{"id": "c1564", "title": "C1564 — Compress the partition family by local merges", "filename": "C1564.md", "role": "Research action", "step": 1564, "sha256": "d3f54807f7ffe7514fed98373fc27dfe80f19ceecd580190f8339b5207c4e9d2", "bytes": 1246, "origins": ["C480–C1634/Research_Cycles/C1483_C1582/c1483_c1582/journal.json#C1564"], "download": "/sources/d3f54807f7ffe7514fed98373fc27dfe80f19ceecd580190f8339b5207c4e9d2.md", "format": "md", "derived": true, "tags": [], "excerpt": "Can one local quantity describe every retained-boundary choice?", "content": "# C1564 — Compress the partition family by local merges\n\n## Question\n\nCan one local quantity describe every retained-boundary choice?\n\n## Sources\n\n```json\n[]\n```\n\n## Opened utc\n\n2026-09-29T02:42:15.195307+00:00\n\n## Results\n\n```json\n{\n  \"MT\": {\n    \"full_total\": 7290,\n    \"D_a_600\": -990,\n    \"D_600_950\": 4320,\n    \"D_950_c\": 4320,\n    \"D_a_1550\": 0,\n    \"D_1550_c\": -990,\n    \"D_a600_950\": 5310\n  },\n  \"LXX\": {\n    \"full_total\": 12230,\n    \"D_a_600\": 0,\n    \"D_600_950\": 4320,\n    \"D_950_c\": -1710,\n    \"D_a_1550\": 0,\n    \"D_1550_c\": -7020,\n    \"D_a600_950\": 4320\n  },\n  \"SP\": {\n    \"full_total\": 5690,\n    \"D_a_600\": 0,\n    \"D_600_950\": 4320,\n    \"D_950_c\": 4320,\n    \"D_a_1550\": 0,\n    \"D_1550_c\": 0,\n    \"D_a600_950\": 4320\n  }\n}\n```\n\n## Finding\n\nDefine D(x,y)=I(x+y)−I(x)−I(y). The same merge rule covers all named partitions, with the sharedD(600,950)=4320 andD(a,1550)=0.\n\n## Reassessment\n\nCheck the relation between two different orders of merging the same three source legs.\n\n## Checks\n\n```json\n{}\n```\n\n## Closed utc\n\n2026-09-29T02:42:15.195854+00:00\n\n## Record provenance\n\nExact record hash: `bd30a1fd6f2d3a55dc69376848456e2726a0881d28f683796a6c436ff678c729`\n\nSource journal: `Research_Cycles/C1483_C1582/c1483_c1582/journal.json`", "journalDownload": "/sources/7241bc8dee3ba293341214bcb88dc4f80832f7d0207eb9e07f9364c06d3847c8.json"}