diff --git a/results/campaign7_publication_merged.jsonl b/results/campaign7_publication_merged.jsonl
index 98e6e12..3dc7db1 100644
--- a/results/campaign7_publication_merged.jsonl
+++ b/results/campaign7_publication_merged.jsonl
@@ -106,7 +106,7 @@
 {"ell": 30, "m": 6, "A_terms": [[3, 0], [0, 2], [0, 4]], "B_terms": [[0, 3], [2, 0], [4, 0]], "C_terms": [[15, 3]], "D_terms": [[18, 0]], "n": 360, "k": 8, "d": 16, "fom": 5.6889, "d_method": "deep_milp", "d_milp": 16, "d_bposd": 20, "milp_exact": false, "timestamp": 1773319306.714203, "bliss_hash": "cfd473a954551ba3", "bliss_group_size": 1, "code_id": "30_6_0283", "verified_at": "2026-03-13T01:51:10.330468+00:00", "d_is_exact": false, "d_over_sqrtn": 0.843, "trust_level": "TRUSTED", "time_s": 1098.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 16, "d_original": 16, "fom_deep": 5.6889, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7201.1}, {"w": 16, "opt": false, "t": 7200.0}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.4}, {"w": 16, "opt": false, "t": 7200.1}], "logicals_optimal": 0, "logicals_incumbent": 16, "logicals_failed": 0, "total_logicals": 16, "deep_milp_time_s": 57603.2, "timeout_per_logical": 7200, "deep_verified_at": "2026-03-14T14:09:34.521034+00:00", "d_is_upper_bound": true, "publication_quality": false, "d_milp_initial": 18}
 {"ell": 15, "m": 6, "A_terms": [[2, 2], [7, 3], [7, 4]], "B_terms": [[0, 0], [2, 5], [9, 4]], "C_terms": [[2, 3], [7, 3]], "D_terms": [[2, 5], [7, 5]], "n": 180, "k": 4, "d": 12, "fom": 3.2, "d_method": "deep_milp", "d_milp": 12, "d_bposd": 18, "milp_exact": false, "timestamp": 1773325843.4859178, "bliss_hash": "41fd3648680cd3b5", "bliss_group_size": 1, "code_id": "15_6_0235", "verified_at": "2026-03-13T00:27:57.903650+00:00", "d_is_exact": false, "d_over_sqrtn": 0.894, "trust_level": "TRUSTED", "time_s": 718.8, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 12, "d_original": 18, "fom_deep": 3.2, "milp_exact_deep": false, "per_logical": [{"w": 18, "opt": false, "t": 14400.2}, {"w": 18, "opt": false, "t": 14400.2}, {"w": 12, "opt": true, "t": 5770.4}, {"w": 12, "opt": true, "t": 4706.9}, {"w": 12, "opt": true, "t": 7569.7}, {"w": 12, "opt": true, "t": 2732.9}, {"w": 12, "opt": true, "t": 7655.4}, {"w": 12, "opt": true, "t": 3606.4}], "logicals_optimal": 6, "logicals_incumbent": 2, "logicals_failed": 0, "total_logicals": 8, "deep_milp_time_s": 22008.1, "timeout_per_logical": 14400, "deep_verified_at": "2026-05-29T17:22:50.200775+00:00", "d_is_upper_bound": true, "publication_quality": false, "d_milp_initial": 26}
 {"ell": 15, "m": 6, "A_terms": [[3, 2], [7, 3], [7, 4]], "B_terms": [[0, 0], [3, 5], [10, 4]], "C_terms": [[3, 3], [7, 3]], "D_terms": [[3, 5], [7, 5]], "n": 180, "k": 4, "d": 16, "fom": 5.6889, "d_method": "deep_milp", "d_milp": 16, "d_bposd": 20, "milp_exact": false, "timestamp": 1773332349.4079905, "bliss_hash": "678383d35374d16d", "bliss_group_size": 1, "code_id": "15_6_0236", "verified_at": "2026-03-13T00:32:37.272705+00:00", "d_is_exact": false, "d_over_sqrtn": 1.193, "trust_level": "TRUSTED", "time_s": 714.5, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 16, "d_original": 18, "fom_deep": 5.6889, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": false, "t": 14400.3}, {"w": 16, "opt": false, "t": 14400.4}, {"w": 16, "opt": false, "t": 14400.4}, {"w": 16, "opt": false, "t": 14400.3}, {"w": 16, "opt": false, "t": 14400.4}, {"w": 16, "opt": false, "t": 14400.3}, {"w": 16, "opt": false, "t": 14400.2}, {"w": 16, "opt": false, "t": 14400.3}], "logicals_optimal": 0, "logicals_incumbent": 8, "logicals_failed": 0, "total_logicals": 8, "deep_milp_time_s": 14400.6, "timeout_per_logical": 14400, "deep_verified_at": "2026-05-29T15:16:02.773790+00:00", "d_is_upper_bound": true, "publication_quality": false, "d_milp_initial": 18}
-{"ell": 12, "m": 6, "A_terms": [[2, 2], [4, 3], [4, 4]], "B_terms": [[0, 0], [1, 5], [11, 4]], "C_terms": [[1, 1], [6, 4]], "D_terms": [[2, 0], [9, 3]], "n": 144, "k": 4, "d": 12, "fom": 4.0, "d_method": "deep_milp", "d_milp": 12, "d_bposd": 16, "milp_exact": false, "timestamp": 1773323406.2488904, "bliss_hash": "7989eece4ce9c3cd", "bliss_group_size": 1, "code_id": "12_6_0199", "verified_at": "2026-03-12T23:49:04.595216+00:00", "d_is_exact": false, "d_over_sqrtn": 1.0, "trust_level": "TRUSTED", "time_s": 662.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 16, "d_is_upper_bound": true, "publication_quality": false, "d_deep_milp": 12, "d_original": 12, "fom_deep": 4.0, "milp_exact_deep": false, "per_logical": [{"w": 12, "opt": true, "t": 1796.3}, {"w": 12, "opt": true, "t": 2041.2}, {"w": 12, "opt": false, "t": 3600.1}, {"w": 12, "opt": false, "t": 3600.0}, {"w": 16, "opt": false, "t": 3600.1}, {"w": 23, "opt": false, "t": 3600.1}, {"w": 12, "opt": true, "t": 2715.3}, {"w": 12, "opt": true, "t": 2233.4}], "logicals_optimal": 4, "logicals_incumbent": 4, "logicals_failed": 0, "total_logicals": 8, "deep_milp_time_s": 19341.9, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T17:29:44.277834+00:00"}
+{"ell": 12, "m": 6, "A_terms": [[2, 2], [4, 3], [4, 4]], "B_terms": [[0, 0], [1, 5], [11, 4]], "C_terms": [[1, 1], [6, 4]], "D_terms": [[2, 0], [9, 3]], "n": 144, "k": 4, "d": 12, "fom": 4.0, "d_method": "qubit_paired_zimmermann", "d_milp": 12, "d_bposd": 16, "milp_exact": false, "timestamp": 1773323406.2488904, "bliss_hash": "7989eece4ce9c3cd", "bliss_group_size": 1, "code_id": "12_6_0199", "verified_at": "2026-03-12T23:49:04.595216+00:00", "d_is_exact": true, "d_over_sqrtn": 1.0, "trust_level": "EXACT", "time_s": 662.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 16, "d_is_upper_bound": false, "publication_quality": false, "d_deep_milp": 12, "d_original": 12, "fom_deep": 4.0, "milp_exact_deep": false, "per_logical": [{"w": 12, "opt": true, "t": 1796.3}, {"w": 12, "opt": true, "t": 2041.2}, {"w": 12, "opt": false, "t": 3600.1}, {"w": 12, "opt": false, "t": 3600.0}, {"w": 16, "opt": false, "t": 3600.1}, {"w": 23, "opt": false, "t": 3600.1}, {"w": 12, "opt": true, "t": 2715.3}, {"w": 12, "opt": true, "t": 2233.4}], "logicals_optimal": 4, "logicals_incumbent": 4, "logicals_failed": 0, "total_logicals": 8, "deep_milp_time_s": 19341.9, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T17:29:44.277834+00:00", "d_exactness_source": {"method": "qubit_paired_zimmermann", "release": "oneq-distance-closures-v1.0.0", "searcher_version": "2.0.0", "schema_version": "2.0.0", "code_input_hash": "658d23d8d1748589af574392032a11b1248e3fc1e0d4a7cf147dd38be0be99e1", "witness_hash": "003c4f4058d6fb1a6da918643e7bc8b9886729ba70efb98f484cfb1086bac103", "candidates_per_replica": 8149473282198, "depth_p": 7, "independent_replicas": 2, "upper_bound_verification": "self-contained witness: commutes with every stabilizer, not in S, weight equals d", "lower_bound_verification": "two independent exhaustive executions; full third-party verification requires re-execution -- no succinct proof object", "lower_bound_is_machine_checkable": false}}
 {"ell": 30, "m": 6, "A_terms": [[26, 1], [9, 4], [22, 4]], "B_terms": [[0, 0], [5, 1], [22, 5]], "C_terms": [[22, 4]], "D_terms": [[9, 5], [26, 2]], "n": 360, "k": 10, "d": 16, "fom": 7.1111, "d_method": "deep_milp", "d_milp": 16, "d_bposd": 26, "milp_exact": false, "timestamp": 1773354164.0917578, "bliss_hash": "30ca834eb3d61ddf", "bliss_group_size": 1, "code_id": "30_6_0284", "verified_at": "2026-03-13T01:56:15.019393+00:00", "d_is_exact": false, "d_over_sqrtn": 0.843, "trust_level": "TRUSTED", "time_s": 1107.4, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 16, "d_original": 16, "fom_deep": 7.1111, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": false, "t": 7200.2}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 24, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.3}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.2}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.1}, {"w": 16, "opt": false, "t": 7200.2}, {"w": 16, "opt": false, "t": 7200.3}, {"w": 16, "opt": false, "t": 7200.2}, {"w": 16, "opt": false, "t": 7200.1}], "logicals_optimal": 0, "logicals_incumbent": 20, "logicals_failed": 0, "total_logicals": 20, "deep_milp_time_s": 50403.1, "timeout_per_logical": 7200, "deep_verified_at": "2026-03-14T12:09:34.478552+00:00", "d_is_upper_bound": true, "publication_quality": false}
 {"ell": 15, "m": 6, "A_terms": [[6, 2], [9, 3], [9, 4]], "B_terms": [[0, 0], [6, 5], [0, 4]], "C_terms": [[6, 3], [9, 3]], "D_terms": [[6, 5], [9, 5]], "n": 180, "k": 12, "d": 8, "fom": 4.2667, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 10, "milp_exact": true, "timestamp": 1773326708.3889477, "bliss_hash": "090d2994e573e42e", "bliss_group_size": 2, "code_id": "15_6_0237", "verified_at": "2026-03-13T00:34:25.657925+00:00", "d_is_exact": true, "d_over_sqrtn": 0.596, "trust_level": "EXACT", "time_s": 103.2, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 10, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 15, "m": 6, "A_terms": [[1, 2], [13, 3], [13, 4]], "B_terms": [[0, 0], [1, 5], [11, 4]], "C_terms": [[2, 0], [5, 4]], "D_terms": [[8, 0], [12, 2]], "n": 180, "k": 6, "d": 14, "fom": 6.5333, "d_method": "deep_milp", "d_milp": 14, "d_bposd": 16, "milp_exact": false, "timestamp": 1773322755.5891073, "bliss_hash": "e4e1975dab7c6d11", "bliss_group_size": 1, "code_id": "15_6_0238", "verified_at": "2026-03-13T00:35:15.899346+00:00", "d_is_exact": false, "d_over_sqrtn": 1.043, "trust_level": "TRUSTED", "time_s": 729.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 14, "d_original": 14, "fom_deep": 6.5333, "milp_exact_deep": false, "per_logical": [{"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.2}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.0}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}, {"w": 14, "opt": false, "t": 7200.1}], "logicals_optimal": 0, "logicals_incumbent": 12, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 21600.6, "timeout_per_logical": 7200, "deep_verified_at": "2026-03-14T03:26:18.211239+00:00", "d_is_upper_bound": true, "publication_quality": false}
@@ -140,7 +140,7 @@
 {"ell": 9, "m": 6, "A_terms": [[1, 2], [4, 3], [4, 4]], "B_terms": [[0, 0], [1, 5], [8, 4]], "C_terms": [[1, 4], [7, 3]], "D_terms": [[2, 3], [8, 2]], "n": 108, "k": 6, "d": 10, "fom": 5.5556, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 10, "milp_exact": true, "timestamp": 1773323680.0230513, "bliss_hash": "0dbbe06c4752feb1", "bliss_group_size": 1, "code_id": "9_6_0138", "verified_at": "2026-03-12T23:14:25.042457+00:00", "d_is_exact": true, "d_over_sqrtn": 0.962, "trust_level": "EXACT", "time_s": 259.0, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 12, "m": 6, "A_terms": [[2, 2], [7, 3], [7, 4]], "B_terms": [[0, 0], [2, 5], [9, 4]], "C_terms": [[2, 3], [7, 3]], "D_terms": [[2, 5], [7, 5]], "n": 144, "k": 8, "d": 10, "fom": 5.5556, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 10, "milp_exact": true, "timestamp": 1773324849.6163902, "bliss_hash": "cdad2cd6ca3e1639", "bliss_group_size": 1, "code_id": "12_6_0200", "verified_at": "2026-03-12T23:49:45.114028+00:00", "d_is_exact": true, "d_over_sqrtn": 0.833, "trust_level": "EXACT", "time_s": 499.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 9, "m": 6, "A_terms": [[8, 1], [3, 1], [7, 4]], "B_terms": [[0, 0], [2, 1], [7, 5]], "C_terms": [[3, 4], [7, 4]], "D_terms": [[3, 5], [8, 2]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 10, "milp_exact": false, "timestamp": 1773339933.8686285, "bliss_hash": "219059336f38b732", "bliss_group_size": 4, "code_id": "phase2_61", "verified_at": "2026-05-28T18:00:00+00:00", "d_is_exact": true, "milp_solved": 10, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 490.9, "publication_quality": true, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": true, "per_logical": [{"w": 12, "opt": true, "t": 1209.3}, {"w": 8, "opt": true, "t": 140.4}, {"w": 8, "opt": true, "t": 173.7}, {"w": 8, "opt": true, "t": 123.9}, {"w": 8, "opt": true, "t": 122.5}, {"w": 8, "opt": true, "t": 95.2}, {"w": 8, "opt": true, "t": 117.8}, {"w": 8, "opt": true, "t": 120.6}, {"w": 8, "opt": true, "t": 129.0}, {"w": 8, "opt": true, "t": 148.7}, {"w": 8, "opt": true, "t": 189.3}, {"w": 8, "opt": true, "t": 122.5}], "logicals_optimal": 12, "logicals_incumbent": 0, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 1634.8, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T12:34:37.199790+00:00"}
-{"ell": 12, "m": 6, "A_terms": [[2, 2], [9, 3], [9, 4]], "B_terms": [[0, 0], [2, 5], [11, 4]], "C_terms": [[2, 3], [9, 3]], "D_terms": [[2, 5], [9, 5]], "n": 144, "k": 8, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 10, "milp_exact": false, "timestamp": 1773332349.407755, "bliss_hash": "a8879ca668587ffa", "bliss_group_size": 1, "code_id": "12_6_0201", "verified_at": "2026-03-12T23:49:50.315491+00:00", "d_is_exact": false, "d_over_sqrtn": 0.667, "trust_level": "TRUSTED", "time_s": 672.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 8, "d_original": 10, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": true, "t": 5738.7}, {"w": 16, "opt": false, "t": 14400.4}, {"w": 8, "opt": true, "t": 133.5}, {"w": 8, "opt": true, "t": 161.8}, {"w": 8, "opt": true, "t": 176.0}, {"w": 8, "opt": true, "t": 189.6}, {"w": 8, "opt": true, "t": 98.1}, {"w": 8, "opt": true, "t": 241.4}, {"w": 8, "opt": true, "t": 188.0}, {"w": 8, "opt": true, "t": 141.5}, {"w": 8, "opt": true, "t": 165.6}, {"w": 8, "opt": true, "t": 164.1}, {"w": 8, "opt": true, "t": 226.1}, {"w": 8, "opt": true, "t": 156.1}, {"w": 12, "opt": true, "t": 2320.7}, {"w": 12, "opt": true, "t": 1434.8}], "logicals_optimal": 15, "logicals_incumbent": 1, "logicals_failed": 0, "total_logicals": 16, "deep_milp_time_s": 14400.4, "timeout_per_logical": 14400, "deep_verified_at": "2026-05-29T15:16:02.575972+00:00", "d_is_upper_bound": true, "publication_quality": false, "d_milp_initial": 18}
+{"ell": 12, "m": 6, "A_terms": [[2, 2], [9, 3], [9, 4]], "B_terms": [[0, 0], [2, 5], [11, 4]], "C_terms": [[2, 3], [9, 3]], "D_terms": [[2, 5], [9, 5]], "n": 144, "k": 8, "d": 8, "fom": 3.5556, "d_method": "qubit_paired_zimmermann", "d_milp": 8, "d_bposd": 10, "milp_exact": false, "timestamp": 1773332349.407755, "bliss_hash": "a8879ca668587ffa", "bliss_group_size": 1, "code_id": "12_6_0201", "verified_at": "2026-03-12T23:49:50.315491+00:00", "d_is_exact": true, "d_over_sqrtn": 0.667, "trust_level": "EXACT", "time_s": 672.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 8, "d_original": 10, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": true, "t": 5738.7}, {"w": 16, "opt": false, "t": 14400.4}, {"w": 8, "opt": true, "t": 133.5}, {"w": 8, "opt": true, "t": 161.8}, {"w": 8, "opt": true, "t": 176.0}, {"w": 8, "opt": true, "t": 189.6}, {"w": 8, "opt": true, "t": 98.1}, {"w": 8, "opt": true, "t": 241.4}, {"w": 8, "opt": true, "t": 188.0}, {"w": 8, "opt": true, "t": 141.5}, {"w": 8, "opt": true, "t": 165.6}, {"w": 8, "opt": true, "t": 164.1}, {"w": 8, "opt": true, "t": 226.1}, {"w": 8, "opt": true, "t": 156.1}, {"w": 12, "opt": true, "t": 2320.7}, {"w": 12, "opt": true, "t": 1434.8}], "logicals_optimal": 15, "logicals_incumbent": 1, "logicals_failed": 0, "total_logicals": 16, "deep_milp_time_s": 14400.4, "timeout_per_logical": 14400, "deep_verified_at": "2026-05-29T15:16:02.575972+00:00", "d_is_upper_bound": false, "publication_quality": false, "d_milp_initial": 18, "d_exactness_source": {"method": "qubit_paired_zimmermann", "release": "oneq-distance-closures-v1.0.0", "searcher_version": "2.0.0", "schema_version": "2.0.0", "code_input_hash": "e61a9e67e0309d6593bfb49afd688204e48061a977e348b0eb4f87d7dbb2825d", "witness_hash": "e53bab974ba3b6e02a44a46a85ab694b29217931aa9b9f552e916d935316a8ee", "candidates_per_replica": 4945164656133, "depth_p": 7, "independent_replicas": 2, "upper_bound_verification": "self-contained witness: commutes with every stabilizer, not in S, weight equals d", "lower_bound_verification": "two independent exhaustive executions; full third-party verification requires re-execution -- no succinct proof object", "lower_bound_is_machine_checkable": false}}
 {"ell": 9, "m": 6, "A_terms": [[1, 1], [6, 1], [2, 4]], "B_terms": [[0, 0], [7, 1], [2, 5]], "C_terms": [[2, 1], [6, 1]], "D_terms": [[1, 5], [6, 2]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 10, "milp_exact": false, "timestamp": 1773335664.7743835, "bliss_hash": "aefbcfdd3a5451ad", "bliss_group_size": 5, "code_id": "9_6_0139", "verified_at": "2026-03-12T23:14:57.691896+00:00", "d_is_exact": true, "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 335.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 45, "d_is_upper_bound": false, "publication_quality": true, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": true, "per_logical": [{"w": 12, "opt": true, "t": 1343.2}, {"w": 8, "opt": true, "t": 276.2}, {"w": 8, "opt": true, "t": 147.8}, {"w": 8, "opt": true, "t": 140.3}, {"w": 8, "opt": true, "t": 111.5}, {"w": 8, "opt": true, "t": 226.9}, {"w": 8, "opt": true, "t": 120.2}, {"w": 8, "opt": true, "t": 135.7}, {"w": 8, "opt": true, "t": 172.0}, {"w": 8, "opt": true, "t": 130.7}, {"w": 8, "opt": true, "t": 124.0}, {"w": 8, "opt": true, "t": 107.5}], "logicals_optimal": 12, "logicals_incumbent": 0, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 2061.9, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T12:41:44.331938+00:00"}
 {"ell": 12, "m": 6, "A_terms": [[2, 1], [5, 2], [6, 1]], "B_terms": [[5, 1], [6, 0], [6, 1]], "C_terms": [[4, 1]], "D_terms": [[5, 0], [6, 1]], "n": 144, "k": 4, "d": 12, "fom": 4.0, "d_method": "deep_milp", "d_milp": 12, "d_bposd": 16, "milp_exact": false, "timestamp": 1773338353.1694517, "bliss_hash": "8284ce719018437c", "bliss_group_size": 1, "code_id": "12_6_0202", "verified_at": "2026-03-12T23:50:31.278532+00:00", "d_is_exact": true, "d_over_sqrtn": 1.0, "trust_level": "EXACT", "time_s": 663.8, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_deep_milp": 12, "d_original": 14, "fom_deep": 4.0, "milp_exact_deep": true, "per_logical": [{"w": 12, "opt": true, "t": 3886.1}, {"w": 12, "opt": true, "t": 2808.0}, {"w": 12, "opt": true, "t": 1780.6}, {"w": 12, "opt": true, "t": 2280.9}, {"w": 12, "opt": true, "t": 1868.3}, {"w": 12, "opt": true, "t": 2765.5}, {"w": 12, "opt": true, "t": 2099.2}, {"w": 12, "opt": true, "t": 1319.3}], "logicals_optimal": 8, "logicals_incumbent": 0, "logicals_failed": 0, "total_logicals": 8, "deep_milp_time_s": 19742.8, "timeout_per_logical": 7200, "deep_verified_at": "2026-03-14T04:07:09.423225+00:00", "d_is_upper_bound": false, "publication_quality": true, "d_milp_initial": 14}
 {"ell": 9, "m": 6, "A_terms": [[1, 2], [4, 3], [4, 4]], "B_terms": [[0, 0], [1, 5], [5, 4]], "C_terms": [[1, 1], [4, 4]], "D_terms": [[7, 2]], "n": 108, "k": 4, "d": 10, "fom": 3.7037, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 12, "milp_exact": true, "timestamp": 1773320292.37284, "bliss_hash": "bcc7b9b0bed05ef3", "bliss_group_size": 1, "code_id": "9_6_0140", "verified_at": "2026-03-12T23:16:29.764486+00:00", "d_is_exact": true, "d_over_sqrtn": 0.962, "trust_level": "EXACT", "time_s": 247.8, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 12, "d_is_upper_bound": false, "publication_quality": true}
@@ -245,7 +245,7 @@
 {"ell": 9, "m": 6, "A_terms": [[1, 2], [5, 3], [5, 4]], "B_terms": [[0, 0], [4, 5], [7, 4]], "C_terms": [[7, 1], [8, 4]], "D_terms": [[0, 1], [4, 4]], "n": 108, "k": 4, "d": 10, "fom": 3.7037, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 10, "milp_exact": true, "timestamp": 1773350153.0603561, "bliss_hash": "2b6a61eb38d43963", "bliss_group_size": 1, "code_id": "9_6_0152", "verified_at": "2026-03-12T23:22:03.740472+00:00", "d_is_exact": true, "d_over_sqrtn": 0.962, "trust_level": "EXACT", "time_s": 225.2, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 12, "d_is_upper_bound": false, "publication_quality": true}
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-{"ell": 9, "m": 6, "A_terms": [[3, 1], [4, 4], [5, 4]], "B_terms": [[1, 0], [6, 1], [5, 5]], "C_terms": [[0, 1], [2, 3], [6, 2]], "D_terms": [[8, 5]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773320939.3028934, "bliss_hash": "d8f7c04aec559961", "bliss_group_size": 1, "code_id": "phase2_64", "verified_at": "2026-05-20T23:40:42.213246+00:00", "d_is_exact": false, "d_is_upper_bound": true, "d_bposd_runs": [8, 8, 8, 8, 8], "bposd_spread": 0, "milp_solved": 1, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "TRUSTED", "time_s": 325.5, "publication_quality": false, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 16, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": false, "t": 3600.1}, {"w": 16, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 68.9}, {"w": 8, "opt": true, "t": 69.3}, {"w": 8, "opt": true, "t": 219.0}, {"w": 8, "opt": true, "t": 145.3}, {"w": 8, "opt": true, "t": 101.4}, {"w": 8, "opt": true, "t": 108.8}, {"w": 8, "opt": true, "t": 206.8}, {"w": 8, "opt": true, "t": 102.6}, {"w": 8, "opt": true, "t": 85.9}, {"w": 8, "opt": true, "t": 128.3}], "logicals_optimal": 10, "logicals_incumbent": 2, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 4074.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:15:16.445407+00:00"}
+{"ell": 9, "m": 6, "A_terms": [[3, 1], [4, 4], [5, 4]], "B_terms": [[1, 0], [6, 1], [5, 5]], "C_terms": [[0, 1], [2, 3], [6, 2]], "D_terms": [[8, 5]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "qubit_paired_zimmermann", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773320939.3028934, "bliss_hash": "d8f7c04aec559961", "bliss_group_size": 1, "code_id": "phase2_64", "verified_at": "2026-05-20T23:40:42.213246+00:00", "d_is_exact": true, "d_is_upper_bound": false, "d_bposd_runs": [8, 8, 8, 8, 8], "bposd_spread": 0, "milp_solved": 1, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 325.5, "publication_quality": false, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 16, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 16, "opt": false, "t": 3600.1}, {"w": 16, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 68.9}, {"w": 8, "opt": true, "t": 69.3}, {"w": 8, "opt": true, "t": 219.0}, {"w": 8, "opt": true, "t": 145.3}, {"w": 8, "opt": true, "t": 101.4}, {"w": 8, "opt": true, "t": 108.8}, {"w": 8, "opt": true, "t": 206.8}, {"w": 8, "opt": true, "t": 102.6}, {"w": 8, "opt": true, "t": 85.9}, {"w": 8, "opt": true, "t": 128.3}], "logicals_optimal": 10, "logicals_incumbent": 2, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 4074.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:15:16.445407+00:00", "d_exactness_source": {"method": "qubit_paired_zimmermann", "release": "oneq-distance-closures-v1.0.0", "searcher_version": "2.0.0", "schema_version": "2.0.0", "code_input_hash": "f54c5128f30824459b8798abc19b39745b552acc8aff23cb18225bf350c92842", "witness_hash": "51c14b23bde3ebeb616840bffa177879895ebdaaf70ae3ecead011c9d61fca1f", "candidates_per_replica": 688229434659, "depth_p": 7, "independent_replicas": 2, "upper_bound_verification": "self-contained witness: commutes with every stabilizer, not in S, weight equals d", "lower_bound_verification": "two independent exhaustive executions; full third-party verification requires re-execution -- no succinct proof object", "lower_bound_is_machine_checkable": false}}
 {"ell": 9, "m": 6, "A_terms": [[2, 1], [3, 1], [4, 4]], "B_terms": [[0, 0], [5, 1], [4, 5]], "C_terms": [[1, 2], [6, 3]], "D_terms": [[0, 3], [5, 4]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 8, "milp_exact": true, "timestamp": 1773321324.8370476, "bliss_hash": "60f0306247117381", "bliss_group_size": 1, "code_id": "9_6_0155", "verified_at": "2026-03-12T23:23:08.532343+00:00", "d_is_exact": true, "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 71.5, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 9, "m": 6, "A_terms": [[2, 1], [3, 4], [4, 4]], "B_terms": [[0, 0], [5, 1], [4, 5]], "C_terms": [[0, 2], [5, 3]], "D_terms": [[5, 4]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 8, "milp_exact": true, "timestamp": 1773321336.6054192, "bliss_hash": "7974363627ec8d02", "bliss_group_size": 1, "code_id": "9_6_0156", "verified_at": "2026-03-12T23:24:08.382052+00:00", "d_is_exact": true, "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 117.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 6, "m": 6, "A_terms": [[0, 1], [3, 2], [4, 1]], "B_terms": [[0, 1], [4, 0], [4, 1]], "C_terms": [[3, 2]], "D_terms": [[1, 0]], "n": 72, "k": 4, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 8, "milp_exact": true, "timestamp": 1773322302.4642777, "bliss_hash": "8eb6a69aa82ce749", "bliss_group_size": 1, "code_id": "6_6_0099", "verified_at": "2026-03-12T22:59:14.269526+00:00", "d_is_exact": true, "d_over_sqrtn": 0.943, "trust_level": "EXACT", "time_s": 67.3, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
@@ -256,7 +256,7 @@
 {"ell": 12, "m": 6, "A_terms": [[2, 2], [4, 3], [4, 4]], "B_terms": [[0, 0], [2, 5], [6, 4]], "C_terms": [[2, 3], [4, 3]], "D_terms": [[2, 5], [4, 5]], "n": 144, "k": 8, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": null, "milp_exact": true, "timestamp": 1773326506.0496788, "bliss_hash": "603c60e155e5369e", "bliss_group_size": 1, "code_id": "12_6_0064", "verified_at": "2026-03-12T22:55:42.553572+00:00", "d_is_exact": true, "d_over_sqrtn": 0.667, "trust_level": "EXACT", "time_s": 119.3, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 30, "m": 6, "A_terms": [[15, 2], [10, 3], [10, 4]], "B_terms": [[0, 0], [15, 5], [25, 4]], "C_terms": [[10, 3], [15, 3]], "D_terms": [[10, 5], [15, 5]], "n": 360, "k": 20, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 38, "milp_exact": true, "timestamp": 1773326708.388692, "bliss_hash": "165fa77cbeb51688", "bliss_group_size": 1, "code_id": "30_6_0288", "verified_at": "2026-03-13T02:06:09.950234+00:00", "d_is_exact": true, "d_over_sqrtn": 0.422, "trust_level": "EXACT", "time_s": 138.2, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 9, "m": 6, "A_terms": [[4, 1], [6, 4], [8, 4]], "B_terms": [[0, 0], [1, 1], [8, 5]], "C_terms": [[4, 2], [6, 3]], "D_terms": [[4, 3], [6, 4]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773326849.528276, "bliss_hash": "4b38db5afbf07fc0", "bliss_group_size": 3, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "trust_level": "EXACT", "d_milp_initial": 10, "d_over_sqrtn": 0.77, "d_is_exact": true, "d_is_upper_bound": false, "publication_quality": true, "verified_at": "2026-05-29T12:15:16.304193+00:00", "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": true, "per_logical": [{"w": 8, "opt": true, "t": 162.3}, {"w": 8, "opt": true, "t": 134.9}, {"w": 8, "opt": true, "t": 107.6}, {"w": 8, "opt": true, "t": 45.2}, {"w": 8, "opt": true, "t": 136.3}, {"w": 8, "opt": true, "t": 261.0}, {"w": 8, "opt": true, "t": 138.1}, {"w": 8, "opt": true, "t": 233.8}, {"w": 8, "opt": true, "t": 132.1}, {"w": 8, "opt": true, "t": 149.2}, {"w": 8, "opt": true, "t": 155.0}, {"w": 8, "opt": true, "t": 171.4}], "logicals_optimal": 12, "logicals_incumbent": 0, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 473.9, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T12:15:16.304193+00:00"}
-{"ell": 9, "m": 6, "A_terms": [[4, 1], [6, 4], [8, 4]], "B_terms": [[0, 0], [1, 1], [8, 5]], "C_terms": [[4, 1], [6, 1]], "D_terms": [[4, 2], [6, 5]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773327565.0805209, "bliss_hash": "d9457e4965aaa672", "bliss_group_size": 1, "code_id": "phase2_65", "verified_at": "2026-05-20T23:40:42.235661+00:00", "d_is_exact": false, "d_is_upper_bound": true, "d_bposd_runs": [8, 8, 8, 8, 10], "bposd_spread": 2, "milp_solved": 1, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "TRUSTED", "time_s": 325.2, "publication_quality": false, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 14, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 14, "opt": false, "t": 3600.1}, {"w": 14, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 77.0}, {"w": 8, "opt": true, "t": 129.2}, {"w": 8, "opt": true, "t": 155.5}, {"w": 8, "opt": true, "t": 154.9}, {"w": 8, "opt": true, "t": 123.2}, {"w": 14, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 276.5}, {"w": 8, "opt": true, "t": 125.3}, {"w": 8, "opt": true, "t": 127.5}, {"w": 8, "opt": true, "t": 138.8}], "logicals_optimal": 9, "logicals_incumbent": 3, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 4138.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:16:20.368398+00:00"}
+{"ell": 9, "m": 6, "A_terms": [[4, 1], [6, 4], [8, 4]], "B_terms": [[0, 0], [1, 1], [8, 5]], "C_terms": [[4, 1], [6, 1]], "D_terms": [[4, 2], [6, 5]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "qubit_paired_zimmermann", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773327565.0805209, "bliss_hash": "d9457e4965aaa672", "bliss_group_size": 1, "code_id": "phase2_65", "verified_at": "2026-05-20T23:40:42.235661+00:00", "d_is_exact": true, "d_is_upper_bound": false, "d_bposd_runs": [8, 8, 8, 8, 10], "bposd_spread": 2, "milp_solved": 1, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "EXACT", "time_s": 325.2, "publication_quality": false, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 14, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 14, "opt": false, "t": 3600.1}, {"w": 14, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 77.0}, {"w": 8, "opt": true, "t": 129.2}, {"w": 8, "opt": true, "t": 155.5}, {"w": 8, "opt": true, "t": 154.9}, {"w": 8, "opt": true, "t": 123.2}, {"w": 14, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 276.5}, {"w": 8, "opt": true, "t": 125.3}, {"w": 8, "opt": true, "t": 127.5}, {"w": 8, "opt": true, "t": 138.8}], "logicals_optimal": 9, "logicals_incumbent": 3, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 4138.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:16:20.368398+00:00", "d_exactness_source": {"method": "qubit_paired_zimmermann", "release": "oneq-distance-closures-v1.0.0", "searcher_version": "2.0.0", "schema_version": "2.0.0", "code_input_hash": "5acaeac02707c9a5033c51bddb9fb6c7244b6646226a06098d1302487fcd4406", "witness_hash": "969239c2f2f14bd19bd2930e1900edb63a3bec5ceb89c395e9e21cc7bb05663c", "candidates_per_replica": 688229434659, "depth_p": 7, "independent_replicas": 2, "upper_bound_verification": "self-contained witness: commutes with every stabilizer, not in S, weight equals d", "lower_bound_verification": "two independent exhaustive executions; full third-party verification requires re-execution -- no succinct proof object", "lower_bound_is_machine_checkable": false}}
 {"ell": 9, "m": 6, "A_terms": [[2, 1], [3, 4], [4, 4]], "B_terms": [[0, 0], [5, 1], [4, 5]], "C_terms": [[2, 0], [3, 5]], "D_terms": [[2, 1], [3, 0]], "n": 108, "k": 6, "d": 8, "fom": 3.5556, "d_method": "deep_milp", "d_milp": 8, "d_bposd": 8, "milp_exact": false, "timestamp": 1773327901.3560581, "bliss_hash": "d605bef00eff30f7", "bliss_group_size": 3, "code_id": "phase2_66", "verified_at": "2026-05-20T23:40:42.243432+00:00", "d_is_exact": false, "d_is_upper_bound": true, "d_bposd_runs": [8, 10, 8, 10, 8], "bposd_spread": 2, "milp_solved": 1, "milp_total_logicals": 12, "milp_budget": "300s/logical, 1800s total", "d_over_sqrtn": 0.77, "trust_level": "TRUSTED", "time_s": 325.8, "publication_quality": false, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 15, "d_deep_milp": 8, "d_original": 8, "fom_deep": 3.5556, "milp_exact_deep": false, "per_logical": [{"w": 15, "opt": false, "t": 3600.1}, {"w": 15, "opt": false, "t": 3600.1}, {"w": 8, "opt": true, "t": 86.8}, {"w": 8, "opt": true, "t": 162.4}, {"w": 8, "opt": true, "t": 249.1}, {"w": 8, "opt": true, "t": 146.5}, {"w": 8, "opt": true, "t": 126.0}, {"w": 8, "opt": true, "t": 118.0}, {"w": 8, "opt": true, "t": 123.3}, {"w": 8, "opt": true, "t": 225.2}, {"w": 8, "opt": true, "t": 168.7}, {"w": 8, "opt": true, "t": 131.1}], "logicals_optimal": 10, "logicals_incumbent": 2, "logicals_failed": 0, "total_logicals": 12, "deep_milp_time_s": 4163.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:16:45.423032+00:00"}
 {"ell": 6, "m": 6, "A_terms": [[0, 1], [3, 2], [4, 1]], "B_terms": [[3, 1], [4, 0], [4, 1]], "C_terms": [[2, 5], [4, 4], [5, 4]], "D_terms": [[0, 4], [3, 4]], "n": 72, "k": 4, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": 8, "milp_exact": true, "timestamp": 1773328273.8755274, "bliss_hash": "1083bea302fa5c20", "bliss_group_size": 1, "code_id": "6_6_0101", "verified_at": "2026-05-28T18:00:00+00:00", "d_is_exact": true, "d_over_sqrtn": 0.943, "trust_level": "EXACT", "time_s": 194.7, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "milp_solved": 8, "milp_total_logicals": 8, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 6, "m": 6, "A_terms": [[0, 1], [3, 2], [4, 1]], "B_terms": [[0, 1], [4, 0], [4, 1]], "C_terms": [[3, 2], [3, 5]], "D_terms": [[1, 0], [1, 3]], "n": 72, "k": 4, "d": 8, "fom": 3.5556, "d_method": "milp_exact", "d_milp": 8, "d_bposd": null, "milp_exact": true, "timestamp": 1773328749.7572532, "bliss_hash": "fe7fdc72ce36427a", "bliss_group_size": 1, "code_id": "6_6_0065", "verified_at": "2026-03-12T22:55:43.667269+00:00", "d_is_exact": true, "d_over_sqrtn": 0.943, "trust_level": "EXACT", "time_s": 35.0, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
@@ -302,7 +302,7 @@
 {"ell": 12, "m": 6, "A_terms": [[2, 2], [11, 3], [11, 4]], "B_terms": [[0, 0], [1, 5], [3, 4]], "C_terms": [[10, 4]], "D_terms": [[1, 5], [11, 0]], "n": 144, "k": 4, "d": 10, "fom": 2.7778, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 12, "milp_exact": true, "timestamp": 1773330700.4525917, "bliss_hash": "8ebcf329341b87f2", "bliss_group_size": 1, "code_id": "12_6_0216", "verified_at": "2026-03-13T00:01:35.081915+00:00", "d_is_exact": true, "d_over_sqrtn": 0.833, "trust_level": "EXACT", "time_s": 416.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 12, "m": 6, "A_terms": [[3, 0], [0, 4], [0, 2]], "B_terms": [[0, 2], [5, 0], [3, 0]], "C_terms": [[11, 3]], "D_terms": [[4, 5]], "n": 144, "k": 4, "d": 10, "fom": 2.7778, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 10, "milp_exact": true, "timestamp": 1773333631.8938198, "bliss_hash": "6e529af83d40bad8", "bliss_group_size": 1, "code_id": "12_6_0217", "verified_at": "2026-03-13T00:01:36.973329+00:00", "d_is_exact": true, "d_over_sqrtn": 0.833, "trust_level": "EXACT", "time_s": 120.1, "lc_hadamard": true, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": true, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 9, "m": 6, "A_terms": [[3, 1], [4, 2], [7, 0]], "B_terms": [[0, 0], [1, 1], [8, 2]], "C_terms": [[6, 0]], "D_terms": [[7, 2]], "n": 108, "k": 2, "d": 12, "fom": 2.6667, "d_method": "deep_milp", "d_milp": 12, "d_bposd": 12, "milp_exact": false, "timestamp": 1773320168.2431736, "bliss_hash": "a454a7e0b05a321f", "bliss_group_size": 1, "code_id": "9_6_0171", "verified_at": "2026-03-12T23:28:25.762742+00:00", "d_is_exact": true, "d_over_sqrtn": 1.155, "trust_level": "EXACT", "time_s": 328.3, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 14, "d_is_upper_bound": false, "publication_quality": true, "d_deep_milp": 12, "d_original": 12, "fom_deep": 2.6667, "milp_exact_deep": true, "per_logical": [{"w": 12, "opt": true, "t": 1688.0}, {"w": 12, "opt": true, "t": 1507.7}, {"w": 12, "opt": true, "t": 2550.4}, {"w": 12, "opt": true, "t": 1807.4}], "logicals_optimal": 4, "logicals_incumbent": 0, "logicals_failed": 0, "total_logicals": 4, "deep_milp_time_s": 3479.0, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:05:21.367487+00:00"}
-{"ell": 9, "m": 6, "A_terms": [[0, 1], [3, 2], [1, 1]], "B_terms": [[0, 1], [1, 0], [1, 1]], "C_terms": [[5, 1]], "D_terms": [[0, 1], [2, 0]], "n": 108, "k": 2, "d": 10, "fom": 1.8519, "d_method": "deep_milp", "d_milp": 10, "d_bposd": 12, "milp_exact": false, "timestamp": 1773328607.96728, "bliss_hash": "426b9d530929e62e", "bliss_group_size": 1, "code_id": "9_6_0172", "verified_at": "2026-03-12T23:28:58.256231+00:00", "d_is_exact": false, "d_over_sqrtn": 0.962, "trust_level": "TRUSTED", "time_s": 330.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 14, "d_is_upper_bound": true, "publication_quality": false, "d_deep_milp": 10, "d_original": 10, "fom_deep": 1.8519, "milp_exact_deep": false, "per_logical": [{"w": 10, "opt": true, "t": 557.5}, {"w": 10, "opt": true, "t": 531.6}, {"w": 21, "opt": false, "t": 3600.3}, {"w": 10, "opt": true, "t": 404.2}], "logicals_optimal": 3, "logicals_incumbent": 1, "logicals_failed": 0, "total_logicals": 4, "deep_milp_time_s": 4659.2, "timeout_per_logical": 3600, "deep_verified_at": "2026-05-29T13:25:01.595544+00:00"}
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 {"ell": 9, "m": 6, "A_terms": [[3, 0], [0, 5], [0, 4]], "B_terms": [[0, 5], [5, 0], [6, 0]], "C_terms": [[7, 2]], "D_terms": [[5, 3], [7, 3]], "n": 108, "k": 2, "d": 10, "fom": 1.8519, "d_method": "milp_exact", "d_milp": 10, "d_bposd": 12, "milp_exact": true, "timestamp": 1773337873.8960743, "bliss_hash": "d36d179ba477b6dc", "bliss_group_size": 1, "code_id": "9_6_0174", "verified_at": "2026-03-12T23:30:24.499500+00:00", "d_is_exact": true, "d_over_sqrtn": 0.962, "trust_level": "EXACT", "time_s": 265.1, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_milp_initial": 12, "d_is_upper_bound": false, "publication_quality": true}
 {"ell": 15, "m": 6, "A_terms": [[9, 2], [3, 3], [3, 4]], "B_terms": [[0, 0], [9, 5], [12, 4]], "C_terms": [[3, 3], [9, 3]], "D_terms": [[3, 5], [9, 5]], "n": 180, "k": 12, "d": 6, "fom": 2.4, "d_method": "exact_w6", "d_milp": null, "d_bposd": null, "milp_exact": null, "timestamp": 1773326708.3878114, "bliss_hash": "3ac902a0592afe86", "bliss_group_size": 3, "code_id": "phase2_108", "verified_at": "2026-05-20T23:47:32.899887+00:00", "d_is_exact": true, "d_over_sqrtn": 0.447, "trust_level": "EXACT", "time_s": 41.7, "publication_quality": true, "lc_hadamard": false, "lc_uniform": false, "lc_uniform_s1": null, "lc_uniform_s2": null, "lc_nonuniform_IS_HS": true, "lc_uniform_solutions": [], "lc_any": false, "d_is_upper_bound": false}
@@ -339,7 +339,7 @@
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