{"id": "c853", "title": "C853 — Derive the complete paired gain field", "filename": "C853.md", "role": "Research action", "step": 853, "sha256": "0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21", "bytes": 1419, "origins": ["C480–C1634/Research_Cycles/C0832_C0931/journal.json#C853"], "download": "/sources/0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21.md", "format": "md", "derived": true, "tags": ["Inverse"], "excerpt": "Where does the anchor dependence enter the forward construction?", "content": "# C853 — Derive the complete paired gain field\n\n## Question\n\nWhere does the anchor dependence enter the forward construction?\n\n## Inputs\n\n```json\n{}\n```\n\n## Sources\n\n```json\n[\n  \"C852; inherited one-pass gain definition\"\n]\n```\n\n## Opened utc\n\n2026-09-28T02:36:19.444521+00:00\n\n## Results\n\n```json\n{\n  \"gains\": {\n    \"path\": \"model/inverse_gain_field.json\",\n    \"sha256\": \"093b354383add7d87f104fb0d8a32411bab1bb2465eddb6ccb4e78273938c8ba\",\n    \"bytes\": 3362\n  },\n  \"paired_delta\": [\n    7200,\n    990,\n    990,\n    990,\n    990,\n    990,\n    990,\n    990,\n    1980,\n    1980,\n    990,\n    990,\n    990,\n    -6930,\n    -3330,\n    -630,\n    -6840,\n    -4140,\n    -1440,\n    -4050,\n    -3960,\n    0,\n    -360,\n    -1800,\n    -900,\n    -5940,\n    990,\n    -6660,\n    -5670,\n    -2970,\n    -2970,\n    1980\n  ],\n  \"identity\": \"A+I(D−A)=D+g(D−A), with g(s)=I(s)−s\"\n}\n```\n\n## Finding\n\nAll anchor dependence resides in the gain of the original selected duration. The32 differences are one generated field, not32 adjustable translations.\n\n## Reassessment\n\nDerive the long-core no-borrow and borrow branches from digit positions.\n\n## Checks\n\n```json\n{\n  \"gain_difference\": true,\n  \"anchor_gap\": true\n}\n```\n\n## Closed utc\n\n2026-09-28T02:36:19.445226+00:00\n\n## Record provenance\n\nExact record hash: `0a3fb28d7893be93212abd083bf09ca914de9749a357127f1872025dc202a944`\n\nSource journal: `Research_Cycles/C0832_C0931/journal.json`", "journalDownload": "/sources/6a37be4e218f9f467cbde5e9db3723ce9c79dc78cc97d1a289422b96cb9971e0.json", "evidenceLinks": [{"id": "d-093b354383add7d8", "title": "model/inverse_gain_field.json"}]}