{
  "comparison": {
    "c4_projective_block2": {
      "N": 13,
      "basis_mode": "projective",
      "block_size": 2,
      "c2_entries": 294,
      "c2_terms": 7,
      "c4_entries": 49,
      "c4_public_clpn_rows": 1813,
      "c4_terms_bound": 7,
      "c4_vs_c2_entry_ratio": 0.16666666666666666,
      "eta_c4_bound": 0.0,
      "legacy_entries": 13,
      "log_q_sparse_volume_full_block": 2.0,
      "num_blocks": 7,
      "params": "c4_projective_toy_clean",
      "q": 7,
      "repetition_failure_bound_c4": 0.0,
      "v1_terms_dense_blocks": 13
    },
    "c6_projective_surface_block2": {
      "N": 13,
      "block_profiles": [
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=2, projective_entries=8, relation_space_dimension=6, projective_lines=1, raw_weight3_relations=56, weight3_relation_noise=0.0, warning='min relation weight is 3; relation-derived zero-message samples exist')",
        "C6BlockProfile(width=1, projective_entries=1, relation_space_dimension=0, projective_lines=0, raw_weight3_relations=0, weight3_relation_noise=0.0, warning='no weight-3 projective relation in width-one block')"
      ],
      "block_size": 2,
      "c2_full_dictionary_entries": 294,
      "c4_projective_entries": 49,
      "c4_public_clpn_rows": 1813,
      "c4_vs_c2_entry_ratio": 0.16666666666666666,
      "expansion_key_rows": 169,
      "num_blocks": 7,
      "q": 7,
      "rank_capped_relation_dimension": 36,
      "rank_capped_relation_rows": 1332,
      "raw_weight3_relation_rows": 12432,
      "raw_weight3_relations": 336,
      "row_difference_noise": 0.0,
      "row_difference_samples": 32634,
      "weight3_relation_noise": 0.0
    },
    "c7_coordinate_block1": {
      "N": 13,
      "block_size": 1,
      "dense_fallback_terms_bound": 13,
      "eta_dense_fallback_bound": 0.0,
      "eta_preferred_bound": 0.0,
      "mode": "coordinate",
      "num_blocks": 13,
      "params": "c4_projective_toy_clean",
      "preferred_terms_bound": 13,
      "public_clpn_rows": 481,
      "public_entries": 13,
      "public_field_elements_dense": 8177,
      "q": 7,
      "relation_note": "coordinate blocks are linearly independent; no within-block kernel relations",
      "relation_screen_weight": 4,
      "repetition_failure_bound_dense_fallback": 0.0,
      "repetition_failure_bound_preferred": 0.0,
      "security_status": "main research default"
    },
    "c7_coordinate_block2": {
      "N": 13,
      "block_size": 2,
      "dense_fallback_terms_bound": 13,
      "eta_dense_fallback_bound": 0.0,
      "eta_preferred_bound": 0.0,
      "mode": "coordinate",
      "num_blocks": 7,
      "params": "c4_projective_toy_clean",
      "preferred_terms_bound": 14,
      "public_clpn_rows": 481,
      "public_entries": 13,
      "public_field_elements_dense": 8177,
      "q": 7,
      "relation_note": "coordinate blocks are linearly independent; no within-block kernel relations",
      "relation_screen_weight": 4,
      "repetition_failure_bound_dense_fallback": 0.0,
      "repetition_failure_bound_preferred": 0.0,
      "security_status": "main research default"
    },
    "interpretation": "C7 coordinate uses more compaction terms than C4 projective but removes the full projective weight-3 relation surface from the main security candidate."
  },
  "default_estimate": {
    "N": 13,
    "block_size": 1,
    "dense_fallback_terms_bound": 13,
    "eta_dense_fallback_bound": 0.0,
    "eta_preferred_bound": 0.0,
    "mode": "coordinate",
    "num_blocks": 13,
    "params": "c4_projective_toy_clean",
    "preferred_terms_bound": 13,
    "public_clpn_rows": 481,
    "public_entries": 13,
    "public_field_elements_dense": 8177,
    "q": 7,
    "relation_note": "coordinate blocks are linearly independent; no within-block kernel relations",
    "relation_screen_weight": 4,
    "repetition_failure_bound_dense_fallback": 0.0,
    "repetition_failure_bound_preferred": 0.0,
    "security_status": "main research default"
  },
  "experimental_candidates": [
    "C7 screened-random additive masks",
    "C4 projective compaction",
    "C2/C3 dictionaries"
  ],
  "main_candidate": "C7 coordinate relation-resistant compaction",
  "not_ready_for": [
    "production deployment",
    "standardization claims",
    "certified concrete security without independent LPN estimation"
  ],
  "remaining_open_science_questions": [
    "tight sparse/q-ary LPN estimator with large public sample surfaces",
    "stronger error-correcting compactor beyond repetition decoding",
    "measured OpenFHE/TFHE/BFV/BGV/CKKS benchmarks on identical circuits"
  ],
  "status": "ready as a research prototype and manuscript package",
  "stop_condition_met": true,
  "version": "v0.9-C7"
}
