490d C318 — Typed458 source-state decomposition
24 September 2026. Step 5 of the ten-step authorization C314–C323.
The paired458 replacement has a fully typed decomposition on the three rows where C287 is admitted. Its source ingredients are permitted, but the reviewed source passages do not prescribe this exact paired selection.
| Side | Explicit sequence | Net coordinate change |
|---|---|---|
| Cumulative | LXX_OFF Shem_i→LXX_ON Shem_i→LXX_ON Shem_(i+2) | −460+2=−458 |
| Regular | SP Flood_g OFF/T0→MT Flood_g OFF/T0→MT ON→MT ON/T60→MT Flood_(g+1), same boundary | −650+130+60+2=−458 |
Full430 remains fixed. Each source-to-source step retains the selected start/close boundary. No person-companion is applied to MT or to Flood. The cumulative+2 is annual-member selection; the regular+2 is a permitted Noah/Shem/Flood Gear step. They are distinct operations.
The sign convention is explicit: cumulative coordinates are signed BC; regular values in this table are positive BC numbers, equivalently reflected coordinates. The corresponding unreflected signed regular changes would have opposite signs. Calling both actions−458 is valid only in this declared comparison frame.
All five rows admit the initial states and first three regular changes. Both final corners survive only i3/4/5, using SPG1/G2 and restored MTG2/G3. At i6/7 the cumulative final members8/9 and regularGear4 are absent. The formal arithmetic still computes a location there, but no source endpoint is added. Six exact-phase paths are source-admitted; four further component paths are formal failures at these boundaries.
The controlling identity is 650−130−60=460. Therefore both sides have the same displacement and retain17K. The new short span is 600+(460−2)=1058=2K, equivalent to the inherited 598+460. File_18's regular variant fork, cumulative restoration rule, Flood table and restored-MT examples support the ingredients. This is a transparent relation between two previously admitted configurations, not an independent second derivation of every numeric premise.
Verification and limits
57 main assertions and 14 frozen-input/predecessor checks passed. A second main replay produced byte-identical DATA and RESULTS. Separate review scope and agreement are recorded in the evidence. All frozen originals and standing controls remain unchanged. These are verification counts, not independent-witness counts.
Signs and source roles remain explicit. Three admissible compositions do not authorize the missing annual members orGear4, nor establish a prescribed selector.
Mirror/529 remains the focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction x=1 January AD2; no civil year zero. Regular Gears remain Noah/Shem/Flood only. SP minus-one companion is local to SP Noah/Shem. No cumulative/upstream Gear, new endpoint or phase, fitted anchor, global axis, z-law, canonical or graph edit. Capture now; canonize later. Source state, event identity, generated coordinate and phase ancestry remain distinct. Exact arithmetic and source membership do not establish intention or independent historical witnesses.
Decision after this result
C319, proposed and unexecuted: Hold all source contexts fixed and toggle the cumulative+2 annual selection and regular+2 Gear selection independently in a four-case sensitivity test. Which17K and all-K relations actually require coupling them?
The decomposition exposes two distinct choices. Testing them independently will distinguish a source-permitted rectangle from the extra selection needed for its2K+15K form.