{"id": "c148", "title": "C148 — Exact partitions share dependencies rather than independent confirmations", "filename": "490d_C148_529_Mirror_Bounded_Step_20260923.md", "role": "Research action", "step": 148, "sha256": "9613efd9ce0737af443ec5bf2481d7e925ac884e47c0f0534bc41650b0d0baaa", "bytes": 2317, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C136_C155_529_Square_Batch_20260923/C148/490d_C148_529_Mirror_Bounded_Step_20260923.md"], "download": "/sources/9613efd9ce0737af443ec5bf2481d7e925ac884e47c0f0534bc41650b0d0baaa.md", "format": "md", "derived": false, "tags": ["Regular", "Mirror / 529"], "excerpt": "C148 — Exact partitions share dependencies rather than independent confirmations\n\n23 September 2026 · Bounded step 13 of 20 (C136–C155).\n\nThe 20K total, equal 3K leg, conserved 17K route and square residual relations follow from the local basis. The certificate gives exact signed equation combinations; adding these con", "content": "# C148 — Exact partitions share dependencies rather than independent confirmations\n\n23 September 2026 · Bounded step 13 of 20 (C136–C155).\n\n**The 20K total, equal 3K leg, conserved 17K route and square residual relations follow from the local basis.** The certificate gives exact signed equation combinations; adding these consequences does not raise its rank.\n\nExamples:\n\n* (A−X)+(D+X)=A+D=20K.\n* (b+q)−(z+q)=b−z=3K.\n* (D+X)−(D−b)−(b+q)=X−q=6K−868=4K+190.\n* (D+X)−(D−b)−(M−f)=b+f+X−M=15K.\n\nThe last identity becomes b+f=13K−δ when X−M=2K+δ. The equal-diagonal conditions similarly force U−D=X−M, and therefore the square's ±δ residuals. The Noah split follows from X−Z=7K.\n\nConsequently, once the retained basis is accepted, observing all three δ=0 manifestations does not supply three independent new constraints. This is a useful explanatory reduction, not a dismissal of the source comparisons. The remaining evidential question is why the particular source profiles and alignments provide this basis in the first place.\n\nThe certificate's dependence proofs apply to numerical equations. They cannot manufacture an absent source endpoint, identify two different event roles, or convert generated z into an attested event.\n\n## Source and scope control\n\nAll numerical bases in this packet stand for paired coordinates: BC base B is (B+1)t/Bn BC; reflected AD base A is AD At/(A+1)n. Thus a cross-Mirror same-season span is B+A, after the civil no-year-zero subtraction. AD stations are reflected source events, not historical AD occurrences. K=529 throughout.\n\nRegular Gears remain restricted to Noah/Shem/Flood. Creation and Conquest are fixed source-field selections. C133–C135 corrections remain controlling. The C127 graph and canonical controls are frozen; source-field admission is distinguished from an existing graph node and from a generated comparison coordinate. No wider N01/N03 expansion or missing N03 Shem join is repaired. Original Reports 01–10 remain previously verified references; interrupted original Reports 11–25 remain unestablished. Check counts are computational assertions, not independent historical witnesses.\n\nEvidence: `CERTIFICATE.json`; **33 passing assertions** in `RESULTS.json`. The assertion list identifies the actual tests.\n"}