{"id": "c943", "title": "C943 — Aggregate projection kernel", "filename": "C943.md", "role": "Research action", "step": 943, "sha256": "07ecbedbf6be88dc53305918e523889438f29bc54484c82c517777d28cd78021", "bytes": 1026, "origins": ["C480–C1634/Research_Cycles/C0932_C1131/journal.json#C943"], "download": "/sources/07ecbedbf6be88dc53305918e523889438f29bc54484c82c517777d28cd78021.md", "format": "md", "derived": true, "tags": [], "excerpt": "What aggregate information can original and reversed totals determine?", "content": "# C943 — Aggregate projection kernel\n\n## Question\n\nWhat aggregate information can original and reversed totals determine?\n\n## Inputs\n\n```json\n{\n  \"rows\": [\n    [\n      100,\n      10,\n      1\n    ],\n    [\n      1,\n      10,\n      100\n    ]\n  ]\n}\n```\n\n## Sources\n\n```json\n[\n  \"C938\",\n  \"C942\"\n]\n```\n\n## Opened utc\n\n2026-09-28T03:42:45.381897+00:00\n\n## Results\n\n```json\n{\n  \"rank\": 2,\n  \"primitive_integer_kernel\": [\n    10,\n    -101,\n    10\n  ],\n  \"kernel_products\": [\n    0,\n    0\n  ],\n  \"nonzero_minor\": 990\n}\n```\n\n## Finding\n\nThe two measurements have rank two over rational aggregate coordinates, with kernel (10, −101, 10).\n\n## Reassessment\n\nApply the finite digit bounds before concluding that a free aggregate parameter remains.\n\n## Checks\n\n```json\n{\n  \"annihilation\": true,\n  \"rank_two\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T03:42:45.382664+00:00\n\n## Record provenance\n\nExact record hash: `b7d12ea7f3d307a5f32686493207ee1d0aa6e7ce3900bed358c963f710abe77d`\n\nSource journal: `Research_Cycles/C0932_C1131/journal.json`", "journalDownload": "/sources/f6bdc7aaaaa4fd40f1151b367204ddee7f0f9b77a9c43ae8764831b52d862670.json"}