flow: induce search-open-act-return and row-varying loops, each row checked on its own record

CAPABILITIES.md

@@ -166,6 +166,7 @@ improvising or retrying when something is off.
 | Learn one program with branches from two or more recordings, or say which recordings are missing | Released | Synthetic | `openadapt-flow induce`, `disambiguate`; [CAPABILITIES.md (flow)](packages/flow/docs/CAPABILITIES.md) |
 | Learn a guarded branch from several halts fixed the same way | Released | Synthetic | `openadapt-flow teach-branch`, `learning/branch_teach.py` |
 | Run a program over a worklist | Released | Real app | `openadapt-flow for-each` |
+| Learn a worklist loop from recordings that search a record, open it, work it and go back to the list, even when the last row skips the return or rows differ (a field some rows lack, a write some rows get behind a screen check a person accepts). Each pass selects the row's own record by its values, verifies it, and checks that row's write. Certified and governed runs refuse it until qualification covers it | On main ([#1435](https://github.com/OpenAdaptAI/OpenAdapt/pull/1435)) | Synthetic (held-out rows run through the interpreter against an in-memory app) | `openadapt-flow induce`; `Step.target_param` |
 | Typed business decisions inside a run | Released | Synthetic | `business_decision` states, `openadapt-flow business-decisions` |
 | Watch many real runs in the background and mine candidate branches (shadow mode) | On main ([#1212](https://github.com/OpenAdaptAI/OpenAdapt/pull/1212)) | Synthetic | [SHADOW_MINING.md](packages/capture/docs/SHADOW_MINING.md), [LEARN_FROM_MANY_RUNS.md](packages/flow/docs/LEARN_FROM_MANY_RUNS.md) |
 | Fill a workflow's inputs from a referral PDF, fax image or email | Released | Synthetic | `openadapt-flow intake`, [INTAKE.md](packages/flow/docs/INTAKE.md) |

packages/flow/openadapt_flow/compiler/compile.py

@@ -1923,6 +1923,7 @@ def _compile_recording(
     pixel_verify_enabled: bool = False,
     bind_effect_params: bool = False,
     drop_redundant_keys: bool = False,
+    phi_free_identity: bool = True,
 ) -> Workflow:
     """Compile a recording directory into a workflow bundle.
 
@@ -3471,8 +3472,11 @@ def cached_lines(i: int, suffix: str, png: bytes) -> list[OcrLine]:
     # (openadapt_flow.runtime.identity_template). Runs LAST so param-hygiene
     # lint and optional model annotation still see the plaintext. Backward
     # compatible: bundles compiled before this carry the plaintext fields and
-    # replay unchanged.
-    _phi_free_identity(workflow)
+    # replay unchanged. Multi-trace induction compiles with this off and
+    # hashes the bands itself once the loop's row columns are known
+    # (compiler.induction.phi_free_program_identity).
+    if phi_free_identity:
+        _phi_free_identity(workflow)
 
     # PHI governance manifest (audit REM-1): classify the bundle so an operator
     # inventory and the pre-commit/CI guard can act on it.