# Mirror connections across cumulative and regular MT, LXX, and SP

**Comprehensive branch handoff to the original Astra Strategy–Unification work window**  
**Date:** 20 September 2026  
**Authorial context:** Dean's branch discussion, with arithmetic and source checks by the assistant.  
**Status:** Research handoff. Source coordinates, exact arithmetic, generated coordinates, theological interpretation, and unfinished research are distinguished below.

## 1. Receiving-window instructions and main results

Dean has now explicitly authorized this comprehensive handoff. Earlier in this branch he prohibited unsolicited reports while explaining the construction; that prohibition governed the intervening discussion and is superseded for this requested document. This handoff supplements the earlier **490d_MT_Cumulative_Regular_Branch_Handoff_20260920 (1).md**. Its earlier instruction to defer the Mirror is superseded by the subsequent Mirror discussion recorded here. It does not replace results independently completed in the original window.

The main results to carry forward are:

1. The cumulative LXX Cainan-OFF Flood boundary **5291t/5290n BC** and its paired reflection **AD 5290t/5291n** delimit **10580 = 23×460** years. Expansion by **25/23** gives **11500**, the self-Mirror span of the native Cainan-ON boundary **5751t/5750n BC**.
2. Translating the middle MT/LXX cumulative Flood weeks by **5290 = 23×230** produces the Christ-period **6+1+6 = 13** arrangement. Adding the cumulative Shem lifespan **600**, but increasing the translation by **598**, supplies the reflected MT Shem week that completes **7+7 = 14**.
3. SP integrates into the same Christ-period field by Flood translations **4715/5175** and Shem translations **5313/5773**, for Cainan OFF/ON respectively. The SP Flood week and the MT Flood week are exact paired reflections of one another.
4. SP's translated Flood boundaries mark entry into the **6th** and **13th** years in Dean's interpretation; the LXX boundaries mark completion of **6** and **13**. The underlying SP one-year person-station mechanism belongs to **regular** chronology. It is not a new cumulative rail.
5. The SP cumulative Shem week connects point-to-point across the Mirror to MT cumulative Creation by **19320 = 23×840**, or **19780 = 23×860** with cumulative Cainan ON. The full apparent-age addition is **30**, giving **19350 = 45×430** in the OFF comparison.
6. MT cumulative Creation to regular Creation is **9890 = 23×430**. The regular-MT-to-reflected-Conquest bridge is **5520**, giving **15410 = 23×670**, or **15870 = 23²×30** after adding cumulative Cainan. The **6500** expansion route has an explicit *derived intermediate coordinate*; it must not be relabeled as ordinary regular Creation.
7. The selected regular SP G1 Flood closing boundary **3106t/3105n BC**, also reached by the specified regular LXX Cainan-OFF comparison, has self-Mirror span **6210 = 23×270 = 69×90**. It lies **2185 = 23×95** from the cumulative LXX OFF boundary on each side.
8. Their two cross-flank comparisons are **8395 = 23×365**. These named boundaries are the intended entry point for further regular **MT/SP/LXX/BJ** research in the original window. No exhaustive four-source interweaving was established in this branch.

For use below: **source-controlled** means supported by the checked project sources; **checked arithmetic** means exact within the stated endpoint construction; **derived** means a translated or expanded coordinate rather than a newly identified event; **interpretation** identifies Dean's theological reading. Numerical equality alone does not identify events, authorize every selector combination, or establish literary dependence.

The **1876 primer**, the **Moses/1446 primer**, and **Rounded chronology** remain outside this continuation unless Dean reopens them. Actual Exodus/Conquest Mirror comparisons below do not reopen those primer hypotheses.

## 2. Reading the notation and applying the Mirror

### 2.1 Dates, phases, and elapsed years

- Dates are BC unless AD is explicitly written. Within one BC period, forward elapsed time lowers the BC numeral. Dean's conversational “BC date + span” generally means moving forward in time, not adding to the positive BC numeral.
- There is **no year zero**. For matching seasons across eras, elapsed years are **BC numeral + AD numeral − 1**.
- The paired boundary associated with `Nn BC` is **(N+1)t/Nn BC**. On the AD side it is normally **AD (N−1)t/Nn**. The axis-straddling pair is **1t BC / AD 1n**.
- The `t/n` slash pair covers a half-year. It is not an additional full year or an inclusive-count instruction.
- A field such as **5316–5309 BC** spans **seven elapsed years**, with eight integer boundary coordinates. Its Tishri counterpart is **5317t–5310t BC**. The paired opening and closing are **5317t/5316n** and **5310t/5309n**.
- A table's named **Nisan member**, such as **5311**, is an internal selected member. It must not be confused with the Nisan component of every boundary pair.

The branch's five-year member selection uses part of the seven-year unit, leaving a two-year portion; it does not create an additional five-year rail. Also, the automatic **(N+1)t/Nn** phase partner used here is distinct from File_18's separately tabulated **Aaron/Tishri cumulative trunk**, which is 3.5 years from its Moses/Nisan trunk. Those are different phase constructions.

### 2.2 The controlled paired Mirror rule

File_09 controls the following rule [S1]:

\[
Yt/(Y-1)n\;\mathrm{BC}
\quad\longmapsto\quad
\mathrm{AD}\;(Y-1)t/Yn.
\]

The axis is the start of **January 1, AD 1**, at the **1 BC/AD 1** boundary. The simplified phase model uses Tishri ≈ October 1 and Nisan ≈ April 1, so these pairs are January-centered. The rule reverses the assignment of the two numeric years while preserving the ordered half-year `t/n` display.

Examples:

| BC pair | Paired reflection |
|---|---|
| 5751t/5750n BC | AD 5750t/5751n |
| 5291t/5290n BC | AD 5290t/5291n |
| 3106t/3105n BC | AD 3105t/3106n |
| 1407t/1406n BC | AD 1406t/1407n |
| 2t/1n BC | AD 1t/2n |
| 1t BC / AD 1n | 1t BC / AD 1n |

Reflection reverses a whole interval's order: the original closing boundary becomes the reflected opening boundary. Forward translation and reflection are different operations. In particular, the reflection of a translated interval must be computed after reversing its endpoints.

File_09 separately recognizes standalone single-date Mirror comparisons. Do not substitute them for this paired construction. For example, the paired **1407t/1406n BC → AD 1406t/1407n** span is **2812**; the two standalone same-numeral comparisons have widths **2813** and **2811** [S1].

### 2.3 Four different operations used in this handoff

| Operation | What changes | Required distinction |
|---|---|---|
| Translate a date/week | Every endpoint advances or retreats by the stated duration | Does not itself reflect the week |
| Reflect a paired week | BC/AD placement, component display, and endpoint order | Uses the fixed January AD 1 axis |
| Convert an interval by 25/23 or 70/69 | The numerical duration | Dates require a declared fixed endpoint or center |
| Compare symbolic scales | Meaning assigned to corresponding durations | Does not change the literal source chronology |

When an outer pair is expanded “from the Mirror axis,” the branch calculations use the **pair center's distance** from that axis, then preserve the half-year pair. They do not dilate the half-year separation itself. A sum of two reflected bridges can also exclude a central interval; it must not automatically be called the full outer self-Mirror span.

## 3. Source fields and state qualifications

The controlling cumulative register and Creation/Apparent fields were rechecked in File_18 and the cumulative comparative report [S2, S3].

### 3.1 Cumulative Flood and Shem fields

All values in this table are Nisan-coordinate field boundaries; apply the phase rule above to obtain paired boundaries.

| Tradition/state | Flood / Shem-death comparison field | Shem birth / Noah-death field |
|---|---|---|
| LXX native, Cainan ON | **5750–5743** | **6350–6343** |
| LXX leveled, Cainan OFF | **5290–5283** | **5890–5883** |
| MT restored, Cainan ON | **5296–5289** | **5896–5889** |
| MT native, Cainan OFF | **4836–4829** | **5436–5429** |
| SP restored, Cainan ON | **5176–5169** | **5776–5769** |
| SP native, Cainan OFF | **4716–4709** | **5316–5309** |

Each matched Shem birth-to-death field is **600** years. Cumulative Cainan contributes **460**. The comparison labels retain separate node classes: a cumulative Flood marker, cumulative Shem-death seam, and Arphaxad boundary are not thereby identical regular historical events. File_18 additionally distinguishes each source's chief Flood-marker convention [S2].

### 3.2 Full SP cumulative context

The official SP cumulative execution uses **Terah 145**, with Joshua's death at **1296 BC** as its downstream anchor [S2].

| Role | OFF field | OFF Nisan member | ON field | ON Nisan member |
|---|---|---:|---|---:|
| Noah birth | 6266–6259 | 6261 | 6726–6719 | 6721 |
| Shem birth / Noah death | 5316–5309 | 5311 | 5776–5769 | 5771 |
| Flood marker / Shem death / Arphaxad comparison boundary | 4716–4709 | 4711 | 5176–5169 | 5171 |

The Noah field is obtained by adding **950** to the Shem-birth field; the latter is obtained by adding **600** to the Flood field. These are cumulative lifespan-stack relations, not regular birth-spacing rules.

At these Noah/Shem/Flood nodes, SP lies **120 years later** than matching MT cumulative coordinates. This is a local vector: it must not be propagated to cumulative Creation. The common Cainan-OFF Creation envelopes are LXX **14441–14434**, MT **14011–14004**, and SP **13403–13396**; the corresponding offsets there are **+430** and **−608**, not +454 and −120 [S3].

An earlier generated SP Terah-205 comparison added **60** upstream. It remains separate from the official Terah-145 execution and is not needed for the Mirror constructions here. The regular Sojourn-215 selector and the regular SP personal −1 rail are not automatically propagated into the cumulative stack.

### 3.3 Regular states that matter here

Regular Cainan insertion is **130**, distinct from cumulative **460**. In the native full-430, Terah-0 comparison, LXX has Cainan **ON** and MT/SP have Cainan **OFF** [S4].

| Regular source/state | G1 Flood start→close | G2 start→close | G3 start→close |
|---|---|---|---|
| MT native OFF | 2456→2455 | 2458→2457 | 2460→2459 |
| LXX native ON | 3236→3235 | 3238→3237 | 3240→3239 |
| SP native OFF | 3106→3105 | 3108→3107 | 3110→3109 |
| LXX OFF, removing native 130 | 3106→3105 | 3108→3107 | 3110→3109 |

This establishes the precise SP/LXX-OFF co-registration used in the closing-flank argument. **3105 is the closing boundary of the selected G1 Flood year.** It is not the only possible Flood date across all Gears or selectors.

The SP-only personal companion rail applies to Noah and Shem. For example, in the full-430/Terah-0 frame G1 Noah births are **3706/3705**, and G1 Shem births **3206/3205**. In the 215 frame the corresponding G1 Shem births are **2991/2990**. The Flood's own start→close year is a distinct mechanism [S4].

## 4. Earlier MT cumulative–regular foundation

This section is context for the Mirror work; the earlier clarified MT handoff remains the fuller register [S5].

### 4.1 The 690-year straddles

In regular MT G2/Normal:

| Comparison | 430-year frame | 215-year frame | Width |
|---|---|---|---:|
| Flood, Cainan ON/Terah +60 → Shem death, OFF/Terah 0 | 2648→1958 | 2433→1743 | 690 |
| Noah birth, ON/+60 → Shem birth, OFF/0 | 3248→2558 | 3033→2343 | 690 |

The birth comparison translates both endpoints **600 years earlier**; the 215 frame translates both **215 years later**. The eight selector rows retain successive differences **60+70+60+25+60+70+60 = 405** in every date column; see Appendix A.

\[
690=23\times30,\qquad690\times25/23=750,\qquad750-690=60.
\]

Dean's residual examples include **2708→2018 = 690**, after extending 2648 earlier by 60 and selecting the alternate 2018 endpoint, and **2588→1898 = 690**, after extending 1958 later by 60 and selecting 2588. **2708** and **1898** are generated positions in this explanation, not automatically new regular event dates. The named regular **+60 selector is Terah**, not Cainan.

Dean interprets the 690 choice as providing strong residual flexibility in the closed field. The displayed examples establish the flexibility; an exhaustive mathematical maximality theorem was not established here.

### 4.2 Core widths and derivative birth/death clarification

| Selected cumulative MT member | Selected regular MT endpoint | Width |
|---|---|---:|
| 5293, Cainan ON | 2648, G2 Flood, 430/ON/+60 | **2645 = 23×115** |
| 4833, Cainan OFF | 1958, G2 Shem death, 430/OFF/0 | **2875 = 25×115 = 23×125** |
| 5293, ON | 2533, G2 Shem birth, 215/ON/+60 | **2760 = 23×120 = 4×690** |
| 4833, OFF | The same 2533 regular birth | **2300 = 23×100** |

The first two widths differ by **230 = 690−460**, and **2645×25/23 = 2875**. Dean's “expansion without expansion” means that both widths already occur between selected endpoints. It is not the literal equality 23×115 = 23×125.

Other early anchors were **4836→1956 = 2880 = 8×360**, **2880−5 = 2875**, and **4836→6 BC = 4830**. The twice-2645 sequence is **5296→2651→6 BC**, with the selected interior sequence **5293→2648→3 BC**. The 6 BC/3 BC/AD 1/AD 2 anchors carry Dean's **3+3+1** interpretation; equal-season elapsed counts use no year zero.

Dean initially emphasized the interior **4835–4829** and restored **5295–5289 BC** corridors after marking the outer **4836/5296** boundaries. The later Mirror work uses the complete seven-elapsed-year fields, including those opening boundaries.

The original arithmetic target families were:

| Base width | Base−598 | Base+598 |
|---|---:|---:|
| 2645 | 2047 | 3243 |
| 2875 | 2277 | 3473 |
| 2760 | 2162 | 3358 |
| 2300 | 1702 | 2898 |

All entries are divisible by 23. This is a target-width register, not a claim that every target has an established endpoint pair. Dean's Gear-2 core and the role of **598 = 600−2** motivated the comparisons; regular Gear transport and cumulative member selection remain separately labeled.

For the derivative +598 relation, Dean explicitly supplied:

| Shem endpoint | Cumulative MT, Dean's G2 selection | Regular MT G2, 215/ON/+60 | Width |
|---|---:|---:|---:|
| Birth | **5891** | **2533** | **3358** |
| Death | **5291** | **1933** | **3358** |

\[
5891-2533=5291-1933=3358=2760+598,
\]
\[
5891-5291=2533-1933=600,
\qquad3358=23\times146\longrightarrow3650=10\times365.
\]

The two-year cumulative member selection **5893/5293 → 5891/5291** is explicit. Keep Dean's cumulative G2 designation separate from regular Gear labels. It is not permission to relabel either regular endpoint G1/G3.

The earlier finite search found no **2162 = 2760−598** or **1702 = 2300−598** endpoints in its specified MT field, even with three regular Gears. That limited absence does not refute the two explicit +598 birth/death pairings. Other ±598 targets remain separately endpoint-qualified; the present handoff does not claim to settle every one.

## 5. The SP 120/115 observations that led into the Mirror

The local cumulative offset decomposes as **120 = 115+5**. A five-year member selection inside the seven-year field therefore gives **120−5 = 115 = 5×23**.

Initial comparisons included:

| Comparison, BC | Width | Qualification |
|---|---:|---|
| 4831 MT cumulative Flood member → 4716 SP cumulative Flood opening | 115 | Five-year selection from MT opening 4836 |
| 4716 SP cumulative Flood → 3106 SP regular G1 Flood start | 1610 = 14×115 = 70×23 | Regular 430/OFF/Terah 0 |
| 5316 SP cumulative Shem birth → 3706 SP regular G1 Noah birth | 1610 | Both endpoints 600 earlier than preceding row |
| 3106 SP regular G1 Flood start → 2991 SP regular G1 Shem primary birth | 115 | Changes from 430 to 215 frame; same Cainan OFF/Terah 0 |
| 3166 SP G1 Flood start → 3051 SP G1 Shem primary birth | 115 | The parallel Terah +60 comparison |
| 4716→3106→2991 | 1725 = 15×115 = 75×23 | Two consecutive selected bridges |
| 2991→1 BC | 2990 = 130×23 | Ordinary same-era subtraction |

**Label correction:** 3106/3105 is the selected regular G1 **Flood start/close** pair. 2991/2990 is the selected regular G1 **Shem primary/companion birth** pair in the 215 frame. An early conversational message interchanged those event labels; the arithmetic did not authorize that interchange.

Likewise, a phased **3106t/3105n BC** boundary is the Flood **closing** pair. The full Flood year begins at **3107t/3106n BC**. The paired **2991t/2990n BC** used in the initial exploration is a selected phase construction; retain its provenance separately from the annual primary/companion station labels.

## 6. Exodus/Conquest Mirror anchors

The paired anchors are **1447t/1446n BC** and **1407t/1406n BC**. Their cross-anchor Mirror comparisons are:

| BC anchor | Reflected other anchor | Width |
|---|---|---:|
| 1447t/1446n BC | AD 1406t/1407n | **2852 = 23×124** |
| 1407t/1406n BC | AD 1446t/1447n | **2852 = 23×124** |

For example, **1447+1406−1 = 1446+1407−1 = 2852**. This is a cross-anchor span, not either anchor's self-Mirror width.

The regular MT G2 examples were:

- **2458n→1446n BC = 1012 = 23×44**; extending to **AD 1407n** gives **3864 = 1012+2852 = 23×168**.
- **2648n→1406n BC = 1242 = 23×54**; extending to **AD 1447n** gives **4094 = 1242+2852 = 23×178**.

These actual, phase-qualified anchor comparisons do not reopen the quarantined Moses or 1876 primers.

## 7. LXX outer boundary, Cainan restoration, and week reversal

The corrected native LXX boundary is **5751t/5750n BC**, not 5750t/5750n.

| Cumulative LXX state | BC opening boundary | Paired reflection | Self-Mirror width |
|---|---|---|---:|
| Cainan ON | **5751t/5750n BC** | **AD 5750t/5751n** | **11500 = 23×500** |
| Cainan OFF | **5291t/5290n BC** | **AD 5290t/5291n** | **10580 = 23×460** |

The difference between these full widths is **920 = 460+460**. From the pair centers to the fixed axis:

\[
5290=23\times230\xrightarrow{25/23}5750=25\times230.
\]

Thus each OFF center moves outward **460** years and reaches the ON boundary. Equivalently:

\[
10580\times25/23=11500.
\]

The next expansion is:

\[
11500\xrightarrow{25/23}12500,
\qquad5750\xrightarrow{+500}6250\quad\text{on each side}.
\]

The corresponding generated outer pair is **6251t/6250n BC ↔ AD 6250t/6251n**. These are expansion coordinates, not newly identified Flood dates.

At Dean's symbolic scale **1000 years = one day**, each 500-year addition is half a day, or twelve hours; the full **12500** is **12½ symbolic days**. This interpretation is separate from the exact interval arithmetic.

The full seven-year OFF source week is **5291t/5290n → 5284t/5283n BC**. Its chronological reflected order is **AD 5283t/5284n → AD 5290t/5291n**. This order reversal is essential whenever internal week members are compared.

## 8. The four cumulative Flood weeks and the 6+1+6 arrangement

The four descending openings are:

| Field | Opening | Closing |
|---|---|---|
| LXX ON | **5751t/5750n BC** | **5744t/5743n BC** |
| MT ON | **5297t/5296n BC** | **5290t/5289n BC** |
| LXX OFF | **5291t/5290n BC** | **5284t/5283n BC** |
| MT OFF | **4837t/4836n BC** | **4830t/4829n BC** |

Their opening-coordinate gaps are **454+6+454**. Advance the middle MT-ON and LXX-OFF weeks **5290 = 23×230** years:

| Boundary | Original BC phase pair | Translated pair |
|---|---|---|
| MT opens | 5297t/5296n | **7t/6n BC** |
| LXX opens | 5291t/5290n | **1t BC / AD 1n** |
| MT closes | 5290t/5289n | **AD 1t/2n** |
| LXX closes | 5284t/5283n | **AD 7t/8n** |

On the Nisan rail the combined sequence is **6 BC → AD 1 → AD 2 → AD 8**, giving **6+1+6 = 13**. Each source still has its own seven-year interval; the two overlap by one year. Dean reads this as the fallen-creation/curse pattern, with the final year of **6+1+6+1 = 14** initially implied.

The six-year MT/LXX displacement is a relationship between these selected cumulative fields. It is distinct from the SP regular one-year personal mechanism discussed later.

## 9. Shem's 600/598 and completion of the fourteen-year window

Adding **600** to the cumulative Flood date produces the corresponding Shem-birth date. Increasing the forward translation by **598** leaves the landing **two years earlier**:

\[
5290+600=5890,\qquad5290+598=5888=23\times256=23\times2^8.
\]

For MT ON, the Shem week is **5897t/5896n → 5890t/5889n BC**. Advancing it **5888** years gives **9t/8n → 2t/1n BC**. Reflecting that complete interval gives **AD 1t/2n → AD 8t/9n**.

| Component of the completed construction | Opening | Closing | Years |
|---|---|---|---:|
| Translated MT Flood week | **7t/6n BC** | **AD 1t/2n** | **7** |
| Reflected translated MT Shem week | **AD 1t/2n** | **AD 8t/9n** | **7** |

This supplies the previously implied final boundary, giving **7+7 = 14**, or the earlier partition **6+1+6+1**. The LXX Flood week retains its own dates; it is not moved to manufacture this completion.

The shared paired boundary is **AD 1t/2n**, centered on January AD 2. Dean calls this Christ-centered in the nativity-period construction. Do not identify this junction with the distinct fixed Mirror axis at January AD 1. The second week is the reflection of the translated **Shem** week; it is not the direct reflection of the first Flood week.

### 9.1 The square conversion and the separate central gap

\[
5888\times25/23=6400=80^2,
\]
\[
5888+5888=11776=23\times2^9
\longrightarrow12800=80^2+80^2.
\]

These latter sums total **two reflected bridge lengths**. The bridges from the MT Shem outer boundary to **9t/8n BC**, and from **AD 8t/9n** to its reflected outer boundary, leave a **16-year central interval**. Consequently:

\[
5897t/5896n\;\mathrm{BC}
\longrightarrow\mathrm{AD}\;5896t/5897n
=11792=5888+16+5888.
\]

The **11776** doubled bridge total must not replace the **11792** full outer self-Mirror width. Dean's perfection/restoration interpretation attaches to the displayed square arithmetic; the distinction between those geometric spans remains necessary.

### 9.2 Seven versus seven-and-a-half years

Matching-season readings of each completed central week give seven years. Reading its opening Tishri component through its closing Nisan component gives **7½ years**. The two 7½-year envelopes share **AD 1t → AD 2n**, a half-year overlap. Their sum is **15**, while their combined outer interval is **14½ elapsed years**. This is not a new non-overlapping fifteen-year central period.

## 10. The ±460 flanks, residual expansion, and the 7000/7500 scales

Adding Shem's 600 to the four Flood openings gives:

| Source | Shem opening | Held landing | Bridge |
|---|---|---|---:|
| LXX ON | **6351t/6350n BC** | **3t/2n BC** | **6348** |
| MT ON | **5897t/5896n BC** | **9t/8n BC** | **5888** |
| LXX OFF | **5891t/5890n BC** | **3t/2n BC** | **5888** |
| MT OFF | **5437t/5436n BC** | **9t/8n BC** | **5428** |

The two families retain **different landing pairs**, six years apart. The statement “5888 is flanked by ±460” means:

| Relative width | Factorization | After 25/23 |
|---|---|---:|
| 5888−460 = **5428** | 23×236 | **5900** |
| **5888** | 23×256 | **6400** |
| 5888+460 = **6348** | 23×276 | **6900** |

Thus **5888±460 → 6400±500**. It is not a claim that all four source openings land on one common date.

### 10.1 The two-factor residual in 6348

\[
6348=23^2\times12\xrightarrow{25/23}6900=23\times300=69\times100.
\]

The two exact continuations are:

\[
6900\times70/69=7000,
\qquad6900\times25/23=7500.
\]

The **7000** route combines **25/23 then 70/69**; the **7500** route uses **25/23 twice**. The comparable double factor in **5290 = 23²×10** produces **5290→5750→6250** under two applications of 25/23.

### 10.2 Explicit fixed-landing construction

When the **3t/2n BC** landing is held fixed, the generated outer coordinates are:

| Width | BC opening | Fixed BC landing |
|---|---|---|
| 6348 | 6351t/6350n | 3t/2n |
| 6900 | 6903t/6902n | 3t/2n |
| 7000 | 7003t/7002n | 3t/2n |
| 7500 | 7503t/7502n | 3t/2n |

For 7000, the reflected partner is **AD 2t/3n → AD 7002t/7003n**. Hence the two bridges sum to **14000**, but their full outer span includes four central years:

\[
14004=7000+4+7000.
\]

The analogous 7500 construction has **15000** in the two bridges and **15004** in the full outer interval. These generated coordinates are one declared anchoring construction. If instead the original **6351t/6350n BC** opening were held fixed, a 7000-year forward interval would end at **AD 650t/651n**. Therefore a converted duration alone does not determine its new dates.

### 10.3 Dean's scale clarification

Dean explicitly clarified that **7000+7000 chronological years represent the central 7+7 literal years** around Christ; similarly **7500+7500** represents the **7½+7½** readings. This is a **1000:1 symbolic correspondence between durations**, not a claim that the large and small intervals have identical literal endpoints or centers.

The related “one day as 1000 years” imagery assigns 7000/7500 years to 7/7½ symbolic days. With a schematic **360-day year**, 1000 years contain **360000 days**, so the large **14000-year** bridge total contains **14×360000 = 5040000** schematic calendar days. Keep that large-scale count separate from the fourteen literal years and from the overlapping 7½-year envelopes.

## 11. Apparent age, the five-year selection, and SP→MT Creation across the Mirror

### 11.1 The controlled apparent-age allowance is 30

The source fields are [S1, S2]:

| MT cumulative state | Nisan field | Selected Nisan member |
|---|---|---:|
| Creation OFF | **14011–14004** | **14006** |
| Apparent Adam OFF | **14041–14034** | **14036** |
| Creation ON | **14471–14464** | **14466** |
| Apparent Adam ON, derived companion | **14501–14494** | **14496** |

The full apparent-age increment is **30**, localized to the stated overlay. For corresponding ordinary Creation/Flood boundaries:

\[
14011-4836=14004-4829=9175.
\]

Adding 30 produces **9205**. Selecting five years later within the apparent-age envelope produces **9200**:

\[
14036-4836=9200=23\times400,
\qquad9175+30-5=9175+25=9200.
\]

Thus **25** is a net allowance **30−5**, not the full apparent age. The related SP decomposition is **120 = 115+5**. These two five-year pieces must be attached to explicit selections rather than moved freely between comparisons.

**Correction to an earlier assistant response:** the construction **14032t/14031n BC → SP 4717t/4716n BC = 9315** is arithmetically true, but **14031 lies outside the controlled apparent-age field 14041–14034**. The earlier response effectively made a further five-year selection after already using a net 30−5 allowance. Do not retain 14031 or 9315 as a native apparent-age-to-SP bridge. A separate, explicitly derived construction would be needed to use it. Dean's later 19350 comparison correctly uses the full +30.

### 11.2 SP Shem to reflected MT cumulative Creation

The SP Shem week is **5317t/5316n → 5310t/5309n BC**. Reflection reverses the MT Creation week, so the point-to-point comparisons are:

| SP boundary | Reflected MT Creation OFF boundary | Span |
|---|---|---:|
| **5317t/5316n BC** | **AD 14004t/14005n** | **19320** |
| **5310t/5309n BC** | **AD 14011t/14012n** | **19320** |

For example, **5316+14005−1 = 19320**. This aligns complete seven-year fields, with corresponding chronological positions in the already-reflected MT interval.

| MT cumulative target | Opening-side reflected target | Closing-side reflected target | Point-to-point width | Conversion |
|---|---|---|---:|---|
| Creation OFF | AD 14004t/14005n | AD 14011t/14012n | **19320 = 23×840** | **21000** by 25/23 |
| Apparent age OFF | AD 14034t/14035n | AD 14041t/14042n | **19350 = 45×430** | No 23-factor conversion asserted here |
| Creation ON | AD 14464t/14465n | AD 14471t/14472n | **19780 = 23×860 = 23×430×2** | **21500** by 25/23 |

This is a cross-Mirror comparison. Treating 19320 as a same-side BC subtraction would misidentify the construction. The 460 cumulative Cainan difference again converts to **500**.

## 12. MT cumulative→regular Creation and the Conquest week

The MT Creation weeks align by **9890 = 23×430** [S3]. Their point-to-point extension to the reflected Conquest is:

| Boundary | Cumulative MT Creation OFF | Regular MT Creation OFF | Reflected Conquest |
|---|---|---|---|
| Opening | **14012t/14011n BC** | **4122t/4121n BC** | **AD 1399t/1400n** |
| Closing | **14005t/14004n BC** | **4115t/4114n BC** | **AD 1406t/1407n** |

\[
9890+5520=15410=23\times670,
\]
\[
15410+460=15870=23\times690=23^2\times30.
\]

The **5520** Mirror interval is directly controlled in File_09 [S1]. The selected regular **native LXX ON** Creation week is **5502t/5501n → 5495t/5494n BC**, 1380 years earlier than this **native MT OFF** regular week. Thus its Conquest bridge is **5520+1380 = 6900**. The source-state qualification matters: 1380 is not a universal LXX−MT cumulative offset or a common-Cainan-OFF difference.

The proposed four scaled measures are:

| Arithmetic route | Expanded years | Literal-year reading at 1000:1 |
|---|---:|---|
| 5520×25/23 | **6000** | Six years of conquest |
| (5520+460)×25/23 | **6500** | 6½ years |
| 6900×70/69 | **7000** | Seven including rest |
| 6900×25/23 | **7500** | 7½ years |

For **AD 1399t/1400n → AD 1406t/1407n**, matching seasons give seven years; opening Nisan to closing Tishri gives **6½**, and opening Tishri to closing Nisan **7½**. The six-year reading selects the conquest portion within the six-plus-one interpretation. Reflection reverses internal event order; the arithmetic lengths alone do not place the rest year at a new historical endpoint.

### 12.1 Where the 6500 route puts the extra 460

With the regular Creation coordinate held fixed, cumulative Cainan enlarges the **first** leg:

\[
15870=(9890+460)+5520=10350+5520.
\]

To retain **9890** for that first leg instead, the intermediate coordinate must also move 460 years earlier:

| Boundary | Cumulative MT Creation ON | Derived intermediate | Reflected Conquest |
|---|---|---|---|
| Opening | 14472t/14471n BC | **4582t/4581n BC** | AD 1399t/1400n |
| Closing | 14465t/14464n BC | **4575t/4574n BC** | AD 1406t/1407n |

Now **15870 = 9890+5980**, and **5980×25/23 = 6500**. The 4581–4574 field is a **translated intermediate field**. It is not ordinary regular MT Creation or its ordinary Cainan-ON field. Regular Cainan adds **130**, which would produce **4251–4244**, and a different Conquest width **5650**.

Thus the 6500 arithmetic route is explicit, while its intermediate coordinate retains derived status. This distinction was established during the bounded check; it must not disappear in the original window.

## 13. The SP Shem-to-Flood link inside the full Creation–Conquest chain

The two preceding constructions give the same SP Shem-to-ordinary-BC-Conquest distance, with cumulative Cainan canceling:

\[
19320-15410=19780-15870=3910=23\times170.
\]

The complete point-to-point comparison is **5316→1406** and **5309→1399 BC**, both 3910. Its paired fields are **5317t/5316n → 5310t/5309n BC** and **1407t/1406n → 1400t/1399n BC**.

Subtracting the literal matched **600** produces **3310**, not 3312. To obtain the 598 form, use explicit differing week positions:

| Selected Shem-birth member | Selected Flood/Shem-death member | Selected Conquest member | Intervals |
|---|---|---|---|
| **5315t/5314n BC** | **4717t/4716n BC** | **1405t/1404n BC** | **598+3312 = 3910** |
| **5310t/5309n BC** | **4712t/4711n BC** | **1400t/1399n BC** | **598+3312 = 3910** |

The second example uses Shem's closing boundary, the SP Flood's named **4711 Nisan member**, and the Conquest's closing boundary. Both examples use existing members. They do not change the matched cumulative lifespan of 600.

More precisely, write a selected Shem member as **5316−i**, its point-to-point Conquest member as **1406−i**, and the 598-related Flood member as **4718−i**. All three lie in the stated fields for **i = 2,…,7**. That gives six integer boundary selections, covering five elapsed years. It is not a new 598 relation across all eight boundaries of the original full weeks.

The first example extends through the Mirror into the whole chain:

| Node | Paired coordinate | Years from previous node |
|---|---|---:|
| SP cumulative Shem birth / Noah death | **5315t/5314n BC** | — |
| SP cumulative Flood / Shem death | **4717t/4716n BC** | **598** |
| Conquest member | **1405t/1404n BC** | **3312** |
| Reflected regular MT Creation member | **AD 4116t/4117n** | **5520** |
| Reflected cumulative MT Creation OFF member | **AD 14006t/14007n** | **9890** |

\[
19320=598+3312+5520+9890=23(26+144+240+430),
\]
\[
21000=650+3600+6000+10750.
\]

With cumulative Cainan ON the final point becomes **AD 14466t/14467n**. Two placements of the allowance give:

| Intermediate coordinate | Conquest→intermediate | Intermediate→cum Creation ON | Total including initial 3910 | Expanded total |
|---|---:|---:|---:|---:|
| Ordinary reflected regular point **AD 4116t/4117n** | 5520 | 10350 | **19780** | **21500 = 4250+6000+11250** |
| Derived translated point **AD 4576t/4577n** | 5980 | 9890 | **19780** | **21500 = 4250+6500+10750** |

The 500-year converted allowance moves between the last two intervals. It is counted once. This is the concrete meaning of the derived 6500 route in the SP-connected chain.

Dean then explicitly redirected the branch away from further expansion of this Conquest/LXX comparison and back to the Christ-period Flood/Shem Mirror field. The remaining sections preserve that later direction.

## 14. Inserting SP into the Christ-period Flood/Shem Mirror field

### 14.1 Correct SP translation widths

| SP state | Flood translation | Shem translation |
|---|---:|---:|
| Cainan OFF | **4715 = 23×205** | **5313 = 4715+598 = 23×231 = 69×77** |
| Cainan ON | **5175 = 23×225** | **5773 = 5175+598 = 23×251** |

The conversational factors **23×105** and **23×125** were transcription errors for **23×205** and **23×225**. Adding 460 to both the SP source dates and the translation width preserves the same landings in the ON state.

For example:

- **5317t/5316n BC**, advanced **5313**, lands at **4t/3n BC**. Its week closes at **AD 4t/5n**.
- **4717t/4716n BC**, advanced **4715**, lands at **2t/1n BC**. Its week closes at **AD 6t/7n**.

### 14.2 Flood weeks and their paired reflections

| Source | Translated Flood interval | Reflected interval |
|---|---|---|
| MT ON, translate 5290 | **7t/6n BC → AD 1t/2n** | **2t/1n BC → AD 6t/7n** |
| SP OFF, translate 4715 | **2t/1n BC → AD 6t/7n** | **7t/6n BC → AD 1t/2n** |
| LXX OFF, translate 5290 | **1t BC / AD 1n → AD 7t/8n** | **8t/7n BC → 1t BC / AD 1n** |

The central exact identity is:

\[
\boxed{\operatorname{Mirror}(\text{translated SP Flood week})
=\text{translated MT Flood week}}.
\]

The converse follows from reflection being an involution. This concerns the transformed intervals, not identity of the original source events or calendars.

### 14.3 Shem weeks: source +600, translation +598

| Source | Translated Shem interval | Reflected interval |
|---|---|---|
| MT ON, translate 5888 | **9t/8n BC → 2t/1n BC** | **AD 1t/2n → AD 8t/9n** |
| SP OFF, translate 5313 | **4t/3n BC → AD 4t/5n** | **5t/4n BC → AD 3t/4n** |
| LXX OFF, translate 5888 | **3t/2n BC → AD 5t/6n** | **6t/5n BC → AD 2t/3n** |

Each translated Shem interval is **two years earlier** than that source's translated Flood interval. Each reflected Shem interval is **two years later** than its corresponding reflected Flood interval. This sign reversal follows from reflection, and preserves the full 600 source lifespan while exposing the 598 difference between translation widths.

## 15. Dean's ordinal/cardinal interpretation and its proper domain

Dean corrected the proposed next-step framing: **the offset touches regular chronology, not cumulative chronology**. The cumulative Mirror landings exhibit a corresponding ordinal/cardinal pattern; they do not acquire the regular SP personal −1 rule.

Counting the translated MT Flood opening **7t/6n BC** as the start of Year 1:

| Boundary | Paired position | Elapsed from MT opening | Dean's interpretation |
|---|---|---:|---|
| SP Flood opens | **2t/1n BC** | **5** | Entry into the **6th** year/day; creation of man |
| LXX Flood opens | **1t BC / AD 1n** | **6** | Completion of **6** years/days |
| SP Flood closes | **AD 6t/7n** | **12** | Entry into the **13th** year/day; Eve/Fall pattern |
| LXX Flood closes | **AD 7t/8n** | **13** | Completion of **13** years/days |

\[
(5,6)+7=(12,13).
\]

The distinction is **ordinal entry** versus **cardinal completion**. Dean reads Noah's **600th year / 600 completed years** as the larger counterpart to **6th / 6**, repeated seven years later as **13th / 13**. The creation-of-man, creation-of-Eve, and fall-of-mankind labels are his theological interpretation of these model boundaries. This handoff does not claim a new textual proof that Genesis itself assigns all these literal dates.

The source-controlled regular SP mechanism supports both counting forms at qualified endpoints [S4]. In G1, for example:

| SP regular G1 comparison, full-430/Terah-0 | Boundary count |
|---|---:|
| Primary Noah birth 3706 → Flood start 3106 | **600** |
| Companion Noah birth 3705 → Flood start 3106 | **599**, entering year 600 |
| Companion Noah birth 3705 → Flood close 3105 | **600** |

The primary/companion designation does not impose one counting convention on every interval involving that station. The canonical register explicitly binds the convention to the interval and named endpoints. Accordingly, “SP ordinal / LXX cardinal” is the interpretive emphasis in this construction; it must not erase SP's admitted full-600 path or transfer its person-station rail to other sources.

Dean chose not to elaborate every internal interweaving in this branch. He then returned to the outer regular/cumulative flanks, which supply the final integration anchors below.

## 16. Final outer-flank construction: 6210, 2185, 10580, and 8395

### 16.1 The regular SP head flank is the Flood's closing boundary

The selected regular SP G1 Flood spans **3106n→3105n BC**, with Tishri counterparts **3107t→3106t BC**. Its paired boundaries are therefore:

- Opening: **3107t/3106n BC**.
- Closing: **3106t/3105n BC**.

The closing pair reflects to **AD 3105t/3106n**, giving:

\[
3106+3105-1=3105+3106-1
=\boxed{6210=23\times270=69\times90}.
\]

The specified regular LXX Cainan-OFF G1 execution has the same Flood start/close coordinates: native **3236→3235**, less regular Cainan **130**, gives **3106→3105**. This is the precise state qualification behind Dean's SP/LXX-OFF co-registration.

“Outer head flank” here names this selected architectural boundary. It does not assert that 3106 is the largest BC Flood coordinate across every Gear, Sojourn, Cainan, and Terah selector. Equally, Dean's “cumulative LXX tail flank” below is **5291t/5290n**, the opening edge of that OFF cumulative week; the word *tail* must not cause it to be replaced by that week's closing edge 5284t/5283n.

### 16.2 The side flanks are 2185 each

The cumulative LXX OFF boundary is **5291t/5290n BC**. Its separation from the selected regular closing boundary is:

\[
5291-3106=5290-3105
=\boxed{2185=23\times95}.
\]

Reflection preserves that width on the AD side. The complete ordered frame is:

| Position | Paired coordinate | Years from preceding position |
|---|---|---:|
| BC cumulative LXX OFF flank | **5291t/5290n BC** | — |
| BC regular SP/LXX-OFF Flood close | **3106t/3105n BC** | **2185** |
| AD reflected regular Flood close | **AD 3105t/3106n** | **6210** |
| AD reflected cumulative LXX OFF flank | **AD 5290t/5291n** | **2185** |

\[
\boxed{10580=2185+6210+2185=23(95+270+95)=23\times460}.
\]

This recovers the full cumulative LXX Cainan-OFF self-Mirror width already identified in §7, while retaining the regular closing-boundary count in the center.

### 16.3 The two cross-flank bridges are 23×365

| BC source boundary | AD reflected destination boundary | Width |
|---|---|---:|
| **5291t/5290n BC**, cumulative LXX OFF | **AD 3105t/3106n**, regular SP/LXX-OFF Flood close | **8395 = 23×365** |
| **3106t/3105n BC**, regular SP/LXX-OFF Flood close | **AD 5290t/5291n**, cumulative LXX OFF | **8395 = 23×365** |

Both components agree:

\[
5291+3105-1=5290+3106-1=8395,
\]
\[
3106+5290-1=3105+5291-1=8395.
\]

Equivalently:

\[
\boxed{8395=2185+6210=10580-2185=23\times365}.
\]

**This is the final boundary result Dean asked to hand back.** He expects the regular MT/SP/LXX/BJ interweavings to connect here, but explicitly judged a full elaboration too complex for this side discussion. The two named 8395 edges are established; a complete four-source classification is not.

## 17. Correction and interpretation register

The original window should use these resolved forms rather than copying conversational shorthand uncritically.

| Earlier wording or potential conflation | Controlling form |
|---|---|
| LXX outer boundary “5750t/5750n” | **5751t/5750n BC**, explicitly corrected by Dean |
| “5897t/5296n” after adding Shem's 600 | **5897t/5896n BC**; add 600 to both components |
| SP “3106/3105 Shem birth” and “2991/2990 Flood” | **3106/3105 Flood start/close**; **2991/2990 Shem primary/companion birth** in the specified different Sojourn frame |
| Treating 3106t/3105n as the whole regular Flood year | It is the **closing pair**; the full year starts at **3107t/3106n** |
| 4715 = 23×105; ON width = 23×125 | **4715 = 23×205; 5175 = 23×225** |
| “92000” in the five-year discussion | Read as **9200** in context |
| +25 called the full apparent age | Full allowance **30**; **25 = 30−5** is a net selection |
| 14031 treated as a native apparent-age member | Outside **14041–14034**; the earlier **9315** construction is not part of the validated native endpoint set |
| “23×115 = 23×125” | **2645×25/23 = 2875**, with **2875 = 25×115 = 23×125** |
| 600-year translation interpreted as demanding literal −598 and +598 occurrences around every bridge | Preserve the explicit **5891→2533** and **5291→1933** +598 construction; negative-target searches remain separate |
| +60 called Cainan in the 690 residual example | The regular **+60** selector is **Terah**; Cainan is **130 regular / 460 cumulative** |
| The 1380 LXX–MT difference left unqualified | Here it is **regular native LXX ON versus regular native MT OFF** |
| SP's local cumulative −120 propagated to Creation | At common-OFF cumulative Creation, SP is **−608** from MT; −120 controls the stated Noah/Shem/Flood field |
| Regular SP −1 person rail introduced into cumulative fields | Keep it **regular and Noah/Shem-local**; the cumulative landings express an interpreted counterpart |
| Twice 5888 called the full MT Shem outer self-Mirror span | **11776** is the bridge sum; full span is **11792**, including **16** central years |
| 7000+7000 at fixed 3t/2n BC landing called the whole outer span | Bridge sum **14000**; full outer span **14004**, including the central **4** |
| Two 7½-year envelopes called fifteen non-overlapping years | Sum **15**; overlap **½**; outer union **14½** |
| The 6500 route assigned to unmodified regular Creation | Requires **5980 = 5520+460** and the explicitly **derived** intermediate coordinate |
| “Christ-centered” used to move the fixed Mirror axis | The paired axis remains January **AD 1**; the completed central seven-plus-seven junction is **AD 1t/2n**, centered January **AD 2** |

## 18. How the original window should continue

The handoff supplies exact boundary constraints and authorial interpretation. It does not require restarting the wider unification program, repeating completed scans, or following every exploratory next-step suggestion made during this branch. Dean repeatedly redirected those suggestions; his final direction was to identify the outer flanks and return the more intricate four-source work to the original window.

The first bounded integration should attach the following to the existing source-qualified comparison record:

1. The **10580** cumulative LXX-OFF self-Mirror edge, the **6210** regular-SP/LXX-OFF closing-boundary edge, and the two **2185** side edges.
2. The two explicit **8395 = 23×365** cross-flank edges, retaining regular G1/full-430/Terah-0/Cainan-OFF qualifications and the distinct cumulative state.
3. The translated **MT Flood ↔ SP Flood** reflection identity and the three **600/598** Shem translations, with source roles and week selections preserved.
4. The Creation–Conquest support chain **598+3312+5520+9890 = 19320**, together with the separately labeled derived 6500 option.

These form a bounded basis for probing the already active regular **MT/SP/LXX/BJ** interweavings. Use source-defined nodes and qualified ordinal/cardinal intervals before enlarging the search. The branch did not establish new BJ endpoint tables for these Mirror edges. The canonical SP register provides BJ event and birth-position comparisons as separately typed background; its SP-as-primary/BJ-as-derivative project interpretation does not make arithmetic alone proof of historical dependence [S4].

For the existing unification framework, preserve these distinctions:

- Whole-week point-to-point relations, such as **9890** and **19320**, differ from the six selected integer boundary triples supporting the **598+3312** construction.
- Cainan OFF→ON state changes, generated interval expansions, and paired reflection are separately specified operations. Equal numerical outputs do not make them the same source transformation.
- The date-level paired reflection is involutive and reverses translation direction. That arithmetic fact is not, by itself, a theorem licensing one global rewrite system for every historical state.
- Shared coordinate labels do not identify Flood, Shem birth/death, Arphaxad, Creation, or translated intermediate nodes.
- The source-controlled **600** lifespan, the cross-selection **598**, the regular ordinal **599+**, and the one-year Flood duration must remain individually labeled.

The theological reading is that the source traditions emphasize complementary aspects of creation, fall, and restoration, including ordinal entry/cardinal completion, the seventh-year completion, and the large/small scale correspondences. The reported arithmetic supports the stated structural comparisons. It does not independently establish authorial intention for every pattern.

**Best next bounded step for the receiving window:** incorporate and verify the two source-qualified **8395-year cross-flank pairings** within the current comparison structure, then use the existing MT/SP/LXX/BJ work to test their immediate connections. Keep the quarantined primers and Rounded chronology out of that integration. This bounded incorporation does not itself require a broader model or effort escalation; any later exhaustive four-source dependency analysis can be assessed separately.

## 19. Source register and verification provenance

This document uses the conversation as the primary record of Dean's constructions and interpretive intent. The following current project sources were checked for the controlling data and rules; source-derived claims above refer to these labels.

- **[S1] File_09.Cumulative_Architecture(8).md.** Checked its state register, including the paired Mirror rule, January axis, paired-versus-single distinction, the 5520 Conquest comparison, and Creation/Apparent fields. filecitefile_00000000e3a481f7be5144696d124a18L80-L144
- **[S2] File_18.Chronological_Data_Tables(20260919-141048).md.** Checked §§6A–6D: MT Creation/Apparent, cumulative Cainan, SP Terah-145 execution and Flood field, and native LXX cumulative fields. filecitefile_00000000761881f5a570dc3ab657a2e0L1900-L2077
- **[S3] Cumulative_MT-SP-LXX_Creation-Shem_Comparative_Engine_Report_III_20260902(2)(3)(5).md.** Checked the common-Cainan state rules, three-source cumulative fields and local offsets, and the 9890 component-wise cumulative-to-regular Creation bridge. filecitefile_0000000025d481f5be40daa84499bb66
- **[S4] SP_Noah_Shem_Gear_Knot_Canonical_Register_FLOOD_GEAR_CLARIFIED_20260918.md**, revised version 1. Checked the native LXX Cainan state, regular Flood Gears, SP primary/companion paths, ordinal/cardinal qualification, and the separation of Flood duration from person-station adjacency. filecitefile_000000005ac48230b963ec2d34d110cbL1-L240
- **[S5] 490d_MT_Cumulative_Regular_Branch_Handoff_20260920 (1).md.** Checked the earlier MT foundation and the added explicit G2 **3358** birth/death clarification. Its earlier Mirror deferral is superseded for this handoff's scope. filecitefile_000000007af081f5b29297fe7288f2bf

The source excerpts substantiate the underlying chronology register. New normalized intervals, residual expansions, and the final cross-flank constructions are checked arithmetic from the branch, not assertions that all these tables already occur in the canonical sources. No canonical source files were modified to produce this handoff.

## Appendix A. Regular MT and SP selector tables retained for context

All values here are BC and use **G2 / Normal**. The column **Terah** names the 0/+60 selector. A native LXX +780 comparison starts from the native MT-OFF state; do not add another 130 to an already native-ON LXX row.

### A.1 MT

| Sojourn | Cainan | Terah | Flood start | Noah birth | Shem birth | Noah death | Shem death |
|---:|---|---|---:|---:|---:|---:|---:|
| 430 | ON | +60 | 2648 | 3248 | 2748 | 2298 | 2148 |
| 430 | ON | 0 | 2588 | 3188 | 2688 | 2238 | 2088 |
| 430 | OFF | +60 | 2518 | 3118 | 2618 | 2168 | 2018 |
| 430 | OFF | 0 | 2458 | 3058 | 2558 | 2108 | 1958 |
| 215 | ON | +60 | 2433 | 3033 | 2533 | 2083 | 1933 |
| 215 | ON | 0 | 2373 | 2973 | 2473 | 2023 | 1873 |
| 215 | OFF | +60 | 2303 | 2903 | 2403 | 1953 | 1803 |
| 215 | OFF | 0 | 2243 | 2843 | 2343 | 1893 | 1743 |

### A.2 SP primary stations

| Sojourn | Cainan | Terah | Flood start | Noah birth | Shem birth | Noah death | Shem death |
|---:|---|---|---:|---:|---:|---:|---:|
| 430 | ON | +60 | 3298 | 3898 | 3398 | 2948 | 2798 |
| 430 | ON | 0 | 3238 | 3838 | 3338 | 2888 | 2738 |
| 430 | OFF | +60 | 3168 | 3768 | 3268 | 2818 | 2668 |
| 430 | OFF | 0 | 3108 | 3708 | 3208 | 2758 | 2608 |
| 215 | ON | +60 | 3083 | 3683 | 3183 | 2733 | 2583 |
| 215 | ON | 0 | 3023 | 3623 | 3123 | 2673 | 2523 |
| 215 | OFF | +60 | 2953 | 3553 | 3053 | 2603 | 2453 |
| 215 | OFF | 0 | 2893 | 3493 | 2993 | 2543 | 2393 |

Each corresponding primary SP date is 650 years earlier than MT in these selected normalized tables. For the four SP **person** columns, the companion is primary−1. Flood close is separately Flood start−1. The Flood has no personal companion rail. G1/G3 shift the relevant regular G2 stations by **−2/+2** BC-coordinate years; ordinary Arphaxad bindings remain separately controlled.

SP primary 690 straddles include **3298→2608**, **3083→2393**, **3898→3208**, and **3683→2993**. For a companion death comparison, **3297 Flood close → 2607 Shem companion death = 690**; **3298 Flood start → 2607 = 691**. This records the event-boundary/person-rail distinction explicitly.

### A.3 Earlier finite MT multiple-of-230 scan

The previous handoff's finite G2 scan used 48 cumulative coordinates (two Cainan states × three cumulative role fields × eight boundaries) against 40 regular coordinates (eight states × five event columns). It reported ten matches with eight unique widths:

| Cumulative member → regular endpoint, BC | Width |
|---|---:|
| 4833→2533 | 2300 |
| 4833→2303; 5433→2903 | 2530 |
| 5293→2533 | 2760 |
| 5293→2303; 5893→2903 | 2990 |
| 6383→2473 | 3910 |
| 6383→2243 | 4140 |
| 6843→2473 | 4370 |
| 6843→2243 | 4600 |

All listed regular endpoints use the 215 frame. These earlier same-era matches provide context; a shared width such as 3910 does not identify them with the later SP-to-Conquest construction.

## Appendix B. Arithmetic audit model and completion record

The handoff was checked using integer centers for the phase pairs. Assign a paired boundary with Nisan coordinate **N BC** the center **c = 1−N**, and a paired boundary with Nisan coordinate **AD N** the center **c = N**. The fixed Mirror axis is **c = 1**. The display function is:

```text
c <= 0:  (2-c)t/(1-c)n BC
c == 1:  1t BC / AD 1n
c >= 2:  AD (c-1)t/cn
```

Forward translation is **c → c+d**. Paired reflection is **c → 2−c**. For a seven-year interval **[a,b]**, with b−a = 7, its reflected interval is **[2−b, 2−a]**. These formulas reproduce both seasonal same-phase elapsed counts with no year zero. At the date-coordinate level they give **R² = identity** and **R T(d) = T(−d) R**; they do not supply additional source permissions.

Audit coverage includes:

- Regular selector tables, primary lifespans, 405 ladder, and 690 straddles.
- Cumulative 600/950/460 shifts and SP's local 120-year offset.
- LXX 10580/11500 outer widths, 5290→5750→6250 center expansions, and week reversal.
- The four translated MT/LXX Flood boundaries, the 13-year arrangement, and the completed MT 7+7 construction.
- All MT/SP/LXX translated Flood/Shem weeks and their reflected paired endpoints, including SP ON invariance.
- 5888 square conversions and central-gap accounting; 6348 residual routes and generated 7000/7500 endpoints.
- 19320/19350/19780 point-to-point Creation comparisons, 9890/5520/6900 chains, and both explicit placements of the 460 allowance.
- The six admissible integer-boundary 598+3312 triples and the complete 19320/19780 SP-connected chains.
- The 6210/2185/10580 frame and both seasonal checks of the two **8395 = 23×365** cross-flank bridges.

The audit verifies arithmetic and stated field membership. Theological intentionality, a native event interpretation for derived coordinates, and the full MT/SP/LXX/BJ interweaving remain separate research questions. The corrections in §17 are part of the handoff, not optional footnotes to be dropped when extracting its numerical results.

**Final arithmetic audit:** 254 assertions passed, including checks against the endpoint tables written in this document. The paired-Mirror model, source-state qualifications, and explicit correction register govern how those results should be reused.