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diff --git a/research/flossing/directional_lyap_perturb/plots/directional_lyap_perturb_combined.csv b/research/flossing/directional_lyap_perturb/plots/directional_lyap_perturb_combined.csv
new file mode 100644
index 0000000..0491f8c
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+++ b/research/flossing/directional_lyap_perturb/plots/directional_lyap_perturb_combined.csv
@@ -0,0 +1,73 @@
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diff --git a/research/flossing/directional_lyap_perturb/smoke_baseline.meta.json b/research/flossing/directional_lyap_perturb/smoke_baseline.meta.json
new file mode 100644
index 0000000..c7d9104
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/smoke_baseline.meta.json
@@ -0,0 +1,26 @@
+{
+  "args": {
+    "batch_size": 8,
+    "candidates": 4,
+    "ckpt_name": "step_58590",
+    "ckpt_root": "/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_repro",
+    "fd_eps": 0.001,
+    "label": "smoke_baseline",
+    "n_samples": 16,
+    "out_prefix": "research/flossing/directional_lyap_perturb/smoke_baseline",
+    "perturb_afters": "0,8",
+    "seed": 20260607,
+    "sigmas": "0,0.03"
+  },
+  "config_global_batch_size": 768,
+  "data_path": "/home/yurenh2/rrm/data/sudoku-extreme-1k-aug-1000",
+  "n_samples": 16,
+  "perturb_afters": [
+    0,
+    8
+  ],
+  "sigmas": [
+    0.0,
+    0.03
+  ]
+}
+\ No newline at end of file
diff --git a/research/flossing/directional_lyap_perturb/smoke_baseline.summary.csv b/research/flossing/directional_lyap_perturb/smoke_baseline.summary.csv
new file mode 100644
index 0000000..49a997c
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/smoke_baseline.summary.csv
@@ -0,0 +1,5 @@
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diff --git a/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.meta.json b/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.meta.json
new file mode 100644
index 0000000..faeaf65
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.meta.json
@@ -0,0 +1,26 @@
+{
+  "args": {
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+    "candidates": 4,
+    "ckpt_name": "step_58590",
+    "ckpt_root": "/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_repro",
+    "fd_eps": 0.001,
+    "label": "smoke_baseline",
+    "n_samples": 16,
+    "out_prefix": "research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean",
+    "perturb_afters": "0,8",
+    "seed": 20260607,
+    "sigmas": "0,0.03"
+  },
+  "config_global_batch_size": 768,
+  "data_path": "/home/yurenh2/rrm/data/sudoku-extreme-1k-aug-1000",
+  "n_samples": 16,
+  "perturb_afters": [
+    0,
+    8
+  ],
+  "sigmas": [
+    0.0,
+    0.03
+  ]
+}
+\ No newline at end of file
diff --git a/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.summary.csv b/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.summary.csv
new file mode 100644
index 0000000..26ecd07
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/smoke_baseline_fixedclean.summary.csv
@@ -0,0 +1,5 @@
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diff --git a/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.meta.json b/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.meta.json
new file mode 100644
index 0000000..8d623a6
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.meta.json
@@ -0,0 +1,32 @@
+{
+  "args": {
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+    "candidates": 8,
+    "ckpt_name": "step_58590",
+    "ckpt_root": "/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_repro",
+    "fd_eps": 0.001,
+    "label": "trm_baseline_best",
+    "n_samples": 1000,
+    "out_prefix": "research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap",
+    "perturb_afters": "0,4,8,12",
+    "seed": 20260607,
+    "sigmas": "0,0.001,0.003,0.01,0.03,0.1"
+  },
+  "config_global_batch_size": 768,
+  "data_path": "/home/yurenh2/rrm/data/sudoku-extreme-1k-aug-1000",
+  "n_samples": 1000,
+  "perturb_afters": [
+    0,
+    4,
+    8,
+    12
+  ],
+  "sigmas": [
+    0.0,
+    0.001,
+    0.003,
+    0.01,
+    0.03,
+    0.1
+  ]
+}
+\ No newline at end of file
diff --git a/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.summary.csv b/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.summary.csv
new file mode 100644
index 0000000..5e1db0a
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.summary.csv
@@ -0,0 +1,25 @@
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diff --git a/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.meta.json b/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.meta.json
new file mode 100644
index 0000000..ba022ac
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.meta.json
@@ -0,0 +1,32 @@
+{
+  "args": {
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+    "ckpt_name": "step_35805",
+    "ckpt_root": "/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro",
+    "fd_eps": 0.001,
+    "label": "trm_multi4_best",
+    "n_samples": 1000,
+    "out_prefix": "research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap",
+    "perturb_afters": "0,4,8,12",
+    "seed": 20260607,
+    "sigmas": "0,0.001,0.003,0.01,0.03,0.1"
+  },
+  "config_global_batch_size": 768,
+  "data_path": "/home/yurenh2/rrm/data/sudoku-extreme-1k-aug-1000",
+  "n_samples": 1000,
+  "perturb_afters": [
+    0,
+    4,
+    8,
+    12
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+  "sigmas": [
+    0.0,
+    0.001,
+    0.003,
+    0.01,
+    0.03,
+    0.1
+  ]
+}
+\ No newline at end of file
diff --git a/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.summary.csv b/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.summary.csv
new file mode 100644
index 0000000..34bb554
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.summary.csv
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diff --git a/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.meta.json b/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.meta.json
new file mode 100644
index 0000000..9321e41
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.meta.json
@@ -0,0 +1,32 @@
+{
+  "args": {
+    "batch_size": 16,
+    "candidates": 8,
+    "ckpt_name": "step_65100",
+    "ckpt_root": "/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro",
+    "fd_eps": 0.001,
+    "label": "trm_multi4_final",
+    "n_samples": 1000,
+    "out_prefix": "research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap",
+    "perturb_afters": "0,4,8,12",
+    "seed": 20260607,
+    "sigmas": "0,0.001,0.003,0.01,0.03,0.1"
+  },
+  "config_global_batch_size": 768,
+  "data_path": "/home/yurenh2/rrm/data/sudoku-extreme-1k-aug-1000",
+  "n_samples": 1000,
+  "perturb_afters": [
+    0,
+    4,
+    8,
+    12
+  ],
+  "sigmas": [
+    0.0,
+    0.001,
+    0.003,
+    0.01,
+    0.03,
+    0.1
+  ]
+}
+\ No newline at end of file
diff --git a/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.summary.csv b/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.summary.csv
new file mode 100644
index 0000000..9df33ba
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.summary.csv
@@ -0,0 +1,25 @@
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+trm_multi4_final,8,0.01,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8299999833106995,0.8314999938011169,0.9331419467926025,0.8190000057220459,0.843999981880188,-2.597419500350952,1.466092586517334,0.9849397540092468,0.9819276928901672,0.08235294371843338,0.1411764770746231
+trm_multi4_final,8,0.03,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8299999833106995,0.8309999704360962,0.9327530860900879,0.8169999718666077,0.8450000286102295,-2.597419500350952,1.466092586517334,0.9819276928901672,0.9771084189414978,0.0941176488995552,0.15294118225574493
+trm_multi4_final,8,0.1,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8299999833106995,0.8335000276565552,0.9352839589118958,0.8180000185966492,0.8489999771118164,-2.597419500350952,1.466092586517334,0.9855421781539917,0.9819276928901672,0.09117647260427475,0.16470588743686676
+trm_multi4_final,12,0.0,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8339999914169312,0.9340246319770813,0.8339999914169312,0.8339999914169312,-5.133573055267334,2.7817435264587402,1.0,1.0,0.0,0.0
+trm_multi4_final,12,0.001,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8335000276565552,0.9341234564781189,0.8289999961853027,0.8379999995231628,-5.133573055267334,2.7817435264587402,0.9970024228096008,0.9940047860145569,0.012048192322254181,0.024096384644508362
+trm_multi4_final,12,0.003,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8345000147819519,0.9352160692214966,0.8289999961853027,0.8399999737739563,-5.133573055267334,2.7817435264587402,0.9922062158584595,0.9892086386680603,0.04216867312788963,0.0602409653365612
+trm_multi4_final,12,0.01,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8320000171661377,0.9335123300552368,0.824999988079071,0.8389999866485596,-5.133573055267334,2.7817435264587402,0.9892086386680603,0.986810564994812,0.04216867312788963,0.07228915393352509
+trm_multi4_final,12,0.03,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8299999833106995,0.9333456754684448,0.8240000009536743,0.8360000252723694,-5.133573055267334,2.7817435264587402,0.9880095720291138,0.9856114983558655,0.03614457696676254,0.0602409653365612
+trm_multi4_final,12,0.1,1000,8,0.001,/home/yurenh2/rrm/trm/checkpoints/Sudoku-extreme-1k-aug-1000-ACT-torch/pretrain_mlp_t_sudoku_official_gbs768_multi4_loguniform_repro,step_65100,0.8339999914169312,0.8309999704360962,0.9343765377998352,0.824999988079071,0.8370000123977661,-5.133573055267334,2.7817435264587402,0.9898081421852112,0.9880095720291138,0.03313253074884415,0.0602409653365612
diff --git a/research/flossing/directional_lyap_perturb/watch_and_plot.sh b/research/flossing/directional_lyap_perturb/watch_and_plot.sh
new file mode 100644
index 0000000..683d1b8
--- /dev/null
+++ b/research/flossing/directional_lyap_perturb/watch_and_plot.sh
@@ -0,0 +1,32 @@
+#!/usr/bin/env bash
+set -euo pipefail
+
+ROOT=/home/yurenh2/rrm
+PY=/home/yurenh2/miniconda3/envs/rrm/bin/python
+cd "${ROOT}"
+
+PIDS=(
+  research/flossing/directional_lyap_perturb/logs/trm_baseline_best_step58590_n1000_c8_dirlyap.pid
+  research/flossing/directional_lyap_perturb/logs/trm_multi4_best_step35805_n1000_c8_dirlyap.pid
+  research/flossing/directional_lyap_perturb/logs/trm_multi4_final_step65100_n1000_c8_dirlyap.pid
+)
+
+for pf in "${PIDS[@]}"; do
+  pid=$(cat "${pf}")
+  echo "watch ${pf}: ${pid}"
+  while kill -0 "${pid}" 2>/dev/null; do
+    sleep 60
+  done
+  echo "done ${pf}: ${pid}"
+done
+
+"${PY}" research/flossing/plot_directional_lyap_perturb.py \
+  --summaries \
+  research/flossing/directional_lyap_perturb/trm_baseline_best_step58590_n1000_c8_dirlyap.summary.csv \
+  research/flossing/directional_lyap_perturb/trm_multi4_best_step35805_n1000_c8_dirlyap.summary.csv \
+  research/flossing/directional_lyap_perturb/trm_multi4_final_step65100_n1000_c8_dirlyap.summary.csv \
+  --out-dir research/flossing/directional_lyap_perturb/plots \
+  --slice-sigma 0.03
+
+nvidia-smi --query-gpu=index,memory.used,memory.total,utilization.gpu --format=csv,noheader,nounits \
+  > research/flossing/directional_lyap_perturb/plots/final_gpu_status.txt