C128 — Ten-step Mirror synthesis, C119–C128
All ten bounded steps are complete. The principal gain is a source-qualified connection between the local 8×529 construction and the retained 11/13-fold Conquest–Flood paths, together with a complete Peleg-biography palindrome within the same local complement.
Structural results
With K=529, seven native Creation–Conquest pairs now have the exact refinement:
Four retain the qualified Flood continuation:
N02/N04 retain the complete earlier expansion support; N01/N03 remain partial paths with Flood-close endpoints. The new middle boundaries are generated 8K preimages, not newly identified historical events. The equivalent3+10 and11+2 descriptions follow from the same equations and are not independent529 calibrations.
The fixed Moses-birth, Exodus and Moses-death/Conquest annual boundaries have complement windows 1180, 1340, 1420, all centered on 4K=2116. The crossed birth/Exodus span remains 1260; the crossed birth/Conquest span is 1300=1260+40. These are consequences of8Kand the sourced anchors.
Inside the 1420-year Conquest window, the Peleg correspondence forms:
refined by the Isaac/Abram birth pair as:
The two 239-year segments preserve Peleg’s lifespan. The central 4 joins generated 2114 and ordinary reflected 2118 around 2116. The 191 birth-chain relation and 48 Abram-to-Peleg-death interval recover 239, linking C118’s minimal genealogy to the complete biography symmetry.
What is supplied and what follows
The grammar is small but source-sensitive:
| Ingredient | Status |
|---|---|
| Named source records, chronology profiles and phase rules | Controlling inputs |
| Retained 11K and 2K endpoint relations; local 8K construction | Held relations with identified endpoints |
| z+q=8K for a named Conquest member q | Definition of a generated preimage |
| 3K, 10K, 13K refinements | Algebraic consequences |
| S(x)=8K−x=T₈K∘R | Derived local complement; global R unchanged |
| Peleg biography palindrome and famine images | Consequences of complement plus sourced biography/windows |
| Joseph transaction 1875 or 1874 | Proposed narrative assignment |
| Derived 4413 Creation closing origin | Conditional 300→299 compression; excluded from the graph |
The primary famine midpoint remains 1875t BC. Its ordinary reflected image is AD1875n and its 8K-translated image AD2358t. The proposed 1875n and 1874n year boundaries lie on either side; reflection and translation have different suffix behavior. C126 records the full table. The exact Peleg-birth alignment at 1875 does not independently settle the transaction year.
A boundary diagnostic
For any declared Creation/Conquest pair, write ε=c+q−11K and definez=8K−q. Then:
The seven native interior pairs have ε=0. At Conquest 1406, native Creation 4414 has ε=1; conditional 4413 has ε=0. The extra year therefore remains on the left leg instead of disappearing during the 8K insertion.
The unrelated 1874→Peleg-reflection interval has residual −1 from 8K. Summing that width 4231 with native closing 5820 gives 19K numerically, but the intervals overlap and are not consecutive. Their union is 6771 and overlap 3280. C128 records this concrete negative control so opposite residuals cannot silently become a new 19K source path or a common date adjustment.
Completed reports
| Report | Bounded result |
|---|---|
| C119 | Seven native shared-target 3K+8K paths; closing residual preserved |
| C120 | Three sourced annual adjacencies resolve the three old placement freedoms |
| C121 | Both calendar components verify the new 8K preimages |
| C122 | Four retained 3+8+2=13 paths, with full/partial distinctions |
| C123 | Minimal equations and the derived local complement operator |
| C124 | Moses/Exodus/Conquest complement windows and derived 1300 |
| C125 | Peleg’s complete biography palindrome and 191/48 refinement |
| C126 | Two famine images with exact midpoint and candidate-boundary phases |
| C127 | Finite integration preserving historical/generated source identities |
| C128 | Source/consequence register and residual-incidence diagnostic |
The final graph is 208 nodes, 382 durations, 92 global reflections, 12 coordinate equalities, 20 component expressions, 27 component equations; rank 208. C120’s three adjacency relations replace the old diagnostic pins. C127 then defines 30 additional coordinate variables without new source-placement freedom. Earlier graph collections remain unchanged prefixes. Full rank concerns these encoded coordinates, not historical or theological probability.
All ten new checkers passed and each had one isolated byte-identical replay. Earlier research campaigns were not executed. The final ZIP includes all ten reports, checkers, certificates, source hashes, omission/dependency evidence, intermediate checkpoints, and the full graph at C127/GRAPH.json. The reading guide identifies the active files.
Regular Gears remain restricted to Noah/Shem/Flood. No new Gear was applied; no source/canonical file was changed; quarantined primers and other excluded variants remain closed. Dean’s Peleg/nations and integrated theological interpretation remains recorded with its narrative status. Historical recovery status is inherited; this new batch does not establish interrupted original Reports 11–25 as completed.
Best next bounded step: compare the new 3+8+2 refinement with the existing 3+7 Noah construction, checking whether their equal 3×529 segments share source structure or only length. High sufficient.