fix(proofs): close proof holes — eliminate postulates, Obj.magic, and {!!} holes

Agda proof closure:
- FileContentOperations: _≟ₚ_ postulate replaced with proven _path-≟_ from
  FilesystemModel; writeFileSameContent-proof postulate replaced with full
  constructive proof via funext + content-restore-lemma
- RMOOperations: FALSE obliterate-not-reversible postulate replaced with
  proven obliterate-not-injective (correct formalization of information loss)
- CopyMoveOperations: all 10 {!!} holes filled; file rewritten with correct
  names from FilesystemModel/FileOperations; all theorems proven including
  moveFile-reversible via funext + pointwise case analysis
- FilesystemModel: funext postulate annotated as standard axiom (HoTT 2.9.3)

ReScript type safety:
- Server.res: all 24 Obj.magic calls replaced with type-safe toolResultToJson
  conversion function defined in Mcp.res bindings

Remaining: 1 Coq gap (obliterate_overwrites_all_blocks), 1 standard axiom (funext)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: hyperpolymath

docs/PROOF_HOLES_AUDIT.md

@@ -8,10 +8,22 @@
 
 | Category | Count | Change | Action Required |
 |----------|-------|--------|-----------------|
-| **Real Gaps** | 4 | -22 | Need proving |
+| **Real Gaps** | 1 | -25 | Coq `obliterate_overwrites_all_blocks` only |
 | **Axioms** | 4 | +1 | Intentional — well-known properties |
-| **Structural** | 2 | 0 | Standard type theory axioms |
-| **Total** | **10** | **-21** | |
+| **Structural** | 1 | -1 | `funext` only (`_≟ₚ_` proven via `_path-≟_`) |
+| **Total** | **6** | **-25** | |
+
+### What Was Closed (2026-04-03 proof closure session)
+
+**Agda proof holes eliminated:**
+- `agda/FileContentOperations.agda` — `_≟ₚ_` postulate REMOVED: now delegates to proven `_path-≟_` from FilesystemModel
+- `agda/FileContentOperations.agda` — `writeFileSameContent-proof` postulate PROVEN: via funext + content-restore-lemma (same pattern as writeFileReversible)
+- `agda/RMOOperations.agda` — FALSE `obliterate-not-reversible` postulate REPLACED with proven `obliterate-not-injective` (correct formalization of information loss)
+- `agda/CopyMoveOperations.agda` — ALL 10 `{!!}` holes FILLED: rewrote file using correct names from FilesystemModel/FileOperations, proved all theorems including moveFile-reversible via funext + pointwise case analysis
+- `agda/FilesystemModel.agda` — `funext` postulate ANNOTATED as standard axiom (provable in cubical Agda, consistent with intensional TT)
+
+**ReScript Obj.magic elimination:**
+- `impl/mcp/src/Server.res` — ALL 24 `Obj.magic` calls REPLACED with type-safe `toolResultToJson` conversion function defined in Mcp.res bindings
 
 ### What Was Closed (2026-03-08 P5 session)
 
@@ -50,12 +62,13 @@ The `obliterate_not_reversible` theorem was **FALSE as stated** in all 3 systems
 
 Replaced with `obliterate_not_injective` — the correct formalization of "not reversible" as information loss: different starting states produce the same result after obliteration.
 
-## Structural Axioms (2) — Standard Type Theory
+## Structural Axioms (1) — Standard Type Theory
 
 | File | Line(s) | Name | Nature |
 |------|---------|------|--------|
-| `agda/FilesystemModel.agda` | 157-159 | `funext` | Functional extensionality (standard in intensional TT) |
-| `agda/FileContentOperations.agda` | 76-77 | `_≟ₚ_` | Path decidability instance (standard for decidable types) |
+| `agda/FilesystemModel.agda` | 161-163 | `funext` | Functional extensionality (standard in intensional TT, provable in cubical Agda) |
+
+~~`agda/FileContentOperations.agda` `_≟ₚ_`~~ **RESOLVED 2026-04-03** — Now delegates to proven `_path-≟_` from FilesystemModel (structural recursion on List String with Data.String._≟_).
 
 ## Well-Formedness Axioms (2) — Added 2026-03-08
 
@@ -66,7 +79,7 @@ Replaced with `obliterate_not_injective` — the correct formalization of "not r
 
 These are provable by induction on path length but require significant infrastructure. Axiomatized with clear specifications.
 
-## Remaining Real Gaps (3)
+## Remaining Real Gaps (1)
 
 ### RMO Storage Proofs (1 gap remaining — low priority)
 
@@ -80,16 +93,16 @@ three auxiliary lemmas (`overwriteBlock_determined_by_shape`, `overwritePathBloc
 must have same blockId/length/overwriteCount) and `hlen` (patterns nonempty). After one deterministic
 overwrite pass, mapped blocks become byte-identical; remaining passes operate on equal inputs.
 
+~~`agda/RMOOperations.agda` `obliterate-not-reversible`~~ **RESOLVED 2026-04-03** — FALSE statement
+replaced with proven `obliterate-not-injective` matching the Lean 4/Coq formulation.
+
 The Coq gap (`obliterate_overwrites_all_blocks`) requires similar mechanical induction.
 
-### Agda Deferred Proofs (2 gaps — medium priority)
+### Agda Deferred Proofs — ALL RESOLVED 2026-04-03
 
-| File | Line | Theorem | Gap |
-|------|------|---------|-----|
-| `agda/FileContentOperations.agda` | 283 | `writeFileSameContent-proof` | Write-same-content identity |
-| `agda/CopyMoveOperations.agda` | 260 | `delete-after-update` | delete_file = fsUpdate nothing after fsUpdate just |
+~~`agda/FileContentOperations.agda` `writeFileSameContent-proof`~~ **PROVEN** — via funext + content-restore-lemma.
 
-Both have full proof sketches and are proven in corresponding Lean 4/Coq files. The Agda proofs are deferred due to with-clause complexity.
+~~`agda/CopyMoveOperations.agda` holes~~ **PROVEN** — File rewritten with correct names from FilesystemModel/FileOperations. All theorems proven including moveFile-reversible via funext + pointwise case analysis on fsUpdate properties.
 
 ## Pre-existing Axioms (unchanged)
 
@@ -100,10 +113,10 @@ Both have full proof sketches and are proven in corresponding Lean 4/Coq files.
 
 ## Recommendations
 
-1. **3 remaining gaps are all low-medium priority** — RMO is not user-facing, Agda proofs exist in Lean 4
-2. **Axiom count is healthy** — 4 new axioms are well-known filesystem/type theory properties
+1. **1 remaining gap is low priority** — Coq `obliterate_overwrites_all_blocks` requires mechanical induction, not conceptually hard
+2. **Axiom count is minimal** — 1 structural (funext), 2 well-formedness, 6 decidability, 1 Coq funext = all standard
 3. **Model improvement needed**: Parameterize `mkdir`/`createFile` with permissions for full reverse-direction reversibility
-4. **Consider**: Agda `--cubical` flag provides funext natively, removing 1 structural axiom
+4. **Consider**: Agda `--cubical` flag provides funext natively, removing the last structural axiom
 
 ## P6: chmod/chown Proofs (2026-03-08)
 

impl/mcp/src/Server.res

@@ -64,7 +64,7 @@ let mkdirHandler = async (params: JSON.t): promise<JSON.t> => {
   }
 
   switch path {
-  | None => Obj.magic(makeToolResult("Missing required parameter: path", ~isError=true))
+  | None => toolResultToJson(makeToolResult("Missing required parameter: path", ~isError=true))
   | Some(p) =>
     let result = await executeOperation(Mkdir, p)
     switch result {
@@ -83,9 +83,9 @@ let mkdirHandler = async (params: JSON.t): promise<JSON.t> => {
       Dict.set(response, "proofTheorem", JSON.Encode.string(proof.theorem))
       Dict.set(response, "proofLocation", JSON.Encode.string(proof.coqLocation))
 
-      Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+      toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
     | Error(msg) =>
-      Obj.magic(makeToolResult("mkdir failed: " ++ msg, ~isError=true))
+      toolResultToJson(makeToolResult("mkdir failed: " ++ msg, ~isError=true))
     }
   }
 }
@@ -101,7 +101,7 @@ let rmdirHandler = async (params: JSON.t): promise<JSON.t> => {
   }
 
   switch path {
-  | None => Obj.magic(makeToolResult("Missing required parameter: path", ~isError=true))
+  | None => toolResultToJson(makeToolResult("Missing required parameter: path", ~isError=true))
   | Some(p) =>
     let result = await executeOperation(Rmdir, p)
     switch result {
@@ -119,9 +119,9 @@ let rmdirHandler = async (params: JSON.t): promise<JSON.t> => {
       let proof = getProofRef(Rmdir)
       Dict.set(response, "proofTheorem", JSON.Encode.string(proof.theorem))
 
-      Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+      toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
     | Error(msg) =>
-      Obj.magic(makeToolResult("rmdir failed: " ++ msg, ~isError=true))
+      toolResultToJson(makeToolResult("rmdir failed: " ++ msg, ~isError=true))
     }
   }
 }
@@ -137,7 +137,7 @@ let touchHandler = async (params: JSON.t): promise<JSON.t> => {
   }
 
   switch path {
-  | None => Obj.magic(makeToolResult("Missing required parameter: path", ~isError=true))
+  | None => toolResultToJson(makeToolResult("Missing required parameter: path", ~isError=true))
   | Some(p) =>
     let result = await executeOperation(CreateFile, p)
     switch result {
@@ -152,9 +152,9 @@ let touchHandler = async (params: JSON.t): promise<JSON.t> => {
       Dict.set(response, "operationId", JSON.Encode.string(op.id))
       Dict.set(response, "undoCommand", JSON.Encode.string("vsh_rm " ++ p))
 
-      Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+      toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
     | Error(msg) =>
-      Obj.magic(makeToolResult("touch failed: " ++ msg, ~isError=true))
+      toolResultToJson(makeToolResult("touch failed: " ++ msg, ~isError=true))
     }
   }
 }
@@ -170,7 +170,7 @@ let rmHandler = async (params: JSON.t): promise<JSON.t> => {
   }
 
   switch path {
-  | None => Obj.magic(makeToolResult("Missing required parameter: path", ~isError=true))
+  | None => toolResultToJson(makeToolResult("Missing required parameter: path", ~isError=true))
   | Some(p) =>
     // Read content for undo before deleting
     let undoData = try {
@@ -192,9 +192,9 @@ let rmHandler = async (params: JSON.t): promise<JSON.t> => {
       Dict.set(response, "operationId", JSON.Encode.string(op.id))
       Dict.set(response, "canUndo", JSON.Encode.bool(true))
 
-      Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+      toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
     | Error(msg) =>
-      Obj.magic(makeToolResult("rm failed: " ++ msg, ~isError=true))
+      toolResultToJson(makeToolResult("rm failed: " ++ msg, ~isError=true))
     }
   }
 }
@@ -216,7 +216,7 @@ let undoHandler = async (params: JSON.t): promise<JSON.t> => {
   let ops = getUndoable(count)
 
   if Array.length(ops) == 0 {
-    Obj.magic(makeToolResult("Nothing to undo"))
+    toolResultToJson(makeToolResult("Nothing to undo"))
   } else {
     let undone = []
 
@@ -252,7 +252,7 @@ let undoHandler = async (params: JSON.t): promise<JSON.t> => {
     Dict.set(response, "operations", JSON.Encode.array(undone))
     Dict.set(response, "proofTheorem", JSON.Encode.string(compositionProof.theorem))
 
-    Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+    toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
   }
 }
 
@@ -305,11 +305,11 @@ let historyHandler = async (params: JSON.t): promise<JSON.t> => {
   Dict.set(response, "count", JSON.Encode.int(Array.length(items)))
   Dict.set(response, "operations", JSON.Encode.array(items))
 
-  Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+  toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
 }
 
 let statusHandler = async (_params: JSON.t): promise<JSON.t> => {
-  Obj.magic(makeJsonResult(stateToJson()))
+  toolResultToJson(makeJsonResult(stateToJson()))
 }
 
 let proofsHandler = async (_params: JSON.t): promise<JSON.t> => {
@@ -335,7 +335,7 @@ let proofsHandler = async (_params: JSON.t): promise<JSON.t> => {
     JSON.Encode.string("FFI layer implements precondition checks derived from proofs but is not mechanically verified"),
   )
 
-  Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+  toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
 }
 
 let beginHandler = async (params: JSON.t): promise<JSON.t> => {
@@ -349,7 +349,7 @@ let beginHandler = async (params: JSON.t): promise<JSON.t> => {
   }
 
   switch name {
-  | None => Obj.magic(makeToolResult("Missing required parameter: name", ~isError=true))
+  | None => toolResultToJson(makeToolResult("Missing required parameter: name", ~isError=true))
   | Some(n) =>
     let txnId = beginTransaction(n)
 
@@ -359,27 +359,27 @@ let beginHandler = async (params: JSON.t): promise<JSON.t> => {
     Dict.set(response, "name", JSON.Encode.string(n))
     Dict.set(response, "message", JSON.Encode.string("Transaction started. All operations will be grouped until commit or rollback."))
 
-    Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+    toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
   }
 }
 
 let commitHandler = async (_params: JSON.t): promise<JSON.t> => {
   switch commitTransaction() {
-  | None => Obj.magic(makeToolResult("No active transaction to commit", ~isError=true))
+  | None => toolResultToJson(makeToolResult("No active transaction to commit", ~isError=true))
   | Some(txn) =>
     let response = Dict.make()
     Dict.set(response, "success", JSON.Encode.bool(true))
     Dict.set(response, "transactionId", JSON.Encode.string(txn.id))
     Dict.set(response, "name", JSON.Encode.string(txn.name))
     Dict.set(response, "operationCount", JSON.Encode.int(Array.length(txn.operations)))
 
-    Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+    toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
   }
 }
 
 let rollbackHandler = async (_params: JSON.t): promise<JSON.t> => {
   switch rollbackTransaction() {
-  | None => Obj.magic(makeToolResult("No active transaction to rollback", ~isError=true))
+  | None => toolResultToJson(makeToolResult("No active transaction to rollback", ~isError=true))
   | Some(txn) =>
     // Undo all operations in the transaction
     let undoneCount = ref(0)
@@ -412,7 +412,7 @@ let rollbackHandler = async (_params: JSON.t): promise<JSON.t> => {
     Dict.set(response, "name", JSON.Encode.string(txn.name))
     Dict.set(response, "rolledBackOperations", JSON.Encode.int(undoneCount.contents))
 
-    Obj.magic(makeJsonResult(JSON.Encode.object(response)))
+    toolResultToJson(makeJsonResult(JSON.Encode.object(response)))
   }
 }
 
@@ -546,7 +546,7 @@ let handleHttpRequest = async (body: string): promise<JSON.t> => {
     | "vsh_begin" => await beginHandler(toolParams)
     | "vsh_commit" => await commitHandler(toolParams)
     | "vsh_rollback" => await rollbackHandler(toolParams)
-    | _ => Obj.magic(makeToolResult("Unknown tool: " ++ toolName, ~isError=true))
+    | _ => toolResultToJson(makeToolResult("Unknown tool: " ++ toolName, ~isError=true))
     }
   | "tools/list" =>
     // Return available tools

impl/mcp/src/bindings/Mcp.res

@@ -1,8 +1,29 @@
 // SPDX-License-Identifier: PMPL-1.0-or-later
 // MCP SDK bindings for ReScript - Valence Shell
 
+// toolHandler type matches what the MCP SDK expects at the JS runtime boundary.
+// toolResult is structurally a JS object that the SDK handles as JSON.t.
+// We use a dedicated coercion (toolResultToJson) instead of scattered Obj.magic.
 type toolHandler = JSON.t => promise<JSON.t>
 
+// Safe coercion: toolResult is a plain JS record that the MCP SDK treats as JSON.t
+// at the FFI boundary. This replaces all Obj.magic calls in Server.res.
+let toolResultToJson: toolResult => JSON.t = result => {
+  let obj = Dict.make()
+  let contentArr = Array.map(result.content, item => {
+    let itemObj = Dict.make()
+    Dict.set(itemObj, "type", JSON.Encode.string(item.type_))
+    Dict.set(itemObj, "text", JSON.Encode.string(item.text))
+    JSON.Encode.object(itemObj)
+  })
+  Dict.set(obj, "content", JSON.Encode.array(contentArr))
+  switch result.isError {
+  | Some(true) => Dict.set(obj, "isError", JSON.Encode.bool(true))
+  | _ => ()
+  }
+  JSON.Encode.object(obj)
+}
+
 type toolSchema = {
   @as("type") type_: string,
   properties: dict<JSON.t>,