{"id": "c854", "title": "C854 — Explain the990 and1980 branches by decimal borrowing", "filename": "C854.md", "role": "Research action", "step": 854, "sha256": "92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b", "bytes": 1205, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C854"], "download": "/sources/92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "Does subtraction of the1400 anchor gap force the repeated paired differences?", "content": "# C854 — Explain the990 and1980 branches by decimal borrowing\n\n## Question\n\nDoes subtraction of the1400 anchor gap force the repeated paired differences?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C852–853 digit registers\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:36:34.403212+00:00\n\n## Results\n\n```json\n{\n  \"branches\": {\n    \"path\": \"model/inverse_long_core_branches.json\",\n    \"sha256\": \"418a6416c1a58fb34c0422d9915ccb2ad6bd1b44ed9bcc43ccf96f0c7c7c02dd\",\n    \"bytes\": 2979\n  },\n  \"branch_values\": [\n    990,\n    1980\n  ],\n  \"derivation\": \"the shared terminal core digit cancels after positional reversal; leading/tens changes force the remaining gap\"\n}\n```\n\n## Finding\n\nNo borrow yields990; a tens borrow yields1980. These are forced branch values for every applicable source row, rather than separately chosen gaps.\n\n## Reassessment\n\nExplain every shortened-core source row by the same positional rule.\n\n## Checks\n\n```json\n{\n  \"all_applicable\": true,\n  \"only_two\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:36:34.403693+00:00\n\n## Record provenance\n\nExact record hash: `49be08c21aca634f0a12e999b990c4e1b32f4d8f7efdd80960d801c223bc0008`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-418a6416c1a58fb3", "title": "model/inverse_long_core_branches.json"}]}