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        }
      ],
      "matrix": [
        [
          10051,
          9591
        ],
        [
          9591,
          9131
        ]
      ],
      "remainder_matrix": [
        [
          0,
          69
        ],
        [
          69,
          138
        ]
      ]
    }
  ],
  "counts": {
    "matrices": 4,
    "source950_routes": 16,
    "same_phase_route_components": 32
  },
  "normal_form": "T_ab=19K-(a+b)d=(19-a-b)K+(a+b)(K-d), d=460-e",
  "primary_bridge_matrix": [
    [
      10051,
      9591
    ],
    [
      9591,
      9131
    ]
  ],
  "companion_bridge_matrix": [
    [
      10051,
      9592
    ],
    [
      9592,
      9133
    ]
  ],
  "interpretation": "Primary complements are69/138; companion complements70/140. The latter use the explicit compound Cainan plus annual-index gap459. Bridge remainders are duration arithmetic, not calendar residue or newly adopted epoch anchors. Equal bridge constants retain distinct source roles."
}