{"version":1,"checkpoint":1635,"id":"paired-inverse","title":"Paired-anchor Rounded inverse field","start":850,"end":858,"count":9,"description":"Explains the full File52c paired-anchor inverse field from decimal borrowing, core length and retained zeros, with one pass per original duration.","topicIds":["inverse"],"primaryTopicId":"inverse","entrypoints":[{"id":"c853","title":"C853 — Derive the complete paired gain field","textURL":"/read/c853.html","jsonURL":"/documents/c853.json","download":"/sources/0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21.md","filename":"C853.md","sha256":"0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21","role":"Research action"},{"id":"c854","title":"C854 — Explain the990 and1980 branches by decimal borrowing","textURL":"/read/c854.html","jsonURL":"/documents/c854.json","download":"/sources/92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b.md","filename":"C854.md","sha256":"92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b","role":"Research action"},{"id":"c856","title":"C856 — Resolve retained-zero cases without changing the operation","textURL":"/read/c856.html","jsonURL":"/documents/c856.json","download":"/sources/9c17138153ead0ff443d49d98bb37a533fccbe3ff19fe19ac82de1f1c3263be6.md","filename":"C856.md","sha256":"9c17138153ead0ff443d49d98bb37a533fccbe3ff19fe19ac82de1f1c3263be6","role":"Research action"},{"id":"c857","title":"C857 — Test complete coverage and the affine obstruction","textURL":"/read/c857.html","jsonURL":"/documents/c857.json","download":"/sources/237307b70b0a5d967762f6d624e1ce4e50f0df7b2107c9a7ac169f529ad12dcb.md","filename":"C857.md","sha256":"237307b70b0a5d967762f6d624e1ce4e50f0df7b2107c9a7ac169f529ad12dcb","role":"Research action"}],"sourceIds":[{"id":"file52c","title":"File_52c — Rounded Whole-Span Inverse Detailed Study","textURL":"/read/file52c.html","jsonURL":"/documents/file52c.json","download":"/sources/a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.md","filename":"File_52c_Latest_Controlling_Draft.md","sha256":"a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530","role":"Source"}],"cycle":{"id":"whole-family-transfer","title":"Whole-family transfers, NT displays, Keys and carriers","start":832,"end":931},"textURL":"/research/campaigns/paired-inverse.html","jsonURL":"/research/campaigns/paired-inverse.json","retrieval":{"currentAccount":{"id":"synthesis","title":"How the chronological families fit together","textURL":"/read/synthesis.html","jsonURL":"/documents/synthesis.json","download":"/sources/ba66fb0bf2403c72e020b065a0f1d1c775eb493af49c4676bb256a8113ee2dc7.md","filename":"490d_Chronological_Families_Explanation_Through_C1634_Portable.md","sha256":"ba66fb0bf2403c72e020b065a0f1d1c775eb493af49c4676bb256a8113ee2dc7","role":"Synthesis"},"sourceGuideURL":"/study-documents/index.html","sourceGuideMarkdownURL":"/study-documents/source-guide.md","fullCatalogURL":"/catalog.json","instructions":["Read the current explanation, then select the topic matching your question. A topic may join several separate research campaigns.","Read the selected Start here documents before opening a complete numbered-record list. Follow their cited source editions and evidence links as needed.","Use a campaign for one contiguous line of study; use a topic to find related work revisited across campaigns. The topic and campaign JSON lists contain links and edition hashes, not document bodies.","Original numbered records retain their historical scope and source assumptions. Later corrections, accepted source decisions and the current synthesis govern the present account.","If a subject is absent from the published Knowledge Catalog, consult Study documents and the source guide for supporting studies used or referenced in the C-series research."],"classificationNote":"These sections are an editorial navigation map of preserved research. Classification does not revalidate arithmetic or promote every historical finding to an accepted conclusion."},"members":[{"id":"c850","step":850,"title":"C850 — Freeze the full paired-anchor inverse field","textURL":"/read/c850.html","jsonURL":"/documents/c850.json","download":"/sources/7d66e79f8da6eedf4c31f23b5c39e0e6d28ab10734a56ea1d5dc75bb2aca92a6.md","sha256":"7d66e79f8da6eedf4c31f23b5c39e0e6d28ab10734a56ea1d5dc75bb2aca92a6","evidenceLinks":[{"id":"d-dbcb35bf6cfe88b3","title":"model/inverse_inputs.json","textURL":"/read/d-dbcb35bf6cfe88b3.html","jsonURL":"/documents/d-dbcb35bf6cfe88b3.json","download":"/sources/dbcb35bf6cfe88b318b4c8c327e97aa0be06583d5e945c43c9aac8b7f7b80911.json","filename":"inverse_inputs.json","sha256":"dbcb35bf6cfe88b318b4c8c327e97aa0be06583d5e945c43c9aac8b7f7b80911","role":"Evidence"},{"id":"file52c","title":"File 52c","textURL":"/read/file52c.html","jsonURL":"/documents/file52c.json","download":"/sources/a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.md","filename":"File_52c_Latest_Controlling_Draft.md","sha256":"a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530","role":"Source"}]},{"id":"c851","step":851,"title":"C851 — Close the first twenty-step explanatory checkpoint","textURL":"/read/c851.html","jsonURL":"/documents/c851.json","download":"/sources/295ccefe9f36962ded9aa43ea0e08bb670fdf2f6ce3f3ad31f81c548790483a6.md","sha256":"295ccefe9f36962ded9aa43ea0e08bb670fdf2f6ce3f3ad31f81c548790483a6","evidenceLinks":[{"id":"d-18816601d66beb94","title":"deliverables/490d_Chronological_Families_Checkpoint_C851.md","textURL":"/read/d-18816601d66beb94.html","jsonURL":"/documents/d-18816601d66beb94.json","download":"/sources/18816601d66beb94848c9353dd59c9d2cbc13c64b9fad842459de3a7d3e78369.md","filename":"490d_Chronological_Families_Checkpoint_C851.md","sha256":"18816601d66beb94848c9353dd59c9d2cbc13c64b9fad842459de3a7d3e78369","role":"History"}]},{"id":"c852","step":852,"title":"C852 — Reconstruct all existing paired-anchor endpoints","textURL":"/read/c852.html","jsonURL":"/documents/c852.json","download":"/sources/6d5d986a9773d4074a9b125996803215cf80c54d689ce782af77a7ea68c5121b.md","sha256":"6d5d986a9773d4074a9b125996803215cf80c54d689ce782af77a7ea68c5121b","evidenceLinks":[{"id":"d-eea45a0802d05e2a","title":"model/inverse_paired_field.json","textURL":"/read/d-eea45a0802d05e2a.html","jsonURL":"/documents/d-eea45a0802d05e2a.json","download":"/sources/eea45a0802d05e2ada4ee33ae2685da893929e1995083b0df2ebcfa2f86f2ce9.json","filename":"inverse_paired_field.json","sha256":"eea45a0802d05e2ada4ee33ae2685da893929e1995083b0df2ebcfa2f86f2ce9","role":"Evidence"},{"id":"d-dbcb35bf6cfe88b3","title":"model/inverse_inputs.json","textURL":"/read/d-dbcb35bf6cfe88b3.html","jsonURL":"/documents/d-dbcb35bf6cfe88b3.json","download":"/sources/dbcb35bf6cfe88b318b4c8c327e97aa0be06583d5e945c43c9aac8b7f7b80911.json","filename":"inverse_inputs.json","sha256":"dbcb35bf6cfe88b318b4c8c327e97aa0be06583d5e945c43c9aac8b7f7b80911","role":"Evidence"},{"id":"file52c","title":"File 52c","textURL":"/read/file52c.html","jsonURL":"/documents/file52c.json","download":"/sources/a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.md","filename":"File_52c_Latest_Controlling_Draft.md","sha256":"a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530","role":"Source"}]},{"id":"c853","step":853,"title":"C853 — Derive the complete paired gain field","textURL":"/read/c853.html","jsonURL":"/documents/c853.json","download":"/sources/0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21.md","sha256":"0c664fd6026ad35ac6035f23f6172ac810ce661e5625fb132653fd5037c48a21","evidenceLinks":[{"id":"d-093b354383add7d8","title":"model/inverse_gain_field.json","textURL":"/read/d-093b354383add7d8.html","jsonURL":"/documents/d-093b354383add7d8.json","download":"/sources/093b354383add7d87f104fb0d8a32411bab1bb2465eddb6ccb4e78273938c8ba.json","filename":"inverse_gain_field.json","sha256":"093b354383add7d87f104fb0d8a32411bab1bb2465eddb6ccb4e78273938c8ba","role":"Evidence"}]},{"id":"c854","step":854,"title":"C854 — Explain the990 and1980 branches by decimal borrowing","textURL":"/read/c854.html","jsonURL":"/documents/c854.json","download":"/sources/92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b.md","sha256":"92d8d15acaf033911bdbc28a65869dde76b84db961da8ebcca2e41d922d7215b","evidenceLinks":[{"id":"d-418a6416c1a58fb3","title":"model/inverse_long_core_branches.json","textURL":"/read/d-418a6416c1a58fb3.html","jsonURL":"/documents/d-418a6416c1a58fb3.json","download":"/sources/418a6416c1a58fb34c0422d9915ccb2ad6bd1b44ed9bcc43ccf96f0c7c7c02dd.json","filename":"inverse_long_core_branches.json","sha256":"418a6416c1a58fb34c0422d9915ccb2ad6bd1b44ed9bcc43ccf96f0c7c7c02dd","role":"Evidence"}]},{"id":"c855","step":855,"title":"C855 — Explain every shortened-core branch","textURL":"/read/c855.html","jsonURL":"/documents/c855.json","download":"/sources/471dab946358f857256304f97405a3c9720e3d350a5fe01f998e5f3c0fdae27a.md","sha256":"471dab946358f857256304f97405a3c9720e3d350a5fe01f998e5f3c0fdae27a","evidenceLinks":[{"id":"d-fb9e0311663e549b","title":"model/inverse_short_core_branches.json","textURL":"/read/d-fb9e0311663e549b.html","jsonURL":"/documents/d-fb9e0311663e549b.json","download":"/sources/fb9e0311663e549bcb790b83c963c12b4f8c56b5a4c775d265f84df52f81b8c0.json","filename":"inverse_short_core_branches.json","sha256":"fb9e0311663e549bcb790b83c963c12b4f8c56b5a4c775d265f84df52f81b8c0","role":"Evidence"}]},{"id":"c856","step":856,"title":"C856 — Resolve retained-zero cases without changing the operation","textURL":"/read/c856.html","jsonURL":"/documents/c856.json","download":"/sources/9c17138153ead0ff443d49d98bb37a533fccbe3ff19fe19ac82de1f1c3263be6.md","sha256":"9c17138153ead0ff443d49d98bb37a533fccbe3ff19fe19ac82de1f1c3263be6","evidenceLinks":[{"id":"file52c","title":"File 52c","textURL":"/read/file52c.html","jsonURL":"/documents/file52c.json","download":"/sources/a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530.md","filename":"File_52c_Latest_Controlling_Draft.md","sha256":"a5ea84562101158b60d0cf296765d6eff38e7a2abda4e74ad1b353dfd13b9530","role":"Source"}]},{"id":"c857","step":857,"title":"C857 — Test complete coverage and the affine obstruction","textURL":"/read/c857.html","jsonURL":"/documents/c857.json","download":"/sources/237307b70b0a5d967762f6d624e1ce4e50f0df7b2107c9a7ac169f529ad12dcb.md","sha256":"237307b70b0a5d967762f6d624e1ce4e50f0df7b2107c9a7ac169f529ad12dcb","evidenceLinks":[]},{"id":"c858","step":858,"title":"C858 — Integrate the decimal module by its retained register","textURL":"/read/c858.html","jsonURL":"/documents/c858.json","download":"/sources/cda1a36950e780eaa511e8643e759263cef8e25e09eecf04f8705e9dba9d5d97.md","sha256":"cda1a36950e780eaa511e8643e759263cef8e25e09eecf04f8705e9dba9d5d97","evidenceLinks":[{"id":"d-bde0cd431d5efd71","title":"model/inverse_module_summary.json","textURL":"/read/d-bde0cd431d5efd71.html","jsonURL":"/documents/d-bde0cd431d5efd71.json","download":"/sources/bde0cd431d5efd716efd80d92de26b2cf52ba7dd2128c23d73168826f5c48c1f.json","filename":"inverse_module_summary.json","sha256":"bde0cd431d5efd716efd80d92de26b2cf52ba7dd2128c23d73168826f5c48c1f","role":"Evidence"}]}]}