{"id": "c766", "title": "C766 — Join rounding to the mode bridge", "filename": "C766.md", "role": "Research action", "step": 766, "sha256": "3c9d7c72fef36c192291797fbf5f755db1cbe32df8737006178c787a938c4239", "bytes": 1371, "origins": ["C480–C1634/Research_Cycles/C0732_C0831/journal.json#C766"], "download": "/sources/3c9d7c72fef36c192291797fbf5f755db1cbe32df8737006178c787a938c4239.md", "format": "md", "derived": true, "tags": ["Regular", "Cumulative", "Rounded", "Mirror / 529"], "excerpt": "Does bridge rounding follow the difference of the two boundary residuals?", "content": "# C766 — Join rounding to the mode bridge\n\n## Question\n\nDoes bridge rounding follow the difference of the two boundary residuals?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"File51a §3.1 strict regular and §16.2 cumulative tables\"\n]\n```\n\n## Opened utc\n\n2026-09-28T01:57:42.205748+00:00\n\n## Results\n\n```json\n{\n  \"source_packet\": {\n    \"path\": \"model/variant_inputs.json\",\n    \"sha256\": \"637ee29c7bcb34fbdf313690535d3f2035837e6f77940bc0580e5a90295f8cf0\",\n    \"bytes\": 187357\n  },\n  \"bridge\": {\n    \"path\": \"model/MT_rounding_bridge.json\",\n    \"sha256\": \"8b8c6c130a8aaf156453fe1b74b3ffa72d29a9529134efc1678b7f8234a8732f\",\n    \"bytes\": 2560\n  },\n  \"common_nodes\": 22,\n  \"Adam\": {\n    \"name\": \"Adam\",\n    \"G_actual\": 9894,\n    \"G_rounded\": 9900,\n    \"delta_G\": 6,\n    \"D_C_minus_D_R\": 6\n  }\n}\n```\n\n## Finding\n\nOn the literal strict regular comparison, rounded G−actual G equals D_C−D_R at every common node. Rounding modifies the mode bridge through two fields, not one date offset.\n\n## Reassessment\n\nCheck the local bridge-generator identity from adjacent differences.\n\n## Checks\n\n```json\n{\n  \"all_nodes\": true,\n  \"enough_nodes\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T01:57:42.212412+00:00\n\n## Record provenance\n\nExact record hash: `e712d08ab051d820a79d4d24055738c06d738082f19da55b1959e11d44007b3b`\n\nSource journal: `Research_Cycles/C0732_C0831/journal.json`", "journalDownload": "/sources/8ea2b882289fbcea5cf11177923617f0c1d1ad7e6eaa3bffb174c6f89699d97d.json", "evidenceLinks": [{"id": "d-637ee29c7bcb34fb", "title": "model/variant_inputs.json"}, {"id": "d-8b8c6c130a8aaf15", "title": "model/MT_rounding_bridge.json"}, {"id": "d-d8aa38afb2a2df8f", "title": "File 51a"}]}