C135 — P6's sourced 17K route retains a −1/+1 Flood subdivision
23 September 2026 · One bounded continuation of C134. K = 529. The attached File_18 and File_09 match the active controlling copies. C133's corrected P6 alignment and C134's five-row equal-3K comparison remain controlling.
Finding. P6's existing 8993 = 17K interval has a comparison route through admitted native Creation and reflected Conquest and Noah endpoints:
The final 2306 = 4K+190 interval also has an entirely sourced subdivision through the ordinary and alternate MT G3 Flood-start pairs:
Thus P6 retains a Flood-mediated 17K comparison route with opposite one-year residuals. Its exact 2K+190+2K partition remains unadmitted, and its exact Creation–Conquest–Flood 13K prefix is not restored.
The admitted endpoint route
All AD pairs below are reflected source events. They are not assertions that the biblical events occurred historically in those AD years. Every station has a typed source node in the frozen C127 graph.
| Station | Complete pair | Forward interval to next station |
|---|---|---|
LXX cumulative derived-OFF Flood member, P6_c | 5285t/5284n BC | 868 |
Fixed native SP Creation member, C5_creation | 4417t/4416n BC | 5819 = 11K |
Reflected Conquest member, C5_conquest | AD 1403t/1404n | 1057 = 2K−1 |
Reflected ordinary MT G3 Flood start, N04_f | AD 2460t/2461n | 190 |
Reflected alternate MT G3 Flood start, N04_v | AD 2650t/2651n | 1059 = 2K+1 |
Reflected SP G3 companion Noah birth, P6_s | AD 3709t/3710n | — |
The ordinary MT profile is full-430, Terah-zero, Cainan OFF. The retained alternate profile is full-430, Terah +60, Cainan ON. Both Flood stations are G3 starts, with no MT companion added. The SP Noah endpoint alone carries its SP G3 companion tag. Creation and Conquest retain their fixed source-member roles.
Both seasonal components reproduce every interval. In particular,
The complete span is still
The 529-unit accounting remains exact:
Here 868+190=1058=2K is an algebraic grouping of two differently located comparisons. Their separate event roles and positions remain explicit.
Why the symmetric subdivision fails
Starting at admitted Conquest base 1403, an exact 2K advance would require ordinary Flood base 2461. Working backward 2K from admitted Noah base 3709 would require alternate Flood base 2651. The resulting formal pairs would be AD 2461t/2462n and AD 2651t/2652n, neither admitted in the held MT profiles.
The nearest admitted upper boundaries are instead AD 2460t/2461n and AD 2650t/2651n. Selecting those existing G3 starts moves each proposed internal boundary one year earlier. It shortens the Conquest→ordinary-Flood interval by one and lengthens the alternate-Flood→Noah interval by one, while their 190-year profile separation remains intact.
| Subdivision of Conquest→Noah | Ordinary Flood base | Alternate Flood base | Three intervals | Status |
|---|---|---|---|---|
| Required equal-2K subdivision | 2461 | 2651 | 1058 + 190 + 1058 | Formal arithmetic; both Flood pairs unadmitted |
| Existing G3-start subdivision | 2460 | 2650 | 1057 + 190 + 1059 | All intermediate pairs sourced |
The presence of the numerals 2461n and 2651n inside the admitted pairs does not license the missing 2461t and 2651t pairs. Phase identity controls the comparison.
Using the admitted ordinary Flood gives 4416+2460=6876=13K−1 in paired-base shorthand; its componentwise civil span is likewise 6876. It therefore supplies a sourced interval of a different length from the missing P6 13K continuation. The original 1058-sided C10 square also remains unadmitted; this step does not broaden that square's definition.
What the graph proof establishes
The 868 comparison is recovered from N04's existing 868 edge and matched one-year source-member adjacencies for cumulative Flood and native Creation. This derivation does not use P6's 17K edge and does not apply a Gear to Creation or Conquest. The 1057 comparison follows from N04's existing Conquest→Flood 1058 edge after the admitted Conquest advances one year. The 1059 comparison follows from N04's alternate-Flood→Noah 1058 edge and the measured one-year difference between its SP G2 primary Noah and P6's SP G3 companion Noah.
The certificate expresses the complete route as an exact combination of existing graph equations. Several comparison segments are derived relations rather than newly stored direct edges. The aggregate 2306 proof and complete subdivision use the retained 17K interval, so this is a dependent subdivision of an established span, not an independent new 17K calibration.
44 bounded assertions verify source/profile/phase identity, the exact equation combinations, both seasonal components, the opposite one-year residuals and the surviving exclusions. An isolated replay reproduces the certificate and results. No historical graph node or edge is added; the inherited graph remains 208 nodes/rank 208. Regular Gears remain restricted to Noah/Shem/Flood, no canonical file is revised and no historical campaign is rerun. Original interrupted Reports 11–25 remain unestablished.
Best next bounded step: test whether the same admitted boundary choices support a 17K equal-diagonal square with 1059-year sides, while keeping it distinct from the excluded 1058-sided C10 square.