadField"
+  | 142108547152020037174226074218750 => some "ProjectableGeometryTopology"
+  | 142108547152021527767181396484375 => some "CognitiveLoadField"
+  | 170530256582424044609069824218750 => some "CognitiveLoadField"
+  | 710542735760100185871124267578125 => some "ProjectableGeometryTopology"
+  | 3552713678800500929355621337890750 => some "CognitiveLoadField"
+  | 3552713678800500929355621337893750 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 3694822225952520966529846191409375 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 17763568394002504646778106689453125 => some "ProjectableGeometryTopology"
+  | 17763568394002504646778106689468750 => some "ProjectableGeometryTopology"
+  | 17763568394002504646778106933593750 => some "ProjectableGeometryTopology"
+  | 17763568394002504646778107910156250 => some "ProjectableGeometryTopology"
+  | 17905676941154524683952331542971875 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 17905677013914100825786590820312500 => some "SignalShapedRouteCompiler"
+  | 88817841970012523233890533447265625 => some "ProjectableGeometryTopology"
+  | 88817841970594599845409393554687500 => some "SignalShapedRouteCompiler"
+  | 88817842333810441195964813232421875 => some "SignalShapedRouteCompiler"
+  | 88959950517164543271064758300784375 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 444089209850062616169452667236328125 => some "CognitiveLoadField"
+  | 444231318397214636206626892089846875 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 2220446049250313080847263336181640625 => some "ProjectableGeometryTopology"
+  | 2220446049250313080849647521972656250 => some "SignalShapedRouteCompiler"
+  | 2220588157797465100884437561035159375 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 11102372354798717424273490905761721875 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 55511151231257827021183967590341796875 => some "CognitiveLoadField"
+  | 55511293339804979041218757629394534375 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 277555756156289135105907917022705078125 => some "CognitiveLoadField"
+  | 277555898264836287125945091247558596875 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 1387778780781445675529539585113525391250 => some "HoldForUnlawfulOrUnderspecifiedShape"
+  | 1387778780781445680186152458190917968750 => some "CognitiveLoadField"
+  | 1387778780781446257606160640716552734375 => some "CognitiveLoadField"
+  | 1387778780783264664933085441589355468750 => some "CognitiveLoadField"
+  | 1387779491324181435629725456237792968750 => some "CognitiveLoadField"
+  | 6938893903907228377647697925567628906250 => some "SignalShapedRouteCompiler"
+  | 173472347597680709441192448139190673828125 => some "ProjectableGeometryTopology"
+  | 173472347597680709441229701042175292968750 => some "ProjectableGeometryTopology"
+  | 867361737988403547205963742733001708984375 => some "CognitiveLoadField"
+  | 867361737988405366195403039455413818359375 => some "CognitiveLoadField"
+  | 867361738698946282966062426567077636718750 => some "CognitiveLoadField"
+  | 4336808689947702077915892004966735839843750 => some "SignalShapedRouteCompiler"
+  | 4337086245698174025164917111396789550781250 => some "ProjectableGeometryTopology"
+  | 4337086245698174025164917113780975341796875 => some "ProjectableGeometryTopology"
+  | 8673617380594578207819722592830657958984375 => some "ProjectableGeometryTopology"
+  | 21684321005466244969284161925315856933593750 => some "SignalShapedRouteCompiler"
+  | 108420217248550443400745280086994171142578125 => some "ProjectableGeometryTopology"
+  | 108420217248550443400745280086994201660156250 => some "CognitiveLoadField"
+  | 108420217248550443400745280098915100097656250 => some "CognitiveLoadField"
+  | _ => none
+
+/-- Attested shape exact match via spectral-radius color gate. -/
+def classifyExact (m : Matrix8) : Option String :=
+  let profile := computeSpectral m
+  let lam := profile.adjacency_eigenvalue_max.toInt
+  colorToShapeName (spectralRadiusToColor lam)
+
+end SilverSight.PIST.Classify

formal/SilverSight/PIST/Spectral.lean

@@ -0,0 +1,213 @@
+-- SilverSight.PIST.Spectral — minimal fixed-point spectral feature extraction
+--
+-- Ports only the surface needed for the RRC 250-equation classifier:
+--   • integer square root
+--   • power iteration for dominant eigenvalue
+--   • SpectralProfile record
+--   • computeSpectral over an 8×8 Int matrix
+--
+-- This is a stripped-down port of Research Stack's Semantics.PIST.Spectral.
+-- Photonic extensions, tactic-family heuristics, and Kubelka-Munk material
+-- are intentionally omitted to keep SilverSight focused on the RRC gate.
+
+import SilverSight.FixedPoint
+
+namespace SilverSight.PIST.Spectral
+
+open SilverSight.FixedPoint
+open SilverSight.FixedPoint.Q16_16
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §1  Integer square root
+-- ─────────────────────────────────────────────────────────────────────────────
+
+/-- Integer square root via Newton's method. Returns floor(√n). -/
+def isqrt (n : Int) : Int :=
+  if n ≤ 0 then 0
+  else
+    let rec loop (x : Int) (fuel : Nat) : Int :=
+      match fuel with
+      | 0     => x
+      | f + 1 =>
+        let x' := (x + n / x) / 2
+        if x' ≥ x then x else loop x' f
+    loop (n / 2 + 1) 64
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §2  Matrix-vector helpers (pure Int arithmetic)
+-- ─────────────────────────────────────────────────────────────────────────────
+
+@[inline]
+private def getEntry (mat : Array (Array Int)) (i j : Nat) : Int :=
+  mat.getD i #[] |>.getD j 0
+
+private def rowSum (mat : Array (Array Int)) (i n : Nat) : Int :=
+  (List.range n).foldl (fun acc j => acc + getEntry mat i j) 0
+
+private def symmetrize (mat : Array (Array Int)) (n : Nat) : Array (Array Int) :=
+  Array.ofFn (n := n) fun i =>
+    Array.ofFn (n := n) fun j =>
+      (getEntry mat i.val j.val + getEntry mat j.val i.val) / 2
+
+private def buildLaplacian (sym : Array (Array Int)) (n : Nat) : Array (Array Int) :=
+  Array.ofFn (n := n) fun i =>
+    let deg := rowSum sym i.val n
+    Array.ofFn (n := n) fun j =>
+      if i.val = j.val then deg else -(getEntry sym i.val j.val)
+
+private def buildATA (mat : Array (Array Int)) (n : Nat) : Array (Array Int) :=
+  Array.ofFn (n := n) fun i =>
+    Array.ofFn (n := n) fun j =>
+      (List.range n).foldl (fun acc k =>
+        acc + getEntry mat k i.val * getEntry mat k j.val) 0
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §3  Power iteration (Q16_16 fixed-point)
+-- ─────────────────────────────────────────────────────────────────────────────
+
+private def normSqRaw (v : Array Q16_16) : Int :=
+  v.foldl (fun acc x => acc + x.toInt * x.toInt) 0
+
+private def matVecMul (mat : Array (Array Int)) (n : Nat) (v : Array Q16_16) : Array Q16_16 :=
+  Array.ofFn (n := n) fun i =>
+    let s : Int := (List.range n).foldl (fun acc j =>
+      acc + getEntry mat i.val j * (v.getD j zero).toInt) 0
+    ofRawInt s
+
+/-- Dominant eigenvalue of a square Int matrix via power iteration. -/
+def powerIteration (mat : Array (Array Int)) (maxIter : Nat := 100) : Q16_16 :=
+  let n := mat.size
+  if n = 0 then zero
+  else
+    let initVal := ofRawInt ((q16Scale : Int) / (n : Int))
+    let v₀ : Array Q16_16 := Array.replicate n initVal
+    let rec iterate (v : Array Q16_16) (fuel : Nat) : Array Q16_16 :=
+      match fuel with
+      | 0     => v
+      | f + 1 =>
+        let mv  := matVecMul mat n v
+        let nm2 := normSqRaw mv
+        if nm2 ≤ 0 then v
+        else
+          let nm := isqrt nm2
+          if nm = 0 then v
+          else
+            let vn := mv.map (fun x => ofRawInt (x.toInt * q16Scale / nm))
+            iterate vn f
+    let vFinal := iterate v₀ maxIter
+    let mv  := matVecMul mat n vFinal
+    let num : Int := (List.range n).foldl (fun acc i =>
+      acc + (vFinal.getD i zero).toInt * (mv.getD i zero).toInt) 0
+    let den : Int := normSqRaw vFinal
+    if den ≤ 0 then zero
+    else ofRawInt (num * q16Scale / den)
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §4  Spectral profile
+-- ─────────────────────────────────────────────────────────────────────────────
+
+structure SpectralProfile where
+  matrix_size             : Q16_16
+  rank                    : Q16_16
+  spectral_gap            : Q16_16
+  density                 : Q16_16
+  trace_val               : Q16_16
+  frobenius_norm          : Q16_16
+  laplacian_zero_count    : Q16_16
+  adjacency_eigenvalue_max : Q16_16
+  laplacian_eigenvalue_max : Q16_16
+  singular_value_max      : Q16_16
+  deriving Repr
+
+def emptyProfile : SpectralProfile :=
+  { matrix_size             := zero
+    rank                    := zero
+    spectral_gap            := zero
+    density                 := zero
+    trace_val               := zero
+    frobenius_norm          := zero
+    laplacian_zero_count    := zero
+    adjacency_eigenvalue_max := zero
+    laplacian_eigenvalue_max := zero
+    singular_value_max      := zero }
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §5  computeSpectral
+-- ─────────────────────────────────────────────────────────────────────────────
+
+/-- Compute the full spectral profile of a proof transition matrix.
+    Pure Int + Q16_16 arithmetic; no Float. -/
+def computeSpectral (mat : Array (Array Int)) : SpectralProfile :=
+  let n := mat.size
+  if n = 0 then emptyProfile
+  else
+    let sym := symmetrize mat n
+    let lap := buildLaplacian sym n
+
+    let evMax := powerIteration sym
+
+    -- Second eigenvalue via shift-deflation (0.9 * ev_max on the diagonal)
+    let shiftAmt : Int := (evMax.toInt * 58982) / q16Scale
+    let shiftedMat : Array (Array Int) :=
+      Array.ofFn (n := n) fun i =>
+        Array.ofFn (n := n) fun j =>
+          let base := getEntry sym i.val j.val
+          if i.val = j.val then base - shiftAmt else base
+    let evShift := powerIteration shiftedMat
+    let evSecond : Q16_16 :=
+      if evShift.toInt < evMax.toInt
+      then ofRawInt (Int.natAbs (evMax.toInt - evShift.toInt) : Int)
+      else evMax
+    let spectralGap := sub evMax evSecond
+
+    let lapMax := powerIteration lap
+
+    let total : Int := mat.foldl (fun acc row => acc + row.foldl (· + ·) 0) 0
+    let nSqI : Int := (n * n : Nat)
+    let density := if nSqI ≤ 0 then zero else ofRawInt (total * q16Scale / nSqI)
+
+    let traceInt : Int := (List.range n).foldl (fun acc i => acc + getEntry mat i i) 0
+    let traceVal := ofRawInt traceInt
+
+    let frobSq : Int := mat.foldl (fun acc row => acc + row.foldl (fun a c => a + c * c) 0) 0
+    let frobNorm := ofRawInt (isqrt frobSq)
+
+    let rankVal : Int := mat.foldl (fun acc row =>
+      acc + if row.any (· ≠ 0) then 1 else 0) 0
+
+    let lapZero : Int := (List.range n).foldl (fun acc i =>
+      let rs := rowSum mat i n
+      let d  := getEntry mat i i
+      acc + if rs - d = 0 then 1 else 0) 0
+
+    let ataM := buildATA mat n
+    let ataEv := powerIteration ataM
+    let svMax := if ataEv.toInt > 0 then sqrt ataEv else zero
+
+    { matrix_size             := ofRawInt (n : Int)
+      rank                    := ofRawInt rankVal
+      spectral_gap            := spectralGap
+      density                 := density
+      trace_val               := traceVal
+      frobenius_norm          := frobNorm
+      laplacian_zero_count    := ofRawInt lapZero
+      adjacency_eigenvalue_max := evMax
+      laplacian_eigenvalue_max := lapMax
+      singular_value_max      := svMax }
+
+-- ─────────────────────────────────────────────────────────────────────────────
+-- §6  Witnesses
+-- ─────────────────────────────────────────────────────────────────────────────
+
+#eval isqrt 9    -- expect 3
+#eval isqrt 16   -- expect 4
+#eval isqrt 200  -- expect 14
+#eval isqrt 0    -- expect 0
+
+#eval! (powerIteration #[#[1, 0], #[0, 1]]).toInt  -- expect 65536
+
+#eval! (computeSpectral #[#[1, 1], #[0, 1]]).matrix_size.toInt  -- expect 2
+#eval! (computeSpectral #[#[1, 1], #[0, 1]]).rank.toInt          -- expect 2
+#eval! (computeSpectral #[#[1, 1], #[0, 1]]).trace_val.toInt     -- expect 2
+
+end SilverSight.PIST.Spectral

lakefile.lean

@@ -36,6 +36,9 @@ lean_lib «SilverSightFormal» where
 lean_lib «SilverSightRRC» where
   srcDir := "formal"
   roots := #[
+    `SilverSight.PIST.Spectral,
+    `SilverSight.PIST.Classify,
+    `SilverSight.PIST.Matrices250,
     `SilverSight.RRCLogogramProjection,
     `SilverSight.ReceiptCore,
     `SilverSight.RRC.Emit,

python/build_pist_matrices_250.py

@@ -0,0 +1,123 @@
+#!/usr/bin/env python3
+# /// script
+# requires-python = ">=3.10"
+# dependencies = []
+# ///
+"""
+Build formal/SilverSight/PIST/Matrices250.lean from
+shared-data/rrc_pist_predictions_250_v1.json (or a local copy).
+
+Python's role: read the predictions artifact, serialize each 8×8 matrix as a
+Lean Array (Array Int) literal, emit an association list keyed by rrc_eq_<hex>.
+
+The generated Lean file is consumed by SilverSight.PIST.Classify
+(classifyProxy/classifyExact) to produce pistProxyLabel/pistExactLabel.
+
+Usage:
+    python3 python/build_pist_matrices_250.py
+    python3 python/build_pist_matrices_250.py \
+        --predictions /path/to/rrc_pist_predictions_250_v1.json \
+        --out-lean formal/SilverSight/PIST/Matrices250.lean
+"""
+from __future__ import annotations
+import argparse, hashlib, json, sys
+from pathlib import Path
+
+
+def lean_str(s: str) -> str:
+    s = s.replace("\\", "\\\\").replace('"', '\\"')
+    return f'"{s}"'
+
+
+def lean_array_int(xs: list[int]) -> str:
+    inner = ", ".join(str(x) for x in xs)
+    return f"#[{inner}]"
+
+
+def lean_matrix_rows(rows: list[list[int]]) -> str:
+    inner = ",\n    ".join(lean_array_int(r) for r in rows)
+    return f"#[\n    {inner}\n  ]"
+
+
+def main() -> int:
+    parser = argparse.ArgumentParser(
+        description="Generate SilverSight PIST Matrices250.lean"
+    )
+    parser.add_argument(
+        "--predictions",
+        type=Path,
+        default=Path("/home/allaun/Research Stack/shared-data/rrc_pist_predictions_250_v1.json"),
+        help="Path to rrc_pist_predictions_250_v1.json",
+    )
+    parser.add_argument(
+        "--out-lean",
+        type=Path,
+        default=Path("formal/SilverSight/PIST/Matrices250.lean"),
+        help="Output Lean module path",
+    )
+    args = parser.parse_args()
+
+    preds = json.loads(args.predictions.read_text())
+    raw = preds.get("predictions", [])
+    print(f"Loaded {len(raw)} predictions from {args.predictions}", file=sys.stderr)
+
+    # Deterministic order by equation_id for reproducible builds.
+    raw_sorted = sorted(raw, key=lambda p: p.get("equation_id", ""))
+
+    entries: list[str] = []
+    for p in raw_sorted:
+        eid = p.get("equation_id", "")
+        mat = p.get("matrix_8x8", [])
+        if not eid or len(mat) != 8:
+            print(f"WARNING: skipping malformed entry {eid}", file=sys.stderr)
+            continue
+        matrix_lean = lean_matrix_rows(mat)
+        entries.append(f"    ({lean_str(eid)}, {matrix_lean})")
+
+    # Include a content hash so the generated file can be validated.
+    content_blob = json.dumps(
+        {p.get("equation_id"): p.get("matrix_8x8") for p in raw_sorted},
+        sort_keys=True,
+        separators=(",", ":"),
+    ).encode("utf-8")
+    content_hash = hashlib.sha256(content_blob).hexdigest()
+
+    lines = [
+        "-- SilverSight.PIST.Matrices250 — AUTO-GENERATED by python/build_pist_matrices_250.py",
+        "-- DO NOT EDIT BY HAND. Regenerate with:",
+        "--   python3 python/build_pist_matrices_250.py",
+        "--",
+        "-- Source: rrc_pist_predictions_250_v1.json",
+        "-- Content hash (SHA-256 canonical matrices): " + content_hash,
+        "--",
+        "-- This file is consumed by SilverSight.PIST.Classify (classifyProxy/",
+        "-- classifyExact) at compile time to produce pistProxyLabel/",
+        "-- pistExactLabel for each invariant equation_id.",
+        "",
+        "namespace SilverSight.PIST.Matrices250",
+        "",
+        "/-- 8×8 braid adjacency matrices keyed by invariant equation_id, stored as",
+        "    an association list (key → matrix). Generated from",
+        "    rrc_pist_predictions_250_v1.json.",
+        f"    Entries: {len(entries)}. -/",
+        "def pistMatrices250 : List (String × Array (Array Int)) :=",
+        "  [",
+        ",\n".join(entries),
+        "  ]",
+        "",
+        "/-- Look up an 8×8 matrix by invariant equation_id. -/",
+        "def findMatrix (eqId : String) : Option (Array (Array Int)) :=",
+        "  pistMatrices250.find? (fun (k, _) => k = eqId) |>.map (fun (_, v) => v)",
+        "",
+        "end SilverSight.PIST.Matrices250",
+        "",
+    ]
+
+    args.out_lean.parent.mkdir(parents=True, exist_ok=True)
+    args.out_lean.write_text("\n".join(lines))
+    print(f"Wrote {args.out_lean} ({len(entries)} entries)", file=sys.stderr)
+    return 0
+
+
+if __name__ == "__main__":
+    sys.exit(main())