{"id": "c134", "title": "C134 — P6 retains both 3K comparisons and the 3+8 prefix", "filename": "490d_C134_P6_Equal_3K_and_Surviving_3plus8_Prefix_20260922.md", "role": "Research action", "step": 134, "sha256": "dfc432541c3c39cac6d000d238c1a7d3e8a29c91188df6329c51b7273f47ae0b", "bytes": 5513, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C134_P6_Equal_3K_Extension_20260922/490d_C134_P6_Equal_3K_and_Surviving_3plus8_Prefix_20260922.md"], "download": "/sources/dfc432541c3c39cac6d000d238c1a7d3e8a29c91188df6329c51b7273f47ae0b.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Mirror / 529"], "excerpt": "C134 — P6 retains both 3K comparisons and the 3+8 prefix\n\n22 September 2026 · One bounded extension of C129 using C133's corrected P6 alignment. K = 529. The attached File_18 and File_09 remain accessible and match the active controlling copies.\n\nFinding. P6 supplies a fifth valid comparison of the two equal 3K = 1587 ", "content": "# C134 — P6 retains both 3K comparisons and the 3+8 prefix\n\n22 September 2026 · One bounded extension of C129 using C133's corrected P6 alignment. **K = 529.** The attached File_18 and File_09 remain accessible and match the active controlling copies.\n\n**Finding.** P6 supplies a fifth valid comparison of the two equal **3K = 1587** legs. Its Noah leg is **5296→3709 BC**; its native-Creation leg is **4416→2829 BC**, where **2829 is the existing generated 8K preimage of admitted Conquest AD 1403**. All figures in this shorthand are paired bases. Both legs, the generated preimage, and the Conquest connection already occur in the frozen graph. Their comparison adds no historical node or source operator.\n\nThe full Creation–Conquest–Flood **3+8+2** path remains unavailable at P6 because its final 2K would require ordinary MT Flood **AD 2461**, outside the held source field. The missing continuation does not invalidate the existing **3+8** construction ending at Conquest.\n\n## The two first legs and their surviving continuations\n\n| Construction | Complete first-leg BC pairs | Both component spans | Continuation |\n|---|---|---:|---|\n| C10/C12 Noah construction | **5297t/5296n → 3710t/3709n BC** | **1587 = 3K** | To the `7t/6n BC` comparison landing: **3703 = 7K**. |\n| Native Creation / Conquest construction | **4417t/4416n → 2830t/2829n BC** | **1587 = 3K** | To reflected Conquest `AD 1403t/1404n`: **4232 = 8K**. |\n\nThe first row joins an actual **MT cumulative Cainan-ON Flood member** to actual **SP regular G3 companion Noah birth**. Its landing is an existing comparison boundary; the graph makes no independent historical birth claim for it. The second row joins a sourced **fixed native SP Creation member** to a **generated comparison boundary**, then to a sourced reflected Conquest member. Creation and Conquest have no new Gear application.\n\nThe second continuation passes File_09's componentwise civil calculation:\n\n\\[\n2830+1403-1=2829+1404-1=4232=8K.\n\\]\n\nThe full native-Creation prefix similarly gives\n\n\\[\n4417+1403-1=4416+1404-1=5819=11K=3K+8K.\n\\]\n\nIn the existing graph these are **`C127_3K_1403`**, **`C127_8K_1403`**, and **`native11_5`**. Their equations cancel exactly. The Noah first leg is **`P6_3`**; its 3+7 sum and its 3+17 mixed-20K sum also cancel through their existing graph edges. No unavailable Flood member enters any of these proofs.\n\n## The displacement extends to 880\n\nSubtracting the two existing 3K edge equations gives equality of their endpoint displacements. In BC paired bases,\n\n\\[\n\\boxed{5296-4416=3709-2829=880.}\n\\]\n\nThe retained cumulative LXX-OFF member is **5284**. Consequently the same displacement splits as\n\n\\[\n\\boxed{880=(5284-4416)+(5296-5284)=868+12.}\n\\]\n\nThe sourced opening bracket **5296→5290→5284 = 6+6** supplies the 12-year remainder. The mixed-20K edge, paired reflections, opening self-Mirror edge and six-year member edge give the midpoint and doubled remainder as exact dependent equations. The 868 at P6 is a checked comparison between its admitted source endpoints; no new graph edge is inserted for it.\n\n| Row | Noah-construction first leg, BC bases | Creation→generated first leg, BC bases | Endpoint displacement | Doubled opening offset |\n|---|---|---|---:|---:|\n| N01 | 5292→3705 | 4420→2833 | 872 | 4 |\n| N02 | 5293→3706 | 4419→2832 | 874 | 6 |\n| N03 | 5294→3707 | 4418→2831 | 876 | 8 |\n| N04 | 5295→3708 | 4417→2830 | 878 | 10 |\n| **P6** | **5296→3709** | **4416→2829** | **880** | **12** |\n\nThe extended sequences are therefore **872, 874, 876, 878, 880 = 868 + (4, 6, 8, 10, 12)**. They describe a finite correspondence between different source roles. They do not identify Creation with cumulative Flood, Noah with the generated preimage, or establish one constant translation across rows.\n\n## What the extension establishes\n\nP6 retains **3+7**, **3+8**, the equality of their **3K** first legs, its mixed **20K**, and its single **17K** diagonal. The ordinary MT Flood continuation still requires **2461**, and the full 17K square still requires absent cumulative ON **6342 BC** and alternate MT **2651n BC**. The independently supported **2651t** cannot fill that Nisan vacancy. No wider Creation expansion or Shem join is established here.\n\nThis also corrects **C129's fifth-row exclusion**, which paired P6 with Creation4421/generated2834/Conquest1398. C133 established that the actual P6 alignment is **4416/generated2829/Conquest1403**. Thus C129's four main rows and distinction between source roles stand, while its restriction of the equal-3K comparison to four rows is superseded. The full Conquest-mediated **13K** path still has four admitted rows. C05's opening13 comparison at Creation4421/Flood2456 remains the separate opposite boundary.\n\n## Evidence and next step\n\n**42 bounded assertions** verify the current controls, typed endpoints, generated status, exact edge combinations, both seasonal components, the 880 displacement and the remaining exclusions. These assertions are verification checks, not independent witness counts. The inherited graph remains **208 nodes/rank 208**, with no canonical change or new regular Gear; scope remains **Noah/Shem/Flood**. No old campaign was rerun, and original interrupted Reports 11–25 remain unestablished.\n\n**Best next bounded step:** derive P6's surviving **17K** comparison through its admitted Creation, Conquest and reflected Noah endpoints, and test precisely which internal Flood subdivisions remain unsupported.\n", "evidenceLinks": [{"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-45851004c5864229", "title": "File 09"}]}