C129 — Are the two 3×529 legs the same source construction?

22 September 2026 · One bounded comparison of C10/C12 and C119–C128. Set K=529, so 3K=1587.

Finding. Four N01–N04 rows share the width 1587, the same branch labels, and the established 1058-year continuations. They do not share a 3K source segment: the 3+7 leg joins an actual MT cumulative Cainan-ON Flood member to an actual SP regular Noah birth; the 3+8+2 leg joins a native SP regular Creation member to a generated BC preimage of reflected Conquest. The measured offset between the two legs changes by two years from row to row. Their equality establishes a finite, phase-consistent numerical correspondence within the retained packet, not a new source-preserving transfer of events.

The matched field

The numerical entries below are Nisan BC pair bases, except the reflected Conquest column (AD pair base). Thus 5293 BC represents 5294t/5293n BC, and AD1400 represents AD1400t/1401n. N01/N03 have retained partial Creation–Flood expansions; N02/N04 have the full prior expansions. All four displayed prefix paths are admitted.

For the principal N02 row, the actual paired first legs are 5294t/5293n → 3707t/3706n BC and 4420t/4419n → 2833t/2832n BC. Both t-to-t and n-to-n differences equal 1587. The generated endpoint has no assigned historical event. Its further paired connection to the reflected Conquest boundary is 2833t BC → AD1400t and 2832n BC → AD1401n; both cross-axis counts are 4232 after subtracting the absent civil year zero. Reflecting a 3K leg reverses its order; it does not turn Creation into Noah or a generated preimage into cumulative Flood.

What the equality depends on

In N01–N04 order, put $i=0,1,2,3$. For the BC bases, the two constructions give

The Creation construction holds $c_i-z_i=3K$ because $c_i+q_i=11K$ and the generated preimage satisfies $z_i+q_i=8K$; it continues by $f_i-q_i=2K$. The Noah construction holds $A_i-X_i=3K$ between two different, actual source rows; its supplied 3+7 allocation is recorded in C12's R16 and continues by $X_i-Z_i=7K$. The C12 allocation is an endpoint choice in that reconstruction, whereas the generated boundary $z_i$ is a definition following the Conquest attachment. Neither construction supplies the other's first-leg source relationship.

There is nevertheless a checkable relationship between the selected rows:

This is a measured affine displacement, not a constant transport rule. It also separates into the existing C12 input $\ell_i-c_i=868$, where $\ell_i=5288-i$ is the LXX cumulative OFF Flood comparison member, and the cross-cumulative remainder $A_i-\ell_i=4+2i$. Accordingly 872, 874, 876, 878 = 868 + (4, 6, 8, 10). The 868 attachment retains its prior input status; the second term changes with row selection. No extra regular Gear at Creation or cumulative station is introduced to explain it.

The branches have a shared surrounding scaffold. C10's N02 and N04 primary records explicitly compare the sourced regular SP Noah → alternate-profile MT Flood 1058 BC intervals (3706→2648 and 3708→2650) with the distinct reflected Conquest → ordinary MT Flood 1058 AD intervals (1400→2458 and 1402→2460). The alternate MT Flood profile is Cainan ON/Terah +60, 190 years from the ordinary MT Flood coordinate. These are genuine retained 2K correspondences with separately labeled events; they do not identify the preceding 3K legs. N01/N03 retain their partial/close qualifications, including N03's missing full Shem join.

The fifth C10 row, 5296→3709→6 BC, sharpens the boundary. One can pair its 3K arithmetic with native Creation 4421→2834 BC, but the required reflected Conquest member would be AD1398, outside the held Conquest field. C122 therefore rejects its 3+8+2 13K source path even though both isolated 3K subtractions still equal 1587. Numeric equality alone cannot enlarge the admitted four-row domain.

Evidence and decision

The C129 checker made 83 exact checks on the four row matches and the excluded fifth row. Its frozen inputs are controlling File_18/File_09, C10 results/report, C12's basis certificate, C122's certificate/report, the unchanged C127 graph and C128's checkpoint. The input and artifact SHA256 manifests, one isolated byte-identical replay, and all selected dependencies accompany the evidence ZIP. C127 already contains both classes of 3K edges; C129 does not alter that graph or its 208-node, rank-208 state. No earlier campaign was executed, no new regular Gear was used, and original interrupted Reports 11–25 remain unestablished.

Best next bounded step: on the fully supported N02/N04 rows, test whether the retained 868 attachment, the varying cross-cumulative remainder, and the paired 2K continuations yield a dependent closed graph relation, without identifying unlike endpoint roles or adding a source operation. High sufficient.