diff --git a/README.md b/README.md
index 1cafef6..271c5f2 100644
--- a/README.md
+++ b/README.md
@@ -284,4 +284,4 @@ LDSFL-Meander is named after and authored by:
 - Sergio Lopez-Dubon
 - Alessandro Sgarabotto
 - Alessandro Frascati
-- Stefano Lanzoni
+- Stefano Lanzoni\n\n## Documentation\n\n- [Theory-to-code mapping](docs/theory_code_mapping.md)\n- [Validation strategy and known limitations](docs/validation_strategy.md)\n\n
\ No newline at end of file
diff --git a/docs/theory_code_mapping.md b/docs/theory_code_mapping.md
new file mode 100644
index 0000000..e438712
--- /dev/null
+++ b/docs/theory_code_mapping.md
@@ -0,0 +1,162 @@
+# Theory-to-code mapping
+
+This document maps the main LDSFL-Meander modelling concepts to the repository implementation. It is intended to make the code easier to audit, test, and cite as research software.
+
+## Purpose
+
+The repository implements a reduced morphodynamic meander model. The code is organised around a repeatable pipeline:
+
+1. read dimensionless model parameters and an initial centreline;
+2. preprocess the centreline geometry;
+3. evaluate the hydrodynamic/free-flow response;
+4. advance the centreline;
+5. update geometry and morphodynamic parameters;
+6. save geometry, variable history, sinuosity history, and diagnostics.
+
+The mapping below is deliberately implementation-oriented. It does not replace the paper or original derivation; it helps readers find where each model component lives in the code.
+
+## Pipeline map
+
+| Model step | Implementation | Notes |
+|---|---|---|
+| Input parameters | `ldsfl.inputs.read_parameter_table`, `ldsfl.inputs.dimensionless_input_table` | Reads `Input/Parameter.csv` and converts each row into the dimensionless parameters used by the solver. |
+| Initial centreline | `ldsfl.inputs.read_xy`, `ldsfl.profile.preprof_3` | Reads `Input/xy.csv`, computes arclength, resampled coordinates, tangent angle, wavelength, valley length, and initial sinuosity. |
+| Initial curvature | `ldsfl.main.initial_curvature` | Uses the same tangent-angle convention as the geometry update, avoiding a first-step sign flip. |
+| Resistance terms | `ldsfl.resistance.resistance_function_flagbed` | Computes resistance-related coefficients for plane-bed and dune-bed cases. |
+| Flow-field response | `ldsfl.flowfield.parall_u_free` | Main free-boundary flow response used by default runs. Supports NumPy and optional Numba backends. |
+| Periodic flow response | `ldsfl.flowfield_periodic.parall_u_periodic` | Alternative periodic path. Treat as experimental unless specifically validated for the target case. |
+| Centreline migration | `ldsfl.evolution.dxdy2` | Converts flow response into centreline displacement increments with a timestep stability coefficient. |
+| Geometry update | `ldsfl.geometry.geometry4` | Resamples, smooths, detects cutoffs, updates curvature and sinuosity, and writes cutoff geometries. |
+| Parameter update | `ldsfl.evolution.update_parameters` | Updates evolving parameters after geometry changes. |
+| Output writing | `ldsfl.outputs` | Writes geometry snapshots, variable-history CSVs, sinuosity history, and figures. |
+| Stability diagnostics | `ldsfl.main._sinuosity_stability_metrics`, `ldsfl.stability.sinuosity_equivalence_stability` | Moving-window diagnostic is lightweight. Equivalence/HAC diagnostic is explicit because it can be expensive for long histories. |
+| CLI entry point | `run_ldsfl.py` | Provides a command-line interface around `ldsfl.main.run_project`. |
+| GUI entry point | `gui_ldsfl.py` | Interactive interface for running and inspecting simulations. |
+
+## Main runtime call graph
+
+The high-level runtime flow is:
+
+```text
+run_ldsfl.py
+  -> ldsfl.main.run_project()
+      -> ldsfl.main.run_case()
+          -> read inputs
+          -> preprof_3()
+          -> initial_curvature()
+          -> resistance_function_flagbed()
+          -> loop:
+              -> parall_u_free() or parall_u_periodic()
+              -> save_xystcu() / save_variables() at output intervals
+              -> dxdy2()
+              -> geometry4()
+              -> resistance_function_flagbed()
+              -> update_parameters()
+              -> sinuosity diagnostics
+          -> final snapshot and histories
+```
+
+## Boundary-condition status
+
+The default and currently best-supported path is the free-boundary flow solver:
+
+```text
+flow_bc="free"
+```
+
+The periodic path exists for experimentation and comparison:
+
+```text
+flow_bc="periodic"
+```
+
+The periodic path should not be presented as equally validated until it has dedicated regression tests and physical comparison cases. For publication-quality runs, use the free-boundary path unless there is a specific reason and validation record for the periodic path.
+
+## Backend status
+
+The default backend is NumPy:
+
+```text
+backend="numpy"
+```
+
+The optional Numba backend is intended as an acceleration path. It is an optional extra and should be tested against NumPy for the exact solver branch being used.
+
+Current testing distinguishes between:
+
+- default NumPy execution;
+- NumPy serial versus threaded mode accumulation;
+- optional Numba parity where validated;
+- known or suspected backend discrepancies marked as expected failures until investigated.
+
+## Stability diagnostics
+
+Two sinuosity diagnostics are available.
+
+### Lightweight moving-window diagnostic
+
+Implemented in:
+
+```text
+ldsfl.main._sinuosity_stability_metrics
+```
+
+This diagnostic is cheap and suitable for default return values and GUI display.
+
+### Equivalence/HAC diagnostic
+
+Implemented in:
+
+```text
+ldsfl.stability.sinuosity_equivalence_stability
+```
+
+This diagnostic estimates total fitted drift over a post-transient analysis window and checks whether the confidence interval lies within a practical drift tolerance. It is more statistically meaningful, but it is more expensive because it uses a HAC/Newey-West-style covariance calculation.
+
+For that reason, it should be computed only when explicitly needed, for example when:
+
+```text
+stop_on_sinuosity_stability=True
+```
+
+or when the CLI/user explicitly requests it:
+
+```text
+--return-equivalence-stability 1
+```
+
+## Output map
+
+| Output type | Location | Producer |
+|---|---|---|
+| Geometry snapshots | `Output/<case_id>/files/xyu_*.csv` | `ldsfl.outputs.save_xystcu` |
+| Variable history | `Output/<case_id>/files/var_*.csv` | `ldsfl.outputs.save_variables` |
+| Sinuosity history | `Output/<case_id>/files/sinuosity_history_*.csv` | `ldsfl.outputs.save_sinuosity_history` |
+| Planform figures | `Output/<case_id>/figures/` | `ldsfl.outputs.plot_it` |
+| Cutoff files | `Output/<case_id>/files/` | `ldsfl.geometry.save_xy_cut` |
+| Cutoff figures | `Output/<case_id>/figures/` | `ldsfl.geometry.plot_cut` |
+
+## Testing map
+
+| Test topic | Typical files |
+|---|---|
+| CLI parsing and validation | `tests/test_cli_config.py`, CLI-focused tests |
+| Output bookkeeping | `tests/test_variable_history_complete.py` |
+| Initial curvature sign | `tests/test_curvature_sign_consistency.py` |
+| Plot disabling / no-plots behaviour | `tests/test_cutoff_no_plots.py` |
+| Stop criteria and stability | `tests/test_sinuosity_stability_stop.py`, `tests/test_sinuosity_equivalence_performance_guard.py` |
+| Flow-field physics/regression | `tests/test_flowfield_physics_regression.py`, `tests/test_flowfield_backend_guardrails.py` |
+
+## Maintenance notes
+
+When changing the solver, update this document if the change affects:
+
+- model inputs;
+- boundary-condition behaviour;
+- backend behaviour;
+- geometry conventions;
+- timestep/stability logic;
+- output file semantics;
+- validation evidence.
+
+Small refactors that do not change behaviour should still preserve the mapping between the model concepts and the public functions listed here.
diff --git a/docs/validation_strategy.md b/docs/validation_strategy.md
new file mode 100644
index 0000000..5c61291
--- /dev/null
+++ b/docs/validation_strategy.md
@@ -0,0 +1,92 @@
+# Validation strategy and known limitations
+
+This document summarises the current validation strategy for LDSFL-Meander and records known limitations that should be considered when using the model for research or portfolio demonstrations.
+
+## Validation philosophy
+
+The repository uses a layered validation approach:
+
+1. **Unit-level checks** for input parsing, CLI behaviour, and small helper functions.
+2. **Regression tests** for solver-output bookkeeping and numerical conventions.
+3. **Physics-oriented tests** for invariants that should hold independently of a specific benchmark dataset.
+4. **Integration tests** for short reproducible runs.
+5. **Documented expected failures** for paths that are useful to keep visible but are not yet validated.
+
+This is intentionally different from claiming full physical validation for all possible settings. The tests provide guardrails against implementation errors and regressions.
+
+## Current validated behaviours
+
+| Area | Evidence |
+|---|---|
+| CLI case parsing | Tests cover empty cases, invalid case IDs, repeated cases, and ranges. |
+| Initial curvature convention | Test checks that the first curvature calculation matches the geometry update convention. |
+| Variable-history output | Test checks that every solver step is recorded exactly once, including final partial save blocks. |
+| Plot disabling | Test checks that cutoff CSVs can still be written while plotting is disabled. |
+| Stop-on-sinuosity-stability | Test checks that the stability stop can fire before `max_steps`. |
+| Equivalence/HAC performance guard | Test checks that expensive equivalence diagnostics are not computed by default. |
+| Flow-field invariants | Tests check zero-curvature response, linearity in curvature amplitude, and serial/threaded NumPy agreement. |
+
+## Known limitations
+
+### Periodic flow boundary condition
+
+The periodic flow path is present but should be treated as experimental until it has dedicated validation against a trusted reference.
+
+Recommended wording:
+
+```text
+The free-boundary flow solver is the default validated path. The periodic boundary-condition path is retained for experimental comparison and should be validated for the target study before use.
+```
+
+### Optional Numba backend
+
+The Numba backend is optional. It should be used only when installed and when the relevant solver path has been compared against the NumPy backend.
+
+Recommended wording:
+
+```text
+NumPy is the reference backend. Numba is an optional acceleration backend and should be checked against NumPy for the selected solver branch.
+```
+
+### Statistical stability
+
+The moving-window stability diagnostic is lightweight and useful for monitoring. The equivalence/HAC diagnostic is more rigorous but more expensive. It is therefore opt-in unless used for a stopping criterion.
+
+Recommended wording:
+
+```text
+Equivalence-style sinuosity stability is available for publication-style analysis, but it is not computed by default for long runs unless requested.
+```
+
+### Demonstration examples
+
+Short example runs are designed for reproducibility and continuous integration. They are not a substitute for full scientific calibration or site-specific validation.
+
+## Suggested validation roadmap
+
+The following additions would strengthen the repository further:
+
+1. Add one or more external benchmark cases with expected summary outputs.
+2. Add a documented periodic-boundary comparison test if the periodic path is retained.
+3. Add a small analytic transfer-function style test for the free-flow solver if the assumptions can be clearly documented.
+4. Add reproducibility artefacts for a paper figure or reference run.
+5. Add a versioned `docs/validation_matrix.md` table linking each claim in the README to code/tests.
+
+## What to avoid
+
+Avoid mixing unrelated changes into validation PRs. In particular:
+
+- do not combine solver changes with documentation-only changes;
+- do not regenerate large fixture files in the same PR as code refactors;
+- do not enable strict lint gates until the repository is fully lint-clean;
+- do not mark optional accelerated backends as equivalent unless the tested path supports that claim.
+
+## Review checklist
+
+Before merging a validation-related PR, check:
+
+- Does the PR state whether it changes behaviour or only adds tests/docs?
+- Are new tests focused and deterministic?
+- Do tests run without optional dependencies unless explicitly skipped?
+- Does the PR avoid committing generated output files?
+- Does the README avoid overclaiming beyond the available validation evidence?
diff --git a/ldsfl/main.py b/ldsfl/main.py
index 2a0f93b..ced0311 100644
--- a/ldsfl/main.py
+++ b/ldsfl/main.py
@@ -306,7 +306,7 @@ def run_case(
     sinuo_hist: list[float] = [float(sinuo)]
     stability_interval = max(1, int(sinuo_stability_interval))
     use_equivalence_stability = bool(stop_on_sinuosity_stability) or bool(return_equivalence_stability)
-    if use_equivalence_stability:
+    if bool(stop_on_sinuosity_stability):
         stability_info = _combined_sinuosity_stability_metrics(
             step_hist,
             sinuo_hist,
@@ -595,7 +595,7 @@ def run_case(
             steps += 1
             step_hist.append(int(steps))
             sinuo_hist.append(float(sinuo))
-            if use_equivalence_stability and (steps % stability_interval) == 0:
+            if bool(stop_on_sinuosity_stability) and (steps % stability_interval) == 0:
                 stability_info = _combined_sinuosity_stability_metrics(
                     step_hist,
                     sinuo_hist,
@@ -615,7 +615,7 @@ def run_case(
                     window=sinuo_window,
                     rel_tol=sinuo_rel_tol,
                 )
-                if use_equivalence_stability and previous_equivalence is not None:
+                if bool(stop_on_sinuosity_stability) and previous_equivalence is not None:
                     stability_info["equivalence"] = previous_equivalence
 
             jt += 1
diff --git a/tests/test_sinuosity_equivalence_performance_guard.py b/tests/test_sinuosity_equivalence_performance_guard.py
index de071a9..e01aeec 100644
--- a/tests/test_sinuosity_equivalence_performance_guard.py
+++ b/tests/test_sinuosity_equivalence_performance_guard.py
@@ -64,5 +64,5 @@ def fake_equivalence(*args, **kwargs):
         do_plots=False,
     )
 
-    assert calls["n"] >= 1
+    assert calls["n"] == 1
     assert result["sinuosity_stability"]["equivalence"]["stable"] is True