1# Stage 5 robustness checks23Run from the run root. Outputs go to `results/robustness/`; the narrative is `results/robustness.md`.45| Script | Purpose | Output |6|---|---|---|7| `ff_brute.c` (+ `run_ff_brute.sh`) | Independent exhaustive zero-forcing search by first-force normalisation (4·C(2n−4, s−3) sets, counter/worklist closure); no code shared with `code/brute_force.c` | `ff_brute_stdout*.txt`, `ff_brute_time*.txt` |8| `beta_brute.c` (+ `run_beta_brute.sh`) | Exhaustive distribution of \|∂X\| over all p-subsets, n = 13..16 | `beta_brute_stdout.txt` |9| `check_counts.py` | Binomial and Burnside audit of the Stage 4 oracle's recorded counts | `enumeration_counts_check.json` |10| `check_witness_replay.py` | From-scratch replay of all stored witnesses and of the P7 chronology for 12 ≤ n ≤ 300 | `witness_replay.json` |11| `check_boundary_encoding.py` | F(n,p,b) UNSAT at b = β−1 and SAT at b = β against `beta_brute`; comparison with `results/tables/boundary_table.csv` | `boundary_encoding_check.json` |12| `check_deletion_lemma.py` | P9 exhaustive small-set test (D1), negative control (D2), insertion/deletion pipeline on boundary-11 sets (D3) | `deletion_lemma.json` |13| `check_drat_negative_controls.py` | drat-trim must reject a truncated proof, a proof against a satisfiable weakening, and a proof against the wrong CNF; also determines β₁₈(26) | `drat_negative_controls.json` |14| `check_margin.py` | Exact β₁₈(n) for 26 ≤ n ≤ 40 (slack of the certificates) | `margin.json` |15| `attack_local_search.py` | Simulated-annealing attacks: 11-sets that force (A) and 18-sets with boundary ≤ 11 (B), with positive controls; seed 20261030 | `local_search_attacks.json` |16| `collect_robustness_metrics.py` | Collects everything into `summary.json` and `results/metrics.json["robustness"]` | `summary.json` |1718Build: `gcc -O2 -o code/robustness/ff_brute code/robustness/ff_brute.c -lpthread` and likewise for `beta_brute`. The certificate re-check is the Stage 4 script `python3 code/verify_lower_bounds.py 12` (stdout kept in `verify_lower_bounds_rerun_stdout.txt`).19