C02 — Shem’s 299+299 midpoints and their source-frame limits
21 September 2026 · Bounded continuation of C01.
The held full-430 MT/SP/LXX field supplies no named event at the eight selected Shem midpoints. Two exact patriarchal matches appear when the already-retained SP 215 frame is compared with the 430 frame. A third midpoint matches the fixed SKL Short Babel year-coordinate, with seasonal identity still unestablished.
These qualified matches are preserved below. None requires Gear movement above Noah. The C01 13×529 Noah construction remains established; a corresponding Shem construction with the same fixed Creation endpoints is not established.
1. Tested domain
The principal settings remain full-430, Terah +60 OFF, MT/SP Cainan OFF and LXX native Cainan ON. Regular Gear variation is confined to Noah/Shem/Flood. All other patriarchal rows retain their fixed Normal coordinates. Creation stays G2.
The earlier ten-step evidence already includes SP native-215 Shem grids. Those are checked separately as retained controls, without a new general selector sweep.
The audit reconstructs 54 same-rail Shem birth/death cells: nine each for MT and LXX, and nine each for SP primary/companion in both retained sojourn frames. Twelve cells have length 598: eight in the principal full-430 field and four in SP 215. Thirty-six mixed-rail SP candidates have odd lengths and cannot supply 598; they remain parity controls rather than added comparison states.
Each 598 comparison uses G1 birth/G2 death or G2 birth/G3 death. These are cross-Gear endpoint comparisons. Matched Shem biographies remain 600 years.
2. Complete midpoint register
Numbers below are BC Nisan coordinates in the regular table convention. Each triple reads birth → midpoint → death, with 299 years in each half. A coordinate N has the paired display (N+1)t/Nn BC.
| Shem profile | G1 birth / G2 death | G2 birth / G3 death |
|---|---|---|
| MT, 430 | 2556 → 2257 → 1958 | 2558 → 2259 → 1960 |
| SP primary, 430 | 3206 → 2907 → 2608 | 3208 → 2909 → 2610 |
| SP companion, 430 | 3205 → 2906 → 2607 | 3207 → 2908 → 2609 |
| LXX native ON, 430 | 3336 → 3037 → 2738 | 3338 → 3039 → 2740 |
| SP primary, 215 control | 2991 → 2692 → 2393 | 2993 → 2694 → 2395 |
| SP companion, 215 control | 2990 → 2691 → 2392 | 2992 → 2693 → 2394 |
None of these twelve midpoints matches a Noah, Shem or Flood event in the tested four-profile register. None of the eight full-430 midpoints matches the fixed patriarchal birth/death rows of the full-430 MT/SP/LXX profiles either. This is a finite-domain result, not a claim about every repository event or every selector combination.
3. Two exact fixed-patriarch matches across retained frames
| Shem endpoints | Named midpoint | Source qualification |
|---|---|---|
| 3208 → 2909 → 2610 | SP Mahalalel death, 2909 BC | Shem is SP full-430 primary, G2 birth/G3 death; Mahalalel is fixed Normal SP native-215. |
| 2991 → 2692 → 2393 | MT Jared death, 2692 BC | Shem is SP native-215 primary, G1 birth/G2 death; Jared is fixed Normal MT full-430. |
The midpoint dates come directly from File_18:
- §3.1 gives native SP Mahalalel
3804→2909. Its death is not Gear-shifted. Under full-430 its death would be 3124, so the exact 2909 match explicitly requires the native-215 record. - §2.1.3 gives minimum MT Jared
3439→2477; the held full-430 adjustment gives3654→2692. Jared receives no further Gear movement.
Both seasonal components check. For the Jared witness:
These are source-qualified comparisons between different chronological frames. They provide named middle events, while their settings remain part of each witness. They do not supply a same-frame replacement for the Noah midpoint in C01.
4. Fixed SKL anchor: one numerical midpoint match
The SP companion comparison gives:
File_18 §7.1 independently retains 2906 BC as the Sumerian A / SKL Short Tower of Babel anchor. Its SKL Flood coordinate is 20886 BC. The midpoint label must therefore remain Babel, with its own source status.
The 2906 datum is unsuffixed in that primary-anchor table. Its numerical-year agreement is established here; a seasonal identification with the regular Shem midpoint pair 2907t/2906n BC is not established. No SKL ±2, ±720, apparent-age adjustment or Rounded Mirror convention is activated. In particular, the other SP companion midpoint at 2908 is not completed by importing a new SKL Gear into this audit.
This is a captured cross-corpus coordinate match. It remains separate from the phase-qualified patriarchal comparisons above.
5. Why C01’s Noah midpoint does not automatically become a Shem midpoint
C01’s first complete reflected chain is:
with 299+299. Here the numbers are AD Tishri numerals of complete reflected pairs; for example 2458 means AD 2458t/2459n.
The corresponding MT Shem endpoints are each 500 years earlier after reflection:
The two outer events are retained Shem death/birth. The translated middle coordinate 2257 has no named event in the tested regular register. Translating the old SP Noah-death label by 500 does not give it a new source identity. The second C01 chain similarly yields midpoint 2259 without a retained regular event.
Holding C01’s SP Creation members fixed makes the numerical limit precise:
| Endpoint family | First width | Second width | Third width |
|---|---|---|---|
| C01: MT Flood → MT Noah birth → SP Noah birth | 6877 | 7475 | 8125 |
| Corresponding Shem death → MT Shem birth → SP Shem birth | 6377 | 6975 | 7625 |
Every target has moved by −500. The gains 598 and 650 survive, but these three Shem widths are not successive 25/23 expansions:
Thus the preserved interval shape does not preserve the anchored 13-fold expansion. Restoring 6877 by moving the Creation source 500 years earlier would require 4919 or 4917 BC, both outside the held SP Creation field. Those calculated locations are not admitted Creation members.
6. Evidence and research status
Five frozen inputs support evidence/check_c02.py: current File_18 and File_09, C01’s report and result registry, and the original three-Gear domain. The checker independently reconstructs the regular fields, agrees with all 36 cells of the archived Shem grids, examines 96 Noah/Shem/Flood records and 186 fixed patriarchal records, and keeps six fixed SKL primary anchors in a separate registry.
170 checks pass, including input integrity, coherent lifespans, the retained-grid comparisons, endpoint membership, mixed-rail exclusions, exact seasonal halves and the anchored-expansion diagnostic. These are verification assertions, not counts of independent evidence. The prior campaign and C01 calculations were not rerun.
The result preserves two sourced cross-frame patriarchal midpoints and one external year-coordinate match. It also establishes the precise limit of transferring C01’s Noah construction to Shem. No new source node, upstream Gear, revised historical graph, primer or canonical amendment is introduced.
Best next bounded step: express C01’s two Creation-to-Noah chains as qualified extensions of the existing three-coordinate Mirror description, starting with their shared N02/N04 endpoints. Retain the C02 midpoint matches as separate controls. High is sufficient for that bounded coordinate check.