490d C381 — Paired source-path17K compatibility obstruction
24 September 2026. Step 8 of 10 in the C374–C383 authorization.
Repeated paired repairs preserve the endpoint-exchange sum but cannot retain the original17K cross-spans. The complete24-state pairing menu has eight admitted two-step paths. None has the original17K condition at both steps.
Composition forces the cumulative input to move−2 and the regular input+2. The next source frames therefore move their outer corners by
(S,q,R,N) → (S−2,q−2,R+2,N+2).
Both2K sides survive and S+N remains fixed. Every cross-field separation R−S and N−q increases by4. This is a structural obstruction, independent of which P/J label is used on either common edge.
The first original primary rectangle illustrates the result:
| Frame | S | q | R | N | Cross-spans |
|---|---|---|---|---|---|
| Original i=3 pairing | −6345 | −5287 | 2648 | 3706 | 8993 =17K |
| Next composable source pairing | −6347 | −5289 | 2650 | 3708 | 8997 =17K+4 |
The middle source path is cumulative−5885→−5887→−5889 paired with regular3246→3248→3250. Its second cumulative member is available in the wider six-edge cumulative census, but the new pairing is not the original same-index C287 rectangle. The endpoint-exchange sum stays−2639 throughout.
The other original rectangle, at i=5, has no forward regular continuation because its output is Gear3. No source path enters either original17K rectangle from another admitted paired state. The215-year translated branch does not restore the required four-year difference.
Thus the original529-coupled states form a selected set of local comparisons, not a set closed under repeated forward repairs. The surviving moving-pivot structure still permits an algebraic question: do the two different operator orders agree when both pivots move by the common gain?
Verification and limits
38 main checks and 16 frozen-input/predecessor authentication checks passed. A second main replay produced byte-identical DATA/RESULTS. These checks and the source interpretation were performed by the root agent; no new independent-agent review is claimed. All frozen originals and standing controls remain unchanged. Verification counts are not independent-witness counts.
A preserved endpoint sum does not imply preserved17K separation. No branch adjustment, new cumulative member, fitted anchor or Gear4 is introduced to force closure.
Mirror/529 focus: K=529, E=25/23, P=70/69. Global paired Mirror January AD1; local junction January AD2; no civil year zero. Regular Gears are Noah/Shem/Flood only. SP minus-one person companions remain local to SP Noah/Shem; Flood close is a separate boundary. No upstream/cumulative Gear, new endpoint or phase, fitted anchor, global axis, primer reopening, canonical or graph edit. Capture now; canonize later. Source identity, context, modal binding, generated coordinates and phase ancestry stay distinct.
Decision after this result
C382, proposed and unexecuted: Compare J-then-P with P-then-J along the six admitted consecutive source-edge pairs, using their actual moving pivots. Derive the exact affine condition for equality, contrast it with fixed pivots, and identify any reduced coordinate description without extending the source domains.
The source-path obstruction limits a global529 action, but the coordinated pivot shifts may still give an exact local composition law. Testing the operator order can identify that surviving structure precisely.