# collatz_scission palier inference and output directory creation

## Problem

The helper script `applications/collatz/collatz_k_scripts/collatz_scission.py` can produce incorrect certificates in two cases:

- **Incorrect `palier` inference**: when the CSV class column is named generically (e.g. `classe_mod_2^m`) and the covered classes are sparse / small (e.g. values \(<2^8\) while the target modulus is \(2^{13}\)), `palier` was inferred from the maximum class value. This yields a wrong modulus power.
- **Missing output directories**: `run_scission()` writes `out_json_path` without creating parent directories, which can raise `FileNotFoundError` when callers pass a new path under a non-existing folder.

## Root cause

- `infer_palier()` only supported:
  - parsing `2^m` from the class column name, or
  - a fallback heuristic based on the maximum covered residue value.
  This heuristic is not reliable when the class column name does not encode the modulus power.
- `run_scission()` assumed the output directory exists.

## Corrective actions

- **Prefer explicit palier columns**:
  - If the CSV contains a numeric `palier` column, use it.
  - If the CSV contains a numeric `m` / `modulus_power` column (used as exponent in some pipelines), use it.
- **Fallback from filename**: parse `palier2p<m>` from the CSV path when available.
- **Keep legacy fallback**: keep the max-value heuristic as a last resort.
- **Create output directories**: ensure `out_json_path.parent` exists before writing.
- **Do not add spurious residue 0**: skip empty strings instead of coercing to 0 when parsing the class / sister columns.

## Impact

- Certificates generated via `collatz_scission.py` now carry a `palier` that matches the CSV’s intended modulus power when the CSV provides it (or when the filename encodes it).
- Callers can write certificates to new directories without pre-creating them.

## Analysis modalities

- For any certificate JSON, verify:
  - `palier` matches the intended modulus power \(2^m\),
  - `clauses` and `covered` sets do not contain a spurious `0`,
  - directory creation does not fail when writing under a fresh path.

## Deployment

- No environment changes are required.
- The fix is local to:
  - `applications/collatz/collatz_k_scripts/collatz_scission.py`