{"id": "c888", "title": "C888 — Join the NT lattice to the general Key domain theorem", "filename": "C888.md", "role": "Research action", "step": 888, "sha256": "d89de03165d2817c8dee072a1cddf45fba2f45553c430a414a26e7cef52d812d", "bytes": 1321, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C888"], "download": "/sources/d89de03165d2817c8dee072a1cddf45fba2f45553c430a414a26e7cef52d812d.md", "format": "md", "derived": true, "tags": [], "excerpt": "Why are integer years weaker than return to an NT70-year slot?", "content": "# C888 — Join the NT lattice to the general Key domain theorem\n\n## Question\n\nWhy are integer years weaker than return to an NT70-year slot?\n\n## Inputs\n\n```json\n{\n  \"NT_grid_h\": 70\n}\n```\n\n## Sources\n\n```json\n[\n  \"C866–867\",\n  \"C873–874\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:50:15.593174+00:00\n\n## Results\n\n```json\n{\n  \"domain_transfer\": {\n    \"path\": \"model/NT_grid_domain_transfer.json\",\n    \"sha256\": \"8dab8c8f0f0df5055ecf650a69e8f256eeac08bfc956fd91e82019e7da83e1f8\",\n    \"bytes\": 519\n  },\n  \"same_slots\": {\n    \"E\": [\n      0,\n      23,\n      46,\n      69\n    ],\n    \"P\": [\n      0,\n      69\n    ],\n    \"J\": [\n      0\n    ]\n  }\n}\n```\n\n## Finding\n\nThe NT return rule is the h=70 instance of the general theorem. E/P returns remain0,23,46,69 and0,69; J has only the fixed hinge in this finite domain. Integer output and return to a named slot are different requirements, even when these particular finite index sets coincide.\n\n## Reassessment\n\nIntegrate the operator results as grid and anchor registers.\n\n## Checks\n\n```json\n{\n  \"E_matches\": true,\n  \"P_matches\": true,\n  \"J_fixed_only\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:50:15.594580+00:00\n\n## Record provenance\n\nExact record hash: `63fba02f36b2aa6acd92946a06403651b8e2d867f633998bc627341448bcdacd`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-8dab8c8f0f0df505", "title": "model/NT_grid_domain_transfer.json"}]}