feat: preserve Symbol types in JSON serialization

- Add infos_symbol_keys metadata field to track Symbol values
- Implement path-based Symbol restoration during deserialization
- Update _serialize_infos and _deserialize_infos to handle Symbol tracking
- Fix type conversion issues with JSON3.Array using collect()
- Update test expectations to verify Symbol preservation
- All 1722 tests pass

Closes part of #217

Author: ocots

ext/CTModelsJSON.jl

@@ -22,63 +22,98 @@ _apply_over_grid(::Nothing, grid) = nothing
 """
 Convert Dict{Symbol,Any} to Dict{String,Any} for JSON serialization.
 Only serializes JSON-compatible types (numbers, strings, bools, arrays, dicts).
+Returns a tuple: (serialized_dict, symbol_keys) where symbol_keys tracks which values were Symbols.
 """
-function _serialize_infos(infos::Dict{Symbol,Any})::Dict{String,Any}
+function _serialize_infos(infos::Dict{Symbol,Any})::Tuple{Dict{String,Any},Vector{String}}
     result = Dict{String,Any}()
+    symbol_keys = String[]
     for (k, v) in infos
-        result[string(k)] = _serialize_value(v)
+        key_str = string(k)
+        serialized_value, nested_symbols = _serialize_value(v, key_str)
+        result[key_str] = serialized_value
+        append!(symbol_keys, nested_symbols)
     end
-    return result
+    return (result, symbol_keys)
 end
 
 """
 Serialize a single value to JSON-compatible format.
+Returns a tuple: (serialized_value, symbol_paths) where symbol_paths tracks Symbol locations.
 """
-function _serialize_value(v)
+function _serialize_value(v, path::String="")
     if v isa Number || v isa String || v isa Bool || isnothing(v)
-        return v
+        return (v, String[])
     elseif v isa Symbol
-        return string(v)
+        # Mark this path as containing a Symbol
+        return (string(v), [path])
     elseif v isa AbstractVector
-        return [_serialize_value(x) for x in v]
+        serialized = []
+        all_symbols = String[]
+        for (i, x) in enumerate(v)
+            val, syms = _serialize_value(x, "$(path)[$(i-1)]")
+            push!(serialized, val)
+            append!(all_symbols, syms)
+        end
+        return (serialized, all_symbols)
     elseif v isa AbstractDict
         result = Dict{String,Any}()
+        all_symbols = String[]
         for (dk, dv) in v
-            result[string(dk)] = _serialize_value(dv)
+            key_str = string(dk)
+            new_path = isempty(path) ? key_str : "$(path).$(key_str)"
+            val, syms = _serialize_value(dv, new_path)
+            result[key_str] = val
+            append!(all_symbols, syms)
         end
-        return result
+        return (result, all_symbols)
     else
         # For non-serializable types, convert to string representation
-        return string(v)
+        return (string(v), String[])
     end
 end
 
 """
 Convert Dict{String,Any} back to Dict{Symbol,Any} after JSON deserialization.
+Uses symbol_keys metadata to restore Symbol types where they were originally present.
 """
-function _deserialize_infos(blob)::Dict{Symbol,Any}
+function _deserialize_infos(
+    blob, symbol_keys::Vector{String}=String[]
+)::Dict{Symbol,Any}
     if isnothing(blob) || isempty(blob)
         return Dict{Symbol,Any}()
     end
     result = Dict{Symbol,Any}()
     for (k, v) in blob
-        result[Symbol(k)] = _deserialize_value(v)
+        result[Symbol(k)] = _deserialize_value(v, String(k), symbol_keys)
     end
     return result
 end
 
 """
 Deserialize a single value from JSON format.
+Uses symbol_keys to restore Symbol types at the correct paths.
 """
-function _deserialize_value(v)
-    if v isa Number || v isa String || v isa Bool || isnothing(v)
+function _deserialize_value(v, path::String, symbol_keys::Vector{String})
+    if v isa Number || v isa Bool || isnothing(v)
         return v
+    elseif v isa String
+        # Check if this path should be a Symbol
+        if path in symbol_keys
+            return Symbol(v)
+        else
+            return v
+        end
     elseif v isa AbstractVector
-        return [_deserialize_value(x) for x in v]
+        return [
+            _deserialize_value(x, "$(path)[$(i-1)]", symbol_keys) for
+            (i, x) in enumerate(v)
+        ]
     elseif v isa AbstractDict
         result = Dict{Symbol,Any}()
         for (dk, dv) in v
-            result[Symbol(dk)] = _deserialize_value(dv)
+            key_str = string(dk)
+            new_path = isempty(path) ? key_str : "$(path).$(key_str)"
+            result[Symbol(dk)] = _deserialize_value(dv, new_path, symbol_keys)
         end
         return result
     else
@@ -145,10 +180,13 @@ function CTModels.export_ocp_solution(
         "boundary_constraints_dual" => CTModels.boundary_constraints_dual(sol),       # ctVector or Nothing
         "variable_constraints_lb_dual" => CTModels.variable_constraints_lb_dual(sol),    # ctVector or Nothing
         "variable_constraints_ub_dual" => CTModels.variable_constraints_ub_dual(sol),    # ctVector or Nothing
-        # Additional solver infos (Dict{Symbol,Any} → Dict{String,Any} for JSON)
-        "infos" => _serialize_infos(CTModels.infos(sol)),
     )
 
+    # Serialize infos and get Symbol type metadata
+    infos_serialized, symbol_keys = _serialize_infos(CTModels.infos(sol))
+    blob["infos"] = infos_serialized
+    blob["infos_symbol_keys"] = symbol_keys
+
     open(filename * ".json", "w") do io
         JSON3.pretty(io, blob)
     end
@@ -293,9 +331,11 @@ function CTModels.import_ocp_solution(
         variable_constraints_ub_dual = Vector{Float64}(blob["variable_constraints_ub_dual"])
     end
 
-    # get additional solver infos
+    # get additional solver infos with Symbol type restoration
+    symbol_keys_raw = get(blob, "infos_symbol_keys", String[])
+    symbol_keys = collect(String, symbol_keys_raw)  # Convert JSON3.Array/empty array to Vector{String}
     infos = if haskey(blob, "infos")
-        _deserialize_infos(blob["infos"])
+        _deserialize_infos(blob["infos"], symbol_keys)
     else
         Dict{Symbol,Any}()
     end

reports/2026-01-29_Idempotence/PR_DESCRIPTION.md

@@ -0,0 +1,77 @@
+Add idempotence tests for export/import serialization
+
+## Summary
+
+This PR adds comprehensive idempotence tests for the `export_ocp_solution` and `import_ocp_solution` functions to verify that multiple export-import cycles produce stable results with no progressive information loss.
+
+## Changes
+
+### Test Implementation (~460 lines)
+
+**Helper Functions** (`test/suite/serialization/test_export_import.jl`):
+- `compare_trajectories`: Compares function-based trajectories at time points
+- `compare_infos`: Deep comparison of `Dict{Symbol,Any}` with type awareness
+- `compare_solutions`: Comprehensive Solution object comparison with configurable tolerances
+
+**New Test Cases** (7 total):
+- **JSON** (4 tests): Double/triple cycles with duals, without duals, complex infos
+- **JLD2** (3 tests): Double/triple cycles with duals, without duals
+
+### Documentation
+
+**Analysis**: `reports/2026-01-29_Idempotence/analysis/01_serialization_idempotence_analysis.md`
+- Identified 6 potential information loss points
+- Analyzed existing test coverage
+- Future investigation items (function serialization, deepcopy usage)
+
+**Implementation Plan**: `reports/2026-01-29_Idempotence/reference/01_serialization_idempotence_plan.md`
+- Detailed test strategy and verification plan
+
+**Walkthrough**: `reports/2026-01-29_Idempotence/walkthrough.md`
+- Summary of changes and test results
+- Key findings and recommendations
+
+## Test Results
+
+```
+Test Summary:                               | Pass  Total   Time
+CTModels tests                              | 1721   1721  14.4s
+  suite/serialization/test_export_import.jl | 1721   1721  14.4s
+     Testing CTModels tests passed
+```
+
+✅ All tests pass - No regressions
+
+## Key Findings
+
+### Information Preserved ✅
+- All scalar fields (objective, iterations, status, etc.)
+- Time grid and variable (full precision)
+- All trajectories (state, control, costate)
+- All dual variables
+- Infos dictionary structure and values
+
+### Expected Transformations 🔄
+1. **Functions → Discretization**: Analytical functions become interpolated after JSON export/import
+   - Impact: Minimal (within `atol=1e-8`)
+   - **Idempotent after first cycle** ✅
+
+2. **Symbols → Strings**: Symbols in `infos` become strings after JSON serialization
+   - Example: `:optimal` → `"optimal"`
+   - **Idempotent after first cycle** ✅
+
+### Conclusion
+**No progressive information loss**: `sol₁ ≈ sol₂ ≈ sol₃` after multiple cycles.
+
+## Future Work
+
+The analysis identified areas for future investigation:
+- Bidirectional `ctinterpolate`/`ctdeinterpolate` for lossless function serialization
+- Review of `deepcopy` usage in `build_solution` (rationale unclear)
+- Improved JLD2 handling of anonymous functions
+
+See analysis document for details.
+
+## Related Issue
+
+Closes #217

test/suite/serialization/test_export_import.jl

@@ -851,8 +851,9 @@ function test_export_import()
         Test.@test infos2[:nested][:a] == 1
         Test.@test infos2[:nested][:b] == "test"
         Test.@test infos2[:nested][:c] == [1.0, 2.0, 3.0]
-        # Symbol becomes string after JSON serialization
-        Test.@test infos2[:symbol_value] == "optimal"
+        # Symbol is now preserved with type metadata!
+        Test.@test infos2[:symbol_value] == :optimal
+        Test.@test infos2[:symbol_value] isa Symbol
 
         remove_if_exists("idempotence_json_ci1.json")
         remove_if_exists("idempotence_json_ci2.json")