feat(pist): remove dead PISTMachine root; add Trace tactic module

lakefile.toml (PIST lib roots):
- Remove "PISTMachine" — PISTMachine.lean does not exist; dead root
  would cause lake build PIST to fail with "unknown module" error
- "Trace" was already added in the prior dirty change; committed here
  paired with the file it requires

2-Search-Space/PIST/Trace.lean (new):
- Lean 4 tactic `trace_state_json "tag"` for Tier 2 flexure recording
- Emits structured goal-state JSON (target, hypotheses, goal_count)
  prefixed with @@PIST_TRACE_JSON@@ sentinel to logInfo stdout
- Python trace bridge parses the sentinel to capture mid-proof state
- Namespace: PIST.Trace; no sorry, no float, no external deps beyond Lean

Generated with Devin (https://cli.devin.ai/docs)

Co-Authored-By: Devin <158243242+devin-ai-integration[bot]@users.noreply.github.com>

0-Core-Formalism/lean/Semantics/lakefile.toml

@@ -19,7 +19,7 @@ name = "Semantics"
 [[lean_lib]]
 name = "PIST"
 srcDir = "../../../2-Search-Space/PIST"
-roots = ["PIST", "PistBridge", "PistSimulation", "PISTMachine", "TorsionalPIST", "HybridTSMPISTTorus"]
+roots = ["PIST", "PistBridge", "PistSimulation", "TorsionalPIST", "HybridTSMPISTTorus", "Trace"]
 
 [[lean_lib]]
 name = "FAMM"

2-Search-Space/PIST/Trace.lean

@@ -0,0 +1,68 @@
+import Lean
+
+open Lean Elab Tactic Meta
+
+set_option pp.pretty true
+
+/-!
+# PIST Trace — goal-state snapshotter for Tier 2 flexure recording.
+
+Provides a tactic `trace_state_json "tag"` that emits structured goal-state
+snapshots to `logInfo` with a `@@PIST_TRACE_JSON@@` sentinel that the Python
+trace bridge can parse from stdout.
+
+Usage:
+```lean
+import PIST.Trace
+
+theorem t (n : Nat) : n + 0 = n := by
+  trace_state_json "step_0_before"
+  simp
+  trace_state_json "step_0_after"
+```
+-/
+
+namespace PIST.Trace
+
+private def goalToJson (g : MVarId) : MetaM Json := do
+  let decl ← g.getDecl
+  let target ← instantiateMVars decl.type
+  let targetFmt ← ppExpr target
+
+  let mut hyps : Array Json := #[]
+  for localDecl in decl.lctx do
+    if !localDecl.isImplementationDetail then
+      let ty ← instantiateMVars localDecl.type
+      let tyFmt ← ppExpr ty
+      hyps := hyps.push <| Json.mkObj [
+        ("name", Json.str localDecl.userName.toString),
+        ("type", Json.str tyFmt.pretty)
+      ]
+
+  return Json.mkObj [
+    ("target", Json.str targetFmt.pretty),
+    ("goal_index", Json.num (toNat g.index)),
+    ("hypotheses", Json.arr hyps),
+    ("hypothesis_count", Json.num hyps.size)
+  ]
+
+/-- Emit a structured goal-state snapshot tagged with `tag`.
+
+The output is prefixed with `@@PIST_TRACE_JSON@@` so the Python bridge
+can scrape it from Lean's stdout.
+-/
+elab "trace_state_json" tag:str : tactic => do
+  let goals ← getGoals
+  let goalJsons ← goals.mapM goalToJson
+
+  let payload : Json := Json.mkObj [
+    ("event", Json.str "pist_trace_state"),
+    ("tag", Json.str tag.getString),
+    ("goal_count", Json.num goals.size),
+    ("goals", Json.arr goalJsons)
+  ]
+
+  -- Emit to logInfo so it appears in stdout
+  logInfo m!"@@PIST_TRACE_JSON@@{payload.compress}"
+
+end PIST.Trace