{"id":"study-mirror-axis-framework","title":"The 4232 / 8464 / 12696 Mirror framework","filename":"490d_Comprehensive_4232_8464_12696_Mirror_Axis_Report_20260925.md","role":"Study document","step":null,"sha256":"5ec36bbcd2cf215ac76ac71a2557c1cad9b041951cdc190efb96435b394e0f82","bytes":74450,"origins":["User-supplied supporting study edition; inclusion does not change its original claim level."],"download":"/study-documents/files/490d_Comprehensive_4232_8464_12696_Mirror_Axis_Report_20260925.md","format":"md","derived":false,"tags":["Mirror / 529","Regular","Cumulative","Calendar Keys"],"excerpt":"Integrated regular and cumulative Mirror study, distinguishing squared-number radii from doubled translation widths and preserving declared seasonal and civil-count frames.","collection":"study-documents","date":"2026-09-24","dateLabel":"September 24, 2026 · addendum September 25","editionStatus":"Comprehensive working synthesis · bounded arithmetic and interpretation","storage":"study-files","downloadFilename":"490d_Comprehensive_4232_8464_12696_Mirror_Axis_Report_20260925.md","content":"# The 4232 / 8464 / 12696 Mirror framework\n\n## An integrated −y, 0, +y study of regular and cumulative chronology\n\n**Date:** 24 September 2026  \n**For:** Dean and the receiving 490d Strategy–Unification research window.  \n**Status:** Comprehensive working synthesis; exact arithmetic checked in the declared frames. The geometry and theological correspondences remain identified by their respective evidential roles.  \n**Revision basis:** Integrates the complete substantive content of the attached *2116/4232 Terah–Moses Mirror* handoff, its post-C113 resolution, the subsequent 8464 and 12696 studies, the bounded 1380 audit, and Dean’s final Year 14/15 clarification.  \n**Scope:** Capture the completed discussion branch. This is a new report, not a canonical revision or a replay of the main window’s campaign.\n\nThe source handoff is fully integrated into §§3–6. Its original file is also preserved unchanged in the accompanying evidence package. A coverage map appears in Appendix C. Source references such as **[S1]** resolve in Appendix D.\n\n## Receiving-window brief\n\nThe study uses one family of squared-number radii to organize three principal translations:\n\n$$r=2116,\\ 4232,\\ 6348;\\qquad W=2r=4232,\\ 8464,\\ 12696.$$\n\nThe retained Flood-related radius **5290** supplies the additional doubled width **10580**. The important distinction is between a radius and its complete −y-to-+y span: **6348 is the radius; 12696 is its doubled translation width**.\n\nThe central results are:\n\n1. **4232:** Abram/Isaac and Haran/Jacob complementary birth pairs; Peleg/Nahor ±2/±1; covenant 35+35; Entry 480; the Mosaic 1260/1380/1500 sequence; and the now-explicit **1260±3.5** witness construction.\n2. **8464:** the normal-Gear-2 MT Noah/Shem field generates the AD 5406–6506 family. The Flood gives **6000 to the reflected Christ anchor** and **4600 to the reflected Conquest**. Regular Cainan insertion moves upstream sources **130 earlier** and their AD landings **130 earlier**, producing the Flood-to-Entry **4000**.\n3. **12696:** full cumulative seven-year envelopes preserve the upstream Cainan **460** displacement. Flood/Cainan/Shelah comparisons produce **6000**, **6440→7000**, and **6900→7000 or 7500**, with an explicit **+1/−1-year arrangement** around the reflected Conquest week.\n4. The cumulative Creation endpoints give the split **322+138=460**, completed about the Exodus as **350+140=490**, including **350+133+7**. This adds a completed carrier to **26×490**, yielding the composite **27×490**.\n5. The translated Exodus/Conquest pair generates two crossed widths **22540=46×490=460×49**, with midpoint pairs **21t/20n BC** and **AD 20t/21n**. The original January AD 1 Mirror remains fixed.\n6. The squared-number ladder yields **6348→6900→7500**, with **6900→7000** also available. Dean assigns complementary theological meanings to the paired **14000** and **15000** totals: **Year 14 completion/restoration** and **Year 15 renewal, the “eighth day.”**\n\nThe principal research gain is a smaller set of explicit operations governing many linked observations. The report does not treat rearrangements of those operations as independent witnesses.\n\n## 1. Coordinates, phases, and the proposed third dimension\n\n### 1.1 The assigned boundary levels\n\nDean proposes that the familiar horizontal Mirror be retained as the **x** direction, while the new translated levels are organized provisionally along **y**. The **z** relation remains undetermined. The figure is therefore a schematic projection of a proposed three-axis construction, with exact scalar boundary levels and no asserted three-dimensional metric.\n\n![The signed boundary radii and doubled spans](490d_Mirror_Axis_4232_8464_12696_20260924.svg)\n\n| −y radius | BC boundary display | Assignment in this study | +y reflected boundary, retained in the model |\n|---|---|---|---|\n| −2116 = −4×529 | 2117t/2116n BC | Regular Terah → Abram | AD 2116t/2117n |\n| −4232 = −8×529 | 4233t/4232n BC | Regular Creation → Terah, excluding Terah; cumulative Terah → Abram | AD 4232t/4233n |\n| −5290 = −10×529 | 5291t/5290n BC | Flood-related marker; domain assignment left open | AD 5290t/5291n |\n| −6348 = −12×529 | 6349t/6348n BC | Cumulative Creation → Terah, excluding Terah | AD 6348t/6349n |\n\nThe figure omits the repeated +y date labels, as requested. The table records them for reproducibility. **6398**, used once in the initial discussion, is corrected to **6348=3×2116**.\n\nThese assignments specify which translation is being investigated for each source field. The common comparison anchors remain available across fields: Entry **1877t/1876n BC**, Exodus **1447t/1446n BC**, and Conquest **1407t/1406n BC**, with their appropriate reflected counterparts. Moses’ **1526/1446/1406** form the principal biography; **1486** is a secondary age-40 node, retained where it explains an equation but removed from the principal comparison columns. **1846** remains a secondary Entry-family comparison.\n\n### 1.2 Civil labels are retained\n\nA BC label such as **1446 BC** remains printed as 1446, or −1446 when indicating the diagram’s negative side. It is not relabeled −1445. This is a signed-label convention, not astronomical year numbering and not an instruction to introduce a civil year zero.\n\nExact arithmetic uses File_09’s proof coordinates, measured from January 1, AD 1:\n\n$$A(y\\text{ BC},t)=-y+\\tfrac34,\\qquad A(y\\text{ BC},n)=-y+\\tfrac14,$$\n$$A(\\text{AD }y,t)=y-\\tfrac14,\\qquad A(\\text{AD }y,n)=y-\\tfrac34.$$\n\nThese coordinates encode the repository’s normalized seasonal model. Julian and lunar representations are mapped to the schematic 360-day calendar; its two 180-day halves underlie the January center. Exactness here concerns that declared model, not actual lunar-month or Julian-season lengths. Decimal proof coordinates stay in the audit; the report principally retains t/n labels. [S3, Appendix A.3]\n\nThe paired reflection rule is:\n\n$$P_b=(b+1)t/bn\\text{ BC}\\quad\\longleftrightarrow\\quad Q_b=\\text{AD }bt/(b+1)n.$$\n\nThe centers of these pairs are −b and +b. Each pair spans half a schematic year. At the component level, reflection sends **BC yt to AD yn**, and **BC yn to AD yt**; ordering the reflected pair chronologically then produces the displayed AD t/n order.\n\nThus the Conquest comparison is **AD 1406t/1407n**, also writable in reverse display order as **AD 1407n/1406t**. **AD 1406n/1407t** is a different, 1.5-year interval. Merely reversing printed order must never reattach the suffixes to different numbers.\n\n### 1.3 One translation rule governs the tables\n\nAdvancing the BC pair by W years gives:\n\n$$P_b+W=Q_{W-b}=\\text{AD }(W-b)t/(W-b+1)n,$$\n\nwhen the result is on the AD side. Both seasonal checks agree:\n\n$$[(b+1)+(W-b)-1]=[b+(W-b+1)-1]=W.$$\n\nIf the result stays BC, subtract W from the BC year labels normally. This occurs for cumulative Creation under +12696.\n\nA comparison of a translated landing with the ordinary reflected anchor Q_d has signed width:\n\n$$D_W(b,d)=W-b-d.$$\n\nFor the same event on both sides, this reduces to:\n\n$$D_W(b,b)=W-2b=2(r-b),\\qquad W=2r.$$\n\nMost apparently separate observations below are instances of these formulas. Unsuffixed table headings such as “to 1406” mean **to Q₁₄₀₆ on the AD side**, unless another phase state is explicitly declared. A literal BC-to-AD interval instead uses the corresponding civil cross-axis count.\n\n### 1.4 In what sense the boundary acts as a submirror\n\nFor BC magnitude b, the complementary landing label is **Fᵣ(b)=2r−b**. Therefore:\n\n$$F_r(r+d)=r-d,\\qquad F_r(F_r(b))=b.$$\n\nThis exactly expresses the reversal of offsets in the complementary-label representation. On the underlying time coordinate a, translation itself preserves direction. The actual local reflections arise by composing translation and the ordinary Mirror:\n\n$$M(a)=-a,\\qquad T_{2r}(a)=a+2r,$$\n$$S_{+r}=T_{2r}\\circ M: a\\mapsto2r-a,$$\n$$S_{-r}=M\\circ T_{2r}: a\\mapsto-2r-a.$$\n\nThese reflections fix +r and −r respectively. This supplies a precise algebraic meaning for Dean’s provisional **submirror** terminology while retaining the global origin. Establishing a three-dimensional embedding, its z coordinates, distances, or literal line intersections requires additional rules; none are invented here.\n\n## 2. The squared-number and expansion architecture\n\nLet **K=25/23** and **P=70/69**. These symbols name conversion operators; an arrow means a converted duration, not an equality of unconverted quantities.\n\n| Radius r | 529 units | Across −y → +y: 2r | r ×25/23 | r ×(25/23)² |\n| --- | --- | --- | --- | --- |\n| 2116 | 4 | 4232 | 2300 | 2500 |\n| 4232 | 8 | 8464 | 4600 | 5000 |\n| 5290 | 10 | 10580 | 5750 | 6250 |\n| 6348 | 12 | 12696 | 6900 | 7500 |\n\nThe corresponding complete widths are:\n\n| Across −y → +y | First K conversion | Second K conversion |\n|---:|---:|---:|\n| 4232 | 4600 | 5000 |\n| 8464 | 9200 | 10000 |\n| 10580 | 11500 | 12500 |\n| 12696 | 13800 | 15000 |\n\nThe squares are explicit:\n\n$$529=23^2,\\quad2116=46^2,\\quad8464=92^2.$$\n\n**4232=2×46²**, **6348=3×46²**, and **12696=6×46²** are multiples of squares. They are not each themselves perfect squares.\n\nFrom the center outward, one side is partitioned by the retained 5290 marker as:\n\n$$2116+2116+1058+1058=6348.$$\n\nThe first and second K conversions give:\n\n$$2300+2300+1150+1150=6900,$$\n$$2500+2500+1250+1250=7500.$$\n\nReading from the negative outer edge through zero to the positive outer edge reverses the first side’s order, producing Dean’s bilateral arrangements.\n\n| Increment | One side, center outward | One-side total | Both sides |\n|---|---|---:|---:|\n| First K expansion | 184+184+92+92 | **552=24×23** | **1104** |\n| Second K expansion | 200+200+100+100 | **600** | **1200** |\n| Combined | 384+384+192+192 | **1152** | **2304=48²** |\n\nThis corrects two slips in the discussion: **552 is not 23²**, and **100+100+200+200 is 600, not 1100**. The final bilateral gain **15000−12696=2304=48²** remains exact.\n\nDean relates **1152** to the **1150/1152** family and the Noah/Shem ±2 mechanism. This report records the numerical adjacency but does not operate a Gear to convert one into the other. Similarly, the genuine Noah→Shem→Flood→Shem-death partition is **500+100+500=1100**; it is a thematic comparison with the expansion anatomy, not the same sum as the second-stage 600.\n\n## 3. The 4232 layer: patriarchal pairs and covenantal division\n\n### 3.1 Active source frame\n\nUse the selected full-430 / +215 comparison frame: Abram **2166**, Isaac **2066**, Jacob **2006**, Entry **1876**, Exodus **1446**, Conquest **1406 BC**. This selected Abraham–Moses frame can be compared across MT/SP/LXX; their distinct native sojourn settings and the localized −33 corridor remain distinct. Peleg/Nahor values here are specifically MT. The **2226** firstborn uses Dean’s +60 Terah reconstruction; it does not add 60 to every date in the report. [S1; S2]\n\nThe fixed local boundary is **2117t/2116n BC ↔ AD 2116t/2117n**. It remains distinct from January AD 1 and from the two witness-track midpoints introduced below.\n\n### 3.2 Birth pairs\n\n| Starting event, BC | +4232 landing, AD | Identified ordinary reflected event | Offset about 2116 |\n|---|---|---|---|\n| Abram: 2167t/2166n | 2066t/2067n | Isaac birth | +50 ↔ −50 |\n| Isaac: 2067t/2066n | 2166t/2167n | Abram birth | −50 ↔ +50 |\n| Haran / Terah’s firstborn: 2227t/2226n | 2006t/2007n | Jacob birth | +110 ↔ −110 |\n| Jacob: 2007t/2006n | 2226t/2227n | Haran / firstborn counterpart | −110 ↔ +110 |\n\n$$2166+2066=2226+2006=4232.$$\n\nDean’s son-slot reconstruction is **2226 / 2166 / 2106**, Haran/Abram/Nahor. The 60-year separations linking the birth pairs explain their arithmetic dependence. The **50+50=100** Abram–Isaac gap belongs to the original dates. Expanding 4232 to 5000 does not automatically expand those offsets; the recurrence of 50 is the proposed structural association.\n\n### 3.3 Isaac, Jared, and the conception distinction\n\nIsaac’s **2066→1886 BC** lifespan becomes **AD 2166t/2167n→2346t/2347n**, preserving **180**. Relative to Q₁₄₄₆, those boundaries are **720=360+360** and **900** later. Isaac’s death is **230** from the 2116 center, giving **460** between its translated and ordinary reflected positions.\n\nJared **3654 BC** to the working Sodom/Isaac-conception assignment **2067 BC** gives:\n\n$$3654-2067=1587=3\\times529.$$\n\nAppending the bridge gives **1587+4232=5819=11×529**:\n\n$$3655t/3654n\\text{ BC}\\xrightarrow{1587}2068t/2067n\\text{ BC}\n\\xrightarrow{4232}\\text{AD }2165t/2166n.$$\n\nThis landing is **one year before** Abram’s ordinary reflected birth. The conception/birth distinction is preserved. The equal 11×529 scalar in the earlier Conquest handoff does not, by itself, identify its endpoints with this chain.\n\n### 3.4 Peleg and Nahor: ±2 and ±1\n\nNahor here is **Terah’s father**, not Abram’s brother. The retained MT biographies are Peleg **2357→2118** and Nahor **2265→2117 BC**.\n\n| Death, BC | Ordinary reflection, AD | +4232 landing, AD | Positions about Q₂₁₁₆ |\n|---|---|---|---|\n| Peleg: 2119t/2118n | 2118t/2119n | **2114t/2115n** | +2 and −2 |\n| Nahor: 2118t/2117n | 2117t/2118n | **2115t/2116n** | +1 and −1 |\n\nThe initially proposed Peleg landing **2115t/2116n** belongs to Nahor. The corrected Peleg landing preserves the intended ±2 bracket without moving either patriarch by a Gear. The proposed connection with Noah/Shem ±2 is retained as a structural hypothesis.\n\n### 3.5 Entry, Joseph, the nations, and the famine\n\n| Starting pair, BC | +4232 landing, AD | Comparison |\n|---|---|---|\n| Entry: 1877t/1876n | 2356t/2357n | **480 later** than Q₁₈₇₆ |\n| Proposed Joseph boundary: 1876t/1875n | 2357t/2358n | MT Peleg’s birth mirror |\n\nThe equations are **4232−2×1876=480** and **1875+2357=4232**. The AD direction is later, correcting the earlier “480 before” wording.\n\nDean connects Peleg, the division of the earth, Babel/the Table of Nations, Joseph, and the division of the famine week through the themes of **nations and division**. His proposed **1875 BC** transaction boundary follows Jacob’s **1876 BC** arrival and lies in the central portion of the retained **1878–1871** famine.\n\nThe endpoint equation is exact. Its event assignment is a proposal: Genesis 47’s transaction sequence does not independently specify 1875 BC, and the land transfer concerns Egyptian land with the priests exempt. The wider nations correspondence belongs to the theological synthesis. The central year of a seven-year famine is also distinct from its exact halfway instant, which requires seasonal endpoints. These qualifications were already part of the attached handoff and remain in force.\n\n### 3.6 Covenant of Pieces: 35+35\n\nAt the working covenant date **2081 BC**:\n\n$$2116-2081=35,\\qquad4232-2081=2151.$$\n\nThus **2082t/2081n BC +4232 = AD 2151t/2152n**, and the AD comparison is:\n\n$$Q_{2081}\\xrightarrow{35}Q_{2116}\\xrightarrow{35}Q_{2151}.$$\n\nDean connects the bisected **70** with the divided covenant animals, the announced **400-year** residence/affliction period, and the later Babylonian **70**. Genesis 15:13 does not itself name Egypt in the 400-year statement. The selected Egyptian chronology uses **430**, while the 400-year covenant wording supplies the thematic comparison.\n\nThe Hebrew connection is retained precisely: **כָּרַת בְּרִית**, “cut a covenant”; **שֶׁבַע**, “seven”; and oath-taking from **שבע**, illustrated by the seven ewe lambs and oath in Genesis 21. **כרת** and **שבע** are different roots. The “seven oneself” explanation is an etymological proposal, not a rule that every oath required seven acts. [S1, lexical note]\n\n## 4. The 4232 layer: Moses and the 360/180/720 anatomy\n\n| Moses boundary, BC | +4232 landing, AD | Role |\n|---|---|---|\n| 1527t/1526n | 2706t/2707n | Birth; primary |\n| 1487t/1486n | 2746t/2747n | Age 40; secondary explanatory node |\n| 1447t/1446n | 2786t/2787n | Exodus; primary |\n| 1407t/1406n | 2826t/2827n | Death / Conquest; primary |\n\nTwo routes give **1260**:\n\n$$4232-2(1486)=1260,$$\n$$4232-(1526+1446)=1260.$$\n\nThe inverse counterpart construction is equally important:\n\n$$2707t/2706n\\text{ BC}+4232=Q_{1526}.$$\n\nThe generated **2706 BC** is therefore a counterpart of Moses’ reflected birth. It is not assigned a new historical event. It gives:\n\n$$2706\\xrightarrow{1260}1446\\xrightarrow{40}1406\\text{ BC},$$\n$$2706\\xrightarrow{1260}1446\\xrightarrow{1440}6\\text{ BC},$$\n$$2700=1260+1440=(3.5+4)\\times360=7.5\\times360.$$\n\nThe same-season t/n completion is **2707t/2706n→1447t/1446n→7t/6n BC**. The 6 BC Messiah node is the project’s comparison anchor, not a newly inferred birthday.\n\nDean’s additional **time, half-a-time, times** ordering is exact:\n\n| BC comparison | Years | Origin of the generated boundary |\n|---|---:|---|\n| 2706→2346 | **360** | Moses birth counterpart → Isaac death counterpart |\n| 2346→2166 | **180** | Isaac’s lifespan, reversed in the counterpart order |\n| 2166→1446 | **720** | Isaac birth counterpart → held Exodus anchor |\n| Total | **1260** | 360+180+720 |\n\nThe generated Isaac coordinates are **4232−1886=2346** and **4232−2066=2166**. The sum has the same component multiset as **360+720+180**. Its changed order is part of Dean’s chiastic reading.\n\n## 5. The crossed 1380 and the two distinct +120 operations\n\n| Translated AD boundary | Compared with ordinary reflected anchor | Gap |\n|---|---|---:|\n| Conquest Q₂₈₂₆ | Exodus Q₁₄₄₆ | **1380** |\n| Exodus Q₂₇₈₆ | Conquest Q₁₄₀₆ | **1380** |\n\n$$4232-(1446+1406)=1380=3\\times460.$$\n\nThe crossing matters. Comparing translated Exodus with its own mirror gives **1340**; translated Conquest with its own mirror gives **1420**.\n\nThe useful reduction is:\n\n$$1260,\\ 1380,\\ 1500=60(21,23,25).$$\n\n| Step | Operation | Gain |\n|---|---|---:|\n| 1260→1380 | Replace Moses’ 1526 birth with his 1406 death, holding Exodus fixed | **120** |\n| 1380→1500 | Multiply the 1380 width by 25/23 | **120** |\n\nThe equal gains are produced by different operations. **1260×25/23 is not 1380**. The corresponding compatibility equation is **4232=1446+1406+1380**; it is a rearrangement of the same relationship.\n\nThe shared unit remains significant to the proposed synthesis:\n\n$$1380=3\\times460,\\qquad4232\\xrightarrow{K}4600=10\\times460.$$\n\nThe 1500 is an expanded duration. No independently sourced event is assigned to a newly expanded endpoint here.\n\n## 6. Revelation 11–12 and the completed 1260±3.5 construction\n\n### 6.1 Interpretive framework and narrative order\n\nDean understands Revelation as **divinely authored Scripture**, written chiastically and, more precisely, **fractally with integrated symmetries**, interpreting the rest of the Bible. He rejects a purely literalistic reading and a purely human account of its authorship. This report preserves that framework. Arithmetic verifies relationships within the proposed model; the specific correspondence to Revelation’s design remains the theological interpretation being examined.\n\nThe historical birth→Exodus order reverses under the ordinary Mirror:\n\n| Reflected event | AD pair | Position after Exodus mirror |\n|---|---|---:|\n| Exodus | 1446t/1447n | 0 |\n| Moses aged 40 | 1486t/1487n | 40 |\n| Moses’ birth | 1526t/1527n | 80 |\n\nIn Dean’s reading, Revelation 11 supplies the plague/witness/death/revival/ascent template associated with the Exodus; Revelation 12 supplies the birth/woman/dragon/wilderness template associated with Moses’ birth. The **80 years** belong to the reflected chronology, not to an explicit elapsed interval between Revelation’s chapters.\n\nThe woman/wilderness imagery can represent both Moses’ birth into oppression and Israel’s corporate emergence. The **2706→1446→1406** construction transposes Moses’ forty years in Egypt into Israel’s forty wilderness years. Moses/Aaron, Joshua/Zerubbabel, and John the Baptist/Jesus are proposed recurring witnesses to the template.\n\nThe dragon/serpent motif reaches back to Eden. Ezekiel 29’s Pharaoh/Nile-monster imagery is one correspondence; Revelation 11 also joins Sodom and Egypt. Revelation’s witnesses are unnamed. Exodus 1:22 mentions the river decree without naming crocodiles, and Revelation 12 directs its river/flood against the woman. These textual distinctions preserve the proposed typology without making every detail an explicit identification in the text. [S1, §7]\n\n### 6.2 Calendar scale and typological scale\n\n| Relationship | Operation |\n|---|---|\n| 3.5 schematic years = 1260 days | 360 days per schematic year |\n| 7 schematic years = 2520 days | The complete two-half week |\n| 1260 days ↔ 1260 years | Dean’s day-for-year correspondence |\n| 3.5 days ↔ 3.5 years | Smaller accompanying witness interval |\n\nThe Daniel 9 divided-week pattern and Revelation 11–12 supply Dean’s interpretive setting. The two halves at the enlarged scale are **1260+1260=2520**. The smaller **3.5-year** separation accompanies that construction; it is not added to the total 2520.\n\n### 6.3 Exact source components and tracks\n\nRetain **Aaron 1530t BC** and **Moses 1526n BC**, **3.5 years apart** in the selected phase branch. Their lifespans remain **123** and **120**. Their historical deaths therefore do not become 3.5 years apart simply because their births are.\n\nTranslate the births by 4232, then extend each landing backward by one and two 1260-year halves:\n\n| Track | Earlier boundary | Middle boundary | Translated birth |\n|---|---|---|---|\n| Aaron-derived | A₀ = AD **183t** | A₁ = AD **1443t** | A₂ = AD **2703t** |\n| Moses-derived | M₀ = AD **187n** | M₁ = AD **1447n** | M₂ = AD **2707n** |\n\nEach horizontal step is 1260. In each column, the Moses component is 3.5 years later. The compressed **183/186→1443/1446→2703/2706** shorthand uses the neighboring labels; the exact mixed-phase calculation uses **187n/1447n/2707n** from the Moses pairs **186t/187n, 1446t/1447n, 2706t/2707n**.\n\nThe anchored coincidence is **M₁=AD 1447n**, the selected component of the ordinary Exodus mirror. The other track stations are generated template boundaries, not newly dated historical events.\n\n### 6.4 The plus and minus spans are complementary\n\nThe requested plus sequence is:\n\n$$\\text{AD }183t\\xrightarrow{1260}\\text{AD }1443t\\xrightarrow{3.5}\\text{AD }1447n.$$\n\nWith **E=M₁**:\n\n$$E-A_0=1260+3.5=1263.5.$$\n\nThe earlier C113 diagnostic remains valid on the other side:\n\n$$A_2-E=1260-3.5=1256.5.$$\n\nTogether:\n\n$$\\boxed{(1260+3.5)+(1260-3.5)=2520.}$$\n\n| Boundary | Transferred Revelation 11 role |\n|---|---|\n| AD 183t | Opening of the generated 1260-year witness period |\n| AD 1443t | End of that period; beginning of the 3.5-year witness-death interval |\n| AD 1447n | Revival/ascent and corporate national emergence at the Exodus mirror |\n\n“Witness death” here is a role in the transferred template. It is not a redating of Aaron’s or Moses’ actual death. This is the additional operation C113 had not yet executed: extend through the second half-week, then cross from Aaron’s track to the Moses/Exodus boundary.\n\n### 6.5 Exact reflection exchanges the sides\n\n| Track | BC reflection, earlier → later | AD construction, earlier → later |\n|---|---|---|\n| Aaron-derived | 2703n→1443n→183n BC | AD 183t→1443t→2703t |\n| Moses-derived | 2707t→1447t→187t BC | AD 187n→1447n→2707n |\n\n| Side | Before its selected Exodus component | After it |\n|---|---|---|\n| AD | 183t→1447n = **1260+3.5** | 1447n→2703t = **1260−3.5** |\n| BC reflection | 2703n→1447t = **1260−3.5** | 1447t→183n = **1260+3.5** |\n\nThe BC after-Exodus internal order is **3.5+1260**, reversing the AD **1260+3.5** order. Both full tracks retain 2520. The original January axis is unchanged.\n\n**Receiving-window disposition:** replace “1260+3.5 pending explicit endpoints” with **“explicit construction verified, conditional on the adopted 2520-year template.”** C113’s old 32-check checkpoint is a prior result; the present report checks the supplied resolved construction independently. It does not claim to replay the frozen C113 campaign.\n\n## 7. The 8464 layer: regular MT Noah/Shem/Flood\n\n### 7.1 Normal Gear 2, Cainan OFF\n\nThe six selected boundaries are **3058/2578/2558/2458/2108/1958n BC** with their Tishri companions. The bridge is **8464=2×4232**. All three comparison columns refer to ordinary AD reflections of the primary Moses nodes.\n\n| Boundary | Source | Landing +8464 | Birth 1526 | Exodus 1446 | Conquest 1406 |\n| --- | --- | --- | --- | --- | --- |\n| Noah birth | 3059t/3058n BC | AD 5406t/5407n | 3880 | 3960 | 4000 |\n| 120 before Flood | 2579t/2578n BC | AD 5886t/5887n | 4360 | 4440 | 4480 |\n| Shem birth | 2559t/2558n BC | AD 5906t/5907n | 4380 | 4460 | 4500 |\n| Flood start | 2459t/2458n BC | AD 6006t/6007n | 4480 | 4560 | 4600 |\n| Noah death | 2109t/2108n BC | AD 6356t/6357n | 4830 | 4910 | 4950 |\n| Shem death | 1959t/1958n BC | AD 6506t/6507n | 4980 | 5060 | 5100 |\n\nThe removed age-40 column would be obtained by adding 40 to the birth-column spans, or subtracting 40 from the Exodus-column spans. Its removal changes presentation, not the fixed biography.\n\nThe highlighted multiples of 230 are distributed across the primary columns:\n\n$$4830=21\\times230,\\quad5060=22\\times230,\\quad4600=20\\times230.$$\n\nThe Flood-to-Conquest **4600** is especially relevant because **4232K=4600**. It is a raw comparison width in this table and an expanded width in the separate 4232 conversion. Both realizations are retained with their operations named.\n\nThe Shem-death-to-Conquest **5100** is:\n\n$$5100=2\\times2550=2(1260+1290).$$\n\nThe regular biography supplies **500+100+500=1100** from Noah birth through Shem birth and Flood to Shem death. Noah’s life itself is **950**, and Shem’s **600**; the translation preserves both.\n\n### 7.2 The Christ-anchor comparisons\n\nHere the held terminal is the ordinary paired reflection of **7t/6n BC**, namely **AD 6t/7n**.\n\n| Boundary | AD landing base | To reflected Christ AD 6t/7n |\n| --- | --- | --- |\n| Noah birth | 5406 | 5400 |\n| 120 before Flood | 5886 | 5880 |\n| Shem birth | 5906 | 5900 |\n| Flood start | 6006 | 6000 |\n| Noah death | 6356 | 6350 |\n| Shem death | 6506 | 6500 |\n\nThe principal span identities are:\n\n$$5400=15\\times360,\\quad5880=120\\times49,\\quad6000=120\\times50,\\quad6500=13\\times500.$$\n\nThe 120-year countdown preserves **6000−5880=120**, connecting 120 groups of 50 with 120 groups of 49. The Flood landing also lies **4600** beyond the reflected Conquest, while Noah birth lies **4000** beyond it and **3960=11×360** beyond the reflected Exodus.\n\nReflecting the generated 6006 and 5406 landings back to BC gives the equivalent comparisons with the selected cumulative Creation member **14006 BC**:\n\n$$14006-6006=8000,\\qquad14006-5406=8600=4300+4300.$$\n\nThese use the named **14006 member**, not every member of the full Creation envelope.\n\nDean also proposes that the remaining **5906** and **6356** landings connect with the 40- and 100-year Christ-generation alternatives around **AD 35/95** and their counterparts. That proposal is retained for later endpoint specification. The direct AD 6 comparison gives **5900** and **6350**, as printed. A change to a literal BC endpoint or a standalone same-number mirror must be declared rather than inferred from an unsuffixed number.\n\n### 7.3 Regular Cainan ON and the reflected −130 movement\n\nThe insertion adds **130** to the upstream BC magnitudes. Therefore:\n\n$$b\\mapsto b+130,\\qquad8464-b\\mapsto8464-b-130.$$\n\nThe BC sources move earlier and the AD landings also move earlier in chronological time. The landing’s numerical change is **−130**. No cumulative 460 insertion is used in this regular table.\n\n| Boundary | Source | Landing +8464 | Entry 1876 | Exodus 1446 | Conquest 1406 |\n| --- | --- | --- | --- | --- | --- |\n| Noah birth | 3189t/3188n BC | AD 5276t/5277n | 3400 | 3830 | 3870 |\n| 120 before Flood | 2709t/2708n BC | AD 5756t/5757n | 3880 | 4310 | 4350 |\n| Shem birth | 2689t/2688n BC | AD 5776t/5777n | 3900 | 4330 | 4370 |\n| Flood start | 2589t/2588n BC | AD 5876t/5877n | 4000 | 4430 | 4470 |\n| Noah death | 2239t/2238n BC | AD 6226t/6227n | 4350 | 4780 | 4820 |\n| Shem death | 2089t/2088n BC | AD 6376t/6377n | 4500 | 4930 | 4970 |\n\nFor direct side-by-side comparison, the following base labels abbreviate the complete phase pairs above:\n\n| Boundary | BC base OFF → ON | AD base OFF → ON | To Entry | To Exodus | To Conquest |\n| --- | --- | --- | --- | --- | --- |\n| Noah birth | 3058 → 3188 | 5406 → 5276 | 3530 → 3400 | 3960 → 3830 | 4000 → 3870 |\n| 120 before Flood | 2578 → 2708 | 5886 → 5756 | 4010 → 3880 | 4440 → 4310 | 4480 → 4350 |\n| Shem birth | 2558 → 2688 | 5906 → 5776 | 4030 → 3900 | 4460 → 4330 | 4500 → 4370 |\n| Flood start | 2458 → 2588 | 6006 → 5876 | 4130 → 4000 | 4560 → 4430 | 4600 → 4470 |\n| Noah death | 2108 → 2238 | 6356 → 6226 | 4480 → 4350 | 4910 → 4780 | 4950 → 4820 |\n| Shem death | 1958 → 2088 | 6506 → 6376 | 4630 → 4500 | 5060 → 4930 | 5100 → 4970 |\n\nThe main Entry comparison is:\n\n$$2588\\text{ BC}+8464\\longrightarrow Q_{5876},\\qquad5876-1876=4000.$$\n\nNoah’s ON landing gives **5276−1876=3400**. Using the separately declared **1846** comparison gives **5276−1846=3430=70×7×7**. This is the precise form of the proposed +30 observation. It supports examining the 1846 member; it does not replace Entry 1876.\n\nThe source-state distinction remains: SP is **650** and native LXX ON **780** earlier than regular MT OFF at this selected Noah/Shem/Flood field. At fixed W, their landings inherit **−650/−780** movements. These are local regular offsets, not universal cumulative Creation offsets. The report does not open new SP companion or Gear states in the main calculation.\n\n## 8. Regular Cainan’s own lifespan and the Creation/Jared rows\n\n### 8.1 The regular 2551→2091 Cainan lifespan\n\nSecond Cainan’s selected regular lifespan is **2551→2091 BC**, **460 years**, distinct from the **130-year** begetting insertion. Translation by 8464 gives:\n\n$$2552t/2551n\\text{ BC}\\longrightarrow Q_{5913},$$\n$$2092t/2091n\\text{ BC}\\longrightarrow Q_{6373}.$$\n\nDean’s selected comparison is the **one-year-earlier Conquest companion Q₁₄₀₅=AD 1405t/1406n**:\n\n$$5913-1405=4508,\\qquad4508K=4900.$$\n\nThe death counterpart gives **6373−1405=4968**, and **4968K=5400**. Their raw difference is 460 and expanded difference 500. Against the primary Q₁₄₀₆ anchor, the raw values are **4507/4967**. The one-year choice is therefore explicit; §10 shows its relationship to the cumulative envelopes.\n\nDean regards the ON alignments as evidence supporting the reinsertion hypothesis. The present report verifies the placements while preserving that evidential interpretation as his hypothesis.\n\n### 8.2 Creation and Jared, with normal Gear 2 held\n\nThe selected regular nodes are **4114 BC** and **3654 BC**, 460 years apart. Two separately declared bridge states give:\n\n| Boundary | Source BC | +8464 landing AD | To Conquest | +9200 landing AD | To Conquest |\n| --- | --- | --- | --- | --- | --- |\n| Creation | 4115t/4114n | 4350t/4351n | 2944 | 5086t/5087n | 3680 |\n| Jared | 3655t/3654n | 4810t/4811n | 3404 | 5546t/5547n | 4140 |\n\nThe expanded bridge is **8464×25/23=9200**; the earlier “25/25” expression was a typographical error. At W=9200, the Conquest comparisons are:\n\n$$3680=8\\times460\\xrightarrow{K}4000,$$\n$$4140=9\\times460\\xrightarrow{K}4500.$$\n\nThis expands the bridge before generating new coordinates. It is a different operation from expanding an already computed comparison gap.\n\nFor completeness, at W=8464 the direct Q₆ spans are **4344** and **4804**; to the literal BC pair **7t/6n**, the cross-axis spans are **4356** and **4816**. The earlier compressed description “Adam/Jared 4600 and 5100 to Christ” is not obtained from these specified inputs. It is retained in the unresolved ledger, requiring its additional source state or operation rather than being silently repaired. The independently verified Methuselah-derived **4600/4140** Christ comparisons are given in §12.\n\nRegular Creation with Cainan ON was explicitly set aside because Dean associated that route with a Gear-3 Kenan/Cainan construction. It appears only in Appendix A; it does not alter these normal-frame rows.\n\n## 9. The 12696 layer: full cumulative seven-year envelopes\n\nUse **W=12696=2×6348=24×529**. Retain each full seven-elapsed-year Nisan envelope and its Tishri companion. No compression to the interior three-year track is made. A phase-pair envelope spans seven years on matching seasons and 7.5 from its first Tishri boundary to its last Nisan boundary.\n\nThe principal columns use **Q₁₄₄₆** and **Q₁₄₀₆**. They are point-to-fixed-anchor ranges, not a pairing of every source member with a different year of the Conquest week. [S2, §§6A–6B]\n\n### 9.1 Cainan OFF\n\n| Node | Full BC envelope | AD landing +12696 | To Exodus | To Conquest |\n| --- | --- | --- | --- | --- |\n| Methuselah / Enoch-ascension marker | 8133t/8132n → 8126t/8125n | 4564t/4565n → 4571t/4572n | 3118–3125 | 3158–3165 |\n| Lamech / Methuselah-death marker | 7164t/7163n → 7157t/7156n | 5533t/5534n → 5540t/5541n | 4087–4094 | 4127–4134 |\n| Noah | 6387t/6386n → 6380t/6379n | 6310t/6311n → 6317t/6318n | 4864–4871 | 4904–4911 |\n| Shem | 5437t/5436n → 5430t/5429n | 7260t/7261n → 7267t/7268n | 5814–5821 | 5854–5861 |\n| Flood / Arphaxad boundary | 4837t/4836n → 4830t/4829n | 7860t/7861n → 7867t/7868n | 6414–6421 | 6454–6461 |\n| Arphaxad | 4837t/4836n → 4830t/4829n | 7860t/7861n → 7867t/7868n | 6414–6421 | 6454–6461 |\n| Shelah / Cainan-death boundary | 4399t/4398n → 4392t/4391n | 8298t/8299n → 8305t/8306n | 6852–6859 | 6892–6899 |\n| Eber | 3966t/3965n → 3959t/3958n | 8731t/8732n → 8738t/8739n | 7285–7292 | 7325–7332 |\n| Peleg | 3502t/3501n → 3495t/3494n | 9195t/9196n → 9202t/9203n | 7749–7756 | 7789–7796 |\n\n### 9.2 Cainan ON\n\nIn cumulative execution, Arphaxad and all earlier nodes move **460 years earlier**. Shelah and later nodes stay fixed; the new Cainan lifespan occupies **4858–4851→4398–4391 BC**.\n\n| Node | Full BC envelope | AD landing +12696 | To Exodus | To Conquest |\n| --- | --- | --- | --- | --- |\n| Methuselah / Enoch-ascension marker | 8593t/8592n → 8586t/8585n | 4104t/4105n → 4111t/4112n | 2658–2665 | 2698–2705 |\n| Lamech / Methuselah-death marker | 7624t/7623n → 7617t/7616n | 5073t/5074n → 5080t/5081n | 3627–3634 | 3667–3674 |\n| Noah | 6847t/6846n → 6840t/6839n | 5850t/5851n → 5857t/5858n | 4404–4411 | 4444–4451 |\n| Shem | 5897t/5896n → 5890t/5889n | 6800t/6801n → 6807t/6808n | 5354–5361 | 5394–5401 |\n| Flood / Arphaxad boundary | 5297t/5296n → 5290t/5289n | 7400t/7401n → 7407t/7408n | 5954–5961 | 5994–6001 |\n| Arphaxad | 5297t/5296n → 5290t/5289n | 7400t/7401n → 7407t/7408n | 5954–5961 | 5994–6001 |\n| Second Cainan | 4859t/4858n → 4852t/4851n | 7838t/7839n → 7845t/7846n | 6392–6399 | 6432–6439 |\n| Shelah / Cainan-death boundary | 4399t/4398n → 4392t/4391n | 8298t/8299n → 8305t/8306n | 6852–6859 | 6892–6899 |\n| Eber | 3966t/3965n → 3959t/3958n | 8731t/8732n → 8738t/8739n | 7285–7292 | 7325–7332 |\n| Peleg | 3502t/3501n → 3495t/3494n | 9195t/9196n → 9202t/9203n | 7749–7756 | 7789–7796 |\n\nEvery shifted upstream landing is **460 earlier** than its OFF counterpart. The same translation rule explains the regular −130 and cumulative −460 movements, but the two source insertions remain different operations.\n\nLamech is included for completeness and context. The Lamech birth boundary is the cumulative Methuselah-death marker; the Arphaxad/Flood boundary is a distinct marker. Similarly, “Methuselah / Enoch-ascension marker” uses the cumulative sequential construction. It does not say that Enoch’s actual regular ascension occurred at the historical birth of Methuselah.\n\n## 10. The 6000/7000 relationships and the explicit ±1 arrangement\n\n### 10.1 Cainan preserves 460 through both executions\n\nThe closing cumulative members give:\n\n$$4851-2551=4391-2091=2300.$$\n\nBut the two bridges differ by **12696−8464=4232**, so their generated AD landings differ by:\n\n$$4232-2300=1932.$$\n\n| Selected boundary | Regular landing +8464 | Cumulative landing +12696 | Gap |\n|---|---|---|---:|\n| Cainan birth closing member | Q₅₉₁₃ | Q₇₈₄₅ | **1932** |\n| Cainan death / Shelah closing member | Q₆₃₇₃ | Q₈₃₀₅ | **1932** |\n\nRelative to **Q₁₄₀₅**, the cumulative spans are:\n\n$$7845-1405=6440,\\qquad8305-1405=6900,$$\n$$6900-6440=460.$$\n\nThe complementary conversions are:\n\n$$6440K=7000,\\qquad6900P=7000,\\qquad6900K=7500.$$\n\nThe regular birth comparison **4508K=4900** and cumulative birth comparison **6440K=7000** differ by **2100=1932K**. The one-year companion choice is shared by both. This is the requested return to the earlier reminder about **4851−2551=2300**.\n\n### 10.2 Locating the one-year companions across the whole week\n\nThe ordinary reflected Conquest/rest envelope is:\n\n$$C:\\quad Q_{1399}\\longrightarrow Q_{1406}\n\\quad(\\text{AD }1399t/1400n\\longrightarrow1406t/1407n).$$\n\nSubtract the named comparison width from each entire landing envelope, preserving its seven-year width:\n\n| Landing envelope | Subtracted raw width | Resulting comparison envelope | Relative to C |\n|---|---:|---|---:|\n| Flood ON: Q₇₄₀₀→Q₇₄₀₇ | **6000** | Q₁₄₀₀→Q₁₄₀₇ | **+1 year** |\n| Cainan: Q₇₈₃₈→Q₇₈₄₅ | **6440** | Q₁₃₉₈→Q₁₄₀₅ | **−1 year** |\n| Shelah / Cainan death: Q₈₂₉₈→Q₈₃₀₅ | **6900** | Q₁₃₉₈→Q₁₄₀₅ | **−1 year** |\n\nThis is a precise version of Dean’s observation that the six/thousand and seven/thousand readings lie **one year on either side** of the Conquest/rest arrangement. The primary tables remain anchored at Q₁₄₀₆; the companion envelopes are named separately.\n\nFor the selected Flood member **Q₇₄₀₆**, both same-season comparisons to Q₁₄₀₆ are exactly 6000:\n\n$$7406t-1406t=7407n-1407n=6000.$$\n\nThe crossed-suffix wording **7406t−1406n** and **7407n−1407t** instead gives **6000.5** and **5999.5** in the exact phase model. Their mean is 6000. The intended exact pair is retained by matching the suffixes; the half-year information is not discarded.\n\n### 10.3 Solomon’s Temple and the 480-year connection\n\nThe primary comparison is to the **reflected Temple** on the AD side. At the selected members:\n\n| Flood state and landing | To Q₁₄₄₆ Exodus | To Q₁₄₀₆ Conquest | To Q₉₆₆ Temple |\n|---|---:|---:|---:|\n| ON: Q₇₄₀₆ | **5960** | **6000** | **6440** |\n| OFF: Q₇₈₆₆ | **6420** | **6460** | **6900** |\n\n$$6440=5960+480,\\qquad6900=6420+480,$$\n\nbecause **1446−966=480**, whereas **1406−966=440**. The 480 belongs to the Exodus-to-Temple comparison.\n\nFor the complete seven-year Temple windows, distinguish the two proposed date selections:\n\n| Temple BC Nisan envelope | Ordinary AD reflected envelope | Flood ON point-to-point width | Flood OFF point-to-point width |\n|---|---|---:|---:|\n| 966→959 | Q₉₅₉→Q₉₆₆ | **6441** | **6901** |\n| 967→960 companion | Q₉₆₀→Q₉₆₇ | **6440** | **6900** |\n\nThe selected-member Q₉₆₆ comparison above is exact in the primary Temple frame; pairing the complete envelopes gives the explicit one-year distinction. The 7.5 reading uses the full Tishri-to-Nisan spread. First Kings 6 provides the Temple’s 480th-year and seven-year language; the project’s phase and date selections specify how that language is executed here.\n\n## 11. Peleg, the Christ-period window, and the 17500 crossing\n\nPeleg’s translated envelope is **Q₉₁₉₅→Q₉₂₀₂**. Subtracting **9200** gives:\n\n$$6t/5n\\text{ BC}\\longrightarrow\\text{AD }2t/3n.$$\n\nThus Dean’s Christ-period correspondence is exact in the retained phase model. **9200K=10000** is the accompanying converted width. Holding a terminal or opening boundary fixed is required to assign new dates to that converted width; the duration alone does not choose its anchor.\n\nShelah’s translated envelope is **Q₈₂₉₈→Q₈₃₀₅**. Reflect one envelope and pair its members in reverse order with the other:\n\n$$8298+9202=8305+9195=17500.$$\n\nThe full component examples are:\n\n$$8299t/8298n\\text{ BC}\\longrightarrow Q_{9202}=17500,$$\n$$8306t/8305n\\text{ BC}\\longrightarrow Q_{9195}=17500.$$\n\nFor every corresponding member u from 0 through 7:\n\n$$[8298+u]+[9202-u]=17500.$$\n\nThe reversal is essential. Same-order member pairing produces **17493→17507**, not a constant 17500. Ordinary same-AD-side Shelah-to-Peleg subtraction gives **897**. These are different comparisons.\n\nThe exact cross-width is **17500=7×2500=35×500**. Dean reads the Peleg/Christ alignment and the crossing with Shelah as part of the reorganization of the chronology around its central redemptive theme.\n\n## 12. Methuselah / Enoch, the Creation comparison, and the ministry window\n\nThe cumulative landing envelopes are:\n\n| State | AD landing |\n|---|---|\n| Cainan OFF | Q₄₅₆₄→Q₄₅₇₁ |\n| Cainan ON | Q₄₁₀₄→Q₄₁₁₁ |\n\nThey remain exactly **460** apart. The ON landing is **10 years earlier** than the ordinary reflection of normal MT Creation **Q₄₁₁₄→Q₄₁₂₁**. Dean corrected his initial normal-Creation identification: he had in mind a separate round comparison lying ten years later in BC chronology, with year labels ten smaller. This report retains the exact −10 relation and does not overwrite normal Creation.\n\nReflecting the Methuselah-derived landings back to BC gives:\n\n| State | Reflected BC envelope | Paired AD comparison | Constant width |\n|---|---|---|---:|\n| OFF | 4572t/4571n→4565t/4564n | 29t/30n→36t/37n | **4600** |\n| ON | 4112t/4111n→4105t/4104n | 29t/30n→36t/37n | **4140** |\n\nThese hold point-to-point across the seven-year matching-season envelopes. Their K conversions are **5000** and **4500**. The important **4600/4140** spans are therefore independently executable here, with explicit endpoints.\n\nThe full outer seasonal spread of the AD comparison is 7.5 years:\n\n$$\\text{AD }29t\\xrightarrow{3.5}\\text{AD }33n\n\\xrightarrow{3.5}\\text{AD }36t\\xrightarrow{0.5}\\text{AD }37n.$$\n\nThis locates Dean’s preferred **AD 33n** Passion comparison within **3.5+3.5+0.5**. The opening 29t is a selected template boundary; the arithmetic alone does not establish a historical ministry-start date.\n\nThe theological context associates cumulative Methuselah with Enoch’s ascension, Enoch as seventh from Adam, and the Watcher/Jared complex. That event association belongs to the cumulative/Enochic reading, while the table preserves the node’s actual computational role.\n\n## 13. Cumulative Creation: the Exodus-centered 490 completion\n\n### 13.1 Creation remains on the BC side after +12696\n\n| State | Source Nisan BC envelope | After +12696, still BC | Closing member relative to Exodus 1446 |\n|---|---|---|---|\n| Cainan OFF | 14011→14004 | **1315→1308** | 138 later |\n| Cainan ON | 14471→14464 | **1775→1768** | 322 earlier |\n\nTishri companions are one BC label higher. The 460 insertion is preserved:\n\n$$1768-1308=322+138=460.$$\n\nApply the stated Keys separately, with Exodus held fixed:\n\n| Exodus side | Raw width | Conversion | Completed width | Gain | Generated closing endpoint |\n|---|---:|---|---:|---:|---|\n| Older / ON | 322 | ×25/23 | **350** | 28 | **1796 BC** |\n| Younger / OFF | 138 | ×70/69 | **140** | 2 | **1306 BC** |\n\nTherefore:\n\n$$1796\\rightarrow1446\\rightarrow1306\\text{ BC}=350+140=490.$$\n\nThis is the route Dean requested. The earlier substituted **1936→1929→1796→1446** route is a distinct repository construction and does not replace this derivation. [S5]\n\n### 13.2 Carrying the original seven-year unit\n\nMove each full envelope by the displacement obtained at its closing endpoint, keeping its seven-year width:\n\n| State | Translated envelope | Endpoint-calibrated shift | Completed envelope |\n|---|---|---:|---|\n| ON | 1775→1768 BC | 28 earlier | **1803→1796 BC** |\n| OFF | 1315→1308 BC | 2 later | **1313→1306 BC** |\n\nNow:\n\n$$1796\\rightarrow1446\\rightarrow1313\\rightarrow1306\n=350+133+7=483+7=490.$$\n\nThe final seven is already inside **133+7=140**. It must not be added again to 350+140. Corresponding envelope edges remain 490 apart; the inner gap is **483**, and the full outer envelope is **497=7+483+7**.\n\nThis is a declared transported-envelope convention. Scaling every point about the Exodus by its ratio would instead scale the seven-year widths themselves. The report preserves Dean’s full seven-year unit by transporting it after the endpoint conversion.\n\n### 13.3 The 26/27 generation-carrier relationship\n\nThe ordinary cumulative root is:\n\n$$14004-1446=12558=26\\times483,$$\n$$12558P=12740=26\\times490=35\\times364.$$\n\nIts gain is **182=26×7**. The separately completed Cainan comparison contributes:\n\n$$26\\times490+(350+133+7)=27\\times490=13230.$$\n\nDean relates this to the MT count of 26 generations through Moses, or 27 with Cainan. This is a composite completed-carrier total. Applying P uniformly to the unadjusted ON span does not produce it:\n\n$$14464-1446=13018,\\qquad13018P=39620/3\\ne13230.$$\n\nThe repository’s distinct uniform 27-carrier input is **13041=27×483**, which is **23** above 13018. That route and the present split conversion agree in their completed scalar while retaining different source constructions. [S5; S6]\n\nThe split gain **28+2=30** is a derived duration. It is not automatically the repository’s separate Apparent-Age 30, nor the date AD 30.\n\n## 14. The cumulative Moses landings, 22540, and the central crossings\n\n### 14.1 The shared Moses anchors under +12696\n\n| Source node, BC | Landing, AD |\n|---|---|\n| Birth: 1527t/1526n | **11170t/11171n** |\n| Exodus: 1447t/1446n | **11250t/11251n** |\n| Death / Conquest: 1407t/1406n | **11290t/11291n** |\n\nThe translation preserves **80+40=120**. The death landing is Q₁₁₂₉₀; **11291t/11290n** reverses the suffix assignments incorrectly.\n\nReflect these landing pairs and make the crossed comparisons:\n\n| Crossed interval | Width on both phases | Midpoint pair |\n|---|---:|---|\n| 11291t/11290n BC→AD 11250t/11251n | **22540** | **21t/20n BC** |\n| 11251t/11250n BC→AD 11290t/11291n | **22540** | **AD 20t/21n** |\n\nEach phase interval divides into:\n\n$$11270+11270=23\\times490+23\\times490.$$\n\nThe central identity is:\n\n$$\\boxed{22540=46\\times490=460\\times49.}$$\n\nThe two midpoint-pair centers are −20 and +20 in the January-centered proof coordinate, **40 years apart** and symmetric around the original origin. They are not a relocated global axis. A literal crossing of drawn lines in 3D would additionally depend on the still-unassigned embedding.\n\nSubtracting 11270 from the forward Moses landings generates the template:\n\n$$101t/100n\\text{ BC}\\xrightarrow{80}21t/20n\\text{ BC}\n\\xrightarrow{40}\\text{AD }20t/21n.$$\n\nThese are generated comparison coordinates, not historical dates for Moses.\n\n### 14.2 The 1426 midpoint and the census correction\n\nThe chronological midpoint of Exodus and Conquest is:\n\n$$(1446+1406)/2=1426\\text{ BC}.$$\n\nIt yields:\n\n$$12696-1426=11270=230\\times49.$$\n\nThus its translated pair Q₁₁₂₇₀ and ordinary BC reflection have centers exactly ±11270 around January AD 1. This gives the two halves of the 460-Jubilee total directly.\n\nThe proposed census explanation needs correction: Numbers 1:3 counts military-age men **twenty and older**, and Numbers 14:29 applies the judgment to the counted adult generation. The excluded younger generation is a different category. Numbers 1:1 dates that census to the second year after the Exodus, not 1426 BC. Accordingly, **1426 is retained as the exact generated wilderness midpoint**, not as an established census date. [S10]\n\nThe project’s theological identification of January AD 1 with Christ’s naming/circumcision hinge is retained; File_09 distinguishes this January datum from its traditional December 25 nativity association. The mathematical datum does not establish the historical date of Jesus’ birth. [S3]\n\n### 14.3 Temple: 46+3=49 in the optional AD 30 branch\n\nThe repository supplies the Herodian construction comparison **20n BC→AD 27n=46**, with **AD 30n** allowed as an optional Passion state:\n\n| Comparison | Nisan route | Phase companion | Years |\n|---|---|---|---:|\n| Construction head→ministry | 20n BC→AD 27n | 21t BC→AD 26t | **46** |\n| Ministry→optional Passion | AD 27n→AD 30n | AD 26t→AD 29t | **3** |\n| Total | 20n BC→AD 30n | 21t BC→AD 29t | **49** |\n\nThe Tishri endpoint is a generated phase companion, not a claim of an autumn crucifixion. John 2’s forty-six years concerns the Temple’s construction; its three-day resurrection saying is textually distinct from the three-year ministry comparison. Dean’s three-day/three-year association is typological. With the preferred AD 33 endpoint, the same 20 BC head gives **52**, not 49. The optional branch is therefore material and does not displace the project’s preferred Passion date. [S5; S9; S10]\n\n### 14.4 The provisional 1380 exchange joint\n\nThe same total can be expanded in two factorizations:\n\n$$46(460+30)=460(46+3)=22540,$$\n$$46\\times460=21160,$$\n$$46\\times30=460\\times3=1380,$$\n$$21160+1380=22540.$$\n\nIn the declared **49-year Jubilee** register this is **460 Jubilees**. The term **1380 exchange joint** remains provisional branch vocabulary. The factor exchange is exact algebra; the source-endpoint realizations are the proposed structural finding.\n\nThis integrates the earlier material at the level actually demonstrated:\n\n| Construction | Completed result |\n|---|---:|\n| Cumulative Creation→Exodus root | **26×490** |\n| Split Cainan completion about Exodus | **350+133+7=490** |\n| Composite generation carrier | **27×490** |\n| Crossed translated Exodus/Conquest total | **46×490=460×49** |\n| Shared factor-exchange increment | **1380** |\n\nThe report has not demonstrated that all these scalars form one continuous path with unchanged endpoints. It records their exact integration by declared operators and factors, leaving that stronger path-identification question open.\n\n## 15. Creation and Conquest: two Keys, two complementary completions\n\n### 15.1 The complete MT and LXX week comparisons\n\n| Boundary | Regular MT OFF Creation, BC | Regular native LXX ON Creation, BC | Reflected Conquest, AD |\n|---|---|---|---|\n| Opening | **4122t/4121n** | **5502t/5501n** | **1399t/1400n** |\n| Closing | **4115t/4114n** | **5495t/5494n** | **1406t/1407n** |\n\nThe full point-to-point widths are **5520** and **6900** on both phases. The **1380** offset here is specifically between these selected regular native states; it is not a universal MT/LXX offset.\n\n$$4115+1406-1=4114+1407-1=5520,$$\n$$5495+1406-1=5494+1407-1=6900.$$\n\nBoth Keys are exact and already documented in the earlier work:\n\n| Raw span | ×70/69 | ×25/23 |\n|---:|---:|---:|\n| **5520** | **5600** | **6000** |\n| **6900** | **7000** | **7500** |\n\nDean’s six-plus-one conquest/rest interpretation uses **1407t/1406n BC→1401t/1400n BC→1400t/1399n BC**. The 6000/7000 correspondence interprets six and seven units at 1000:1; the 7500 reading retains the 7.5 seasonal envelope. Reflection reverses the ordering of the events within the interval while preserving its length. [S3; S7]\n\n### 15.2 The mixed boundary construction\n\nUniform scaling of every boundary is not required for the construction Dean specified. The selected conversions of cumulative boundary widths are:\n\n| Original radius | First conversion | Selected continuation |\n|---:|---:|---:|\n| 2116 | 2300 | K→**2500** |\n| 4232 | 4600 | K→**5000** |\n| 6348 | 6900 | P→**7000** |\n\nThus:\n\n$$0\\rightarrow2500\\rightarrow5000\\rightarrow7000,$$\n$$2500+2500+2000=7000.$$\n\nThe final **2000 is 7000−5000**, a difference between converted boundary widths. It is not the P conversion of a 2300 segment. Introducing the independently obtained **6000** comparison divides the final 2000 into **1000+1000**, giving the proposed **5+1+1** reading.\n\nThe alternative continuation **6900K=7500** remains equally exact. The retained marker:\n\n$$5290\\xrightarrow{K}5750\\xrightarrow{K}6250$$\n\ngives **6000−250** and **6000+250**, Dean’s **Day 5.75→6.25** crossover between the creation/fall imagery and restored rest. These are successive conversion states; they are not automatically two historical dates or a newly assigned Tishri/Nisan pair.\n\nThis corrects the earlier assistant framing that demanded one common ratio across every boundary. The report retains the mixed construction with each ratio visible.\n\n### 15.3 Year 14 and Year 15: the final theological clarification\n\nDean explicitly requires both readings because they serve separate but complementary purposes in the Creation/Fall/restoration pattern:\n\n| One-side continuation from 6900 | Sum of the paired widths | 1000:1 correspondence | Theological function |\n|---|---:|---|---|\n| P→**7000** | **14000** | **7+7; Year 14** | Completion, covering, restoration |\n| K→**7500** | **15000** | **7.5+7.5; Year 15** | Renewed age; the “eighth day” relative to the preceding seven |\n\nThe extra half-unit on each side supplies **500+500=1000**, the additional symbolic year in the paired total. Dean connects this **14/15** distinction with the Nisan/Tishri festival boundary and the passage into the new age.\n\nFile_70’s Nisan disclosure provides an explicit precedent: the fourteenth expresses **7+7 completion**, followed by the fifteenth as departure/liberation beyond the completed double week. The current Tishri/Nisan and 7000/7500 synthesis is recorded as Dean’s theological interpretation; it does not rewrite every older Creation microstructure row. [S8, §8]\n\nThe “eighth day” here is the renewal motif beyond a completed seven, not an assertion that Tishri 15 is the eighth day of the Feast of Tabernacles.\n\nDean’s Creation/Fall reading includes **5+1+1+5+1+1**, with the Day/Year-13 Eve/Fall complex and the Day/Year-14 restoration, extended to the Day/Year-15 renewal. The current diagram reads outward from the Christ-centered zero in a restorative direction. Ordinary Creation order, reversed Mirror order, the doubled seven, and the 7.5 seasonal envelope should each retain their stated role.\n\nFinally, the paired widths must be distinguished from the full outer span when an older construction retains a central gap. For example, the prior fixed-landing construction around **3t/2n BC** gave **7000+4+7000=14004** and **7500+4+7500=15004**. The 14000/15000 theological totals are the sums of the two large bridges. In the zero-centered radius diagram the doubled radii themselves have no additional central gap. [S7, §10]\n\n## 16. The MT/SP/LXX and 115 background\n\nThe comprehensive prior Mirror study already connects the cumulative and regular chronologies through **115=5×23**, for which **115K=125**. One selected MT pair gives:\n\n$$2645=23\\times115\\xrightarrow{K}2875=25\\times115=23\\times125.$$\n\nThe two widths occur in separately selected source states: cumulative MT ON **5293→regular 2648**, and cumulative MT OFF **4833→regular 1958**. They must not be written as an unconverted equality. [S7, §4.2]\n\nThe local SP cumulative difference decomposes as **120=115+5**; a five-year selection inside the seven-year field exposes 115. Prior examples include **4831→4716=115**, **4716→3106=1610=14×115**, and **3106→2991=115**. The last two use an explicitly selected **SP Gear-1** setting, and the final one changes the sojourn frame. They belong to the earlier background study, not to the normal-Gear-2 execution of the present tables. [S7, §5]\n\nDean interprets the MT/SP/LXX cumulative-Flood intersections with Creation through **5+1+1+6**, with another +1 implied. This report preserves that proposed larger template and the exact component constructions supplied here. It does not claim that every segment of that entire cross-tradition sequence has now been assigned and independently audited as one continuous chain. That mapping is the strongest bounded continuation after this synthesis.\n\nThe earlier **3+7×529** handoff likewise remains source-qualified: **5296→3709→6 BC** uses MT cumulative ON, SP regular G3 companion Noah, and the Christ anchor. It is not silently imported into the main Gear-2 tables. Its total 5290 can support the retained trunk marker without changing its source identities. [S11]\n\n## 17. What the proposed geometry establishes so far\n\nThe mathematical core has an economical form:\n\n$$M(a)=-a,\\qquad T_W(a)=a+W,\\qquad D_W(b,d)=W-b-d,$$\n$$W\\in\\{4232,8464,10580,12696\\},\\qquad K=25/23,\\quad P=70/69.$$\n\nThe principal boundary radii lie in the **529 lattice**. Translation changes source coordinates into complementary landing coordinates; Mirror composition supplies genuine local reflections. Cainan insertion changes upstream coordinates by a fixed amount, and its landing movement follows immediately from the same equation. The regular 130 and cumulative 460 movements converge at Shelah under their separate source rules.\n\nDean describes the reorganization of patterns under these new coordinates as **self-organization**, suggesting an underlying geometric or fractal structure. The demonstrated content is the recurrence of these exact operators and selected endpoint relationships. The squared factors and **2304=48²** gain make a geometric investigation natural, but a square factor alone does not establish a spatial dimension, area, metric, or fractal law.\n\nThe proposed third dimension remains a research direction. A useful eventual data structure would record each event’s source state, ordinary chronological coordinate, selected y-boundary, translation, phase, and conversion state. A z coordinate should be introduced only when its defining relationship has been specified.\n\n## 18. Corrections, dependencies, and the receiving-window task\n\n### 18.1 Corrections carried into this complete report\n\n| Earlier shorthand or assumption | Retained correction |\n|---|---|\n| Triple 2116 written 6398 | **6348** |\n| 8464×25/25=9200 | **8464×25/23=9200** |\n| 552 labeled 23² | **552=24×23** |\n| Second-stage gain 1100 per side | **600 per side; 1200 bilateral** |\n| Peleg translated to 2115t/2116n | Peleg **Q₂₁₁₄**; Nahor **Q₂₁₁₅** |\n| Entry landing 480 “before” its mirror | **480 later** in AD |\n| Reversed AD display with suffixes reassigned | Keep **Q_b=AD bt/(b+1)n**; reorder text only |\n| 1260+3.5 still has no endpoints | Explicit A₀→A₁→M₁ construction, §6 |\n| Birth separation carried to historical deaths | Historical lifespans **123/120** remain fixed; template roles are separate |\n| 6000 from crossed suffixes | Matching phases give **6000**; crossed phases give **6000±0.5** |\n| 6440/6900 to the primary Conquest closing pair | Those closing-member comparisons use **Q₁₄₀₅**, one year earlier |\n| All Temple-week pairings give 6440/6900 | Primary whole weeks give **6441/6901**; companion weeks give **6440/6900** |\n| Methuselah ON landing is normal Creation | It is **10 years earlier** than normal Creation’s AD reflection |\n| Raw Cainan ON Creation span uniformly gives 27×490 | The present result is a **composite split completion** |\n| Death-of-Moses +12696 landing 11291t/11290n | **11290t/11291n** |\n| Census counts twenty and under; dates 1426 | Census threshold is **twenty and older**; **1426 remains a midpoint** |\n| 7000/7500 must share one uniform boundary ratio | Mixed boundary conversions are explicit; both theological readings retained |\n\n### 18.2 Dependency discipline\n\nBirth-pair complements, signed offset reversals, opposite Mirror order, and repeated row differences are consequences of their parent choices. The 1260±3.5 partitions follow from the two selected tracks and the full-week extension. The 22540 factorizations and 1380 exchange follow from their factor identities. Such equivalences clarify the structure but are not separate independent witnesses.\n\nGenerated coordinates receive event identities only where a source or an explicitly declared template supplies them. The Christ, covenant, Temple, and famine interpretations remain linked to their stated endpoints and phase choices. This allows the theological reading to be preserved without turning every numerical landing into an asserted historical date.\n\n### 18.3 Recommended bounded continuation\n\nAdmit this report as the completed discussion-branch intake. Preserve the main-window evidence checkpoint and treat the attached original handoff as superseded for intake purposes by this integrated account, while retaining it as provenance.\n\nThe strongest next task is a **single endpoint ledger for the proposed MT/SP/LXX cumulative-Flood→Creation 5+1+1+6(+1) sequence**, recording each tradition, Cainan state, Gear where allowed, phase, anchor, and Key before calculating its segments. That would test whether the already observed correspondences assemble into one declared construction rather than a set of related scalar comparisons.\n\nDo not reopen the quarantined 1876 half-primer or 1446 thirds-primer campaigns. The present 2116/4232 framework remains its own proposal. Preserve normal Gear 2 in the present core and keep Appendix A separate. **High is sufficient for the bounded endpoint ledger; a geometric z-law has not yet been specified.**\n\n## Appendix A. Quarantined Gear-3 Creation/Jared–famine comparison\n\nDean requested that this be retained as an appendix. It is not used to produce the core results, and it does not authorize general Gear propagation from Noah/Shem/Flood to Creation or Jared.\n\nThe proposed Gear-3 Creation envelope is **4124t/4123n→4117t/4116n BC**. Moving its BC magnitudes 130 earlier gives **4254t/4253n→4247t/4246n BC**. On the signed BC axis this is a −130 movement; printed BC numbers increase by 130.\n\n| Proposed route | Full envelope |\n|---|---|\n| Creation after the stated +130 source adjustment | 4254t/4253n→4247t/4246n BC |\n| +8464 landing | Q₄₂₁₁→Q₄₂₁₈ |\n| Subtract **2340=6.5×360=130×18** | Q₁₈₇₁→Q₁₈₇₈ |\n| Jared counterpart, 460 later than Creation landing | Q₄₆₇₁→Q₄₆₇₈ |\n| Subtract **2800=7×400=2340+460** | Q₁₈₇₁→Q₁₈₇₈ |\n\nThe terminal AD envelope is the ordinary reflection of the selected **1878→1871 BC** famine week. On the AD side the operation is subtraction by 2340 or 2800. Dean connects this to the curse and the dividing of famine patterns. The arithmetic of this proposed route is checked; admission of its upstream Gear transport and the fuller two-famine interpretation remain quarantined.\n\n## Appendix B. Verification and remaining endpoint questions\n\nThe accompanying standard-library Python audit uses exact rational phase coordinates and executes **855 assertions** covering the displayed source-to-landing tables, both seasonal components, all annual members of the cumulative seven-year fields, the witness tracks, the companion weeks, the Creation split, and the Mosaic crossings. The count describes arithmetic/convention checks, not independent evidential witnesses.\n\nThe separately supplied *1380 Exchange Joint* audit is preserved as provenance. Its earlier **121/121** result and the main window’s C113 **32-check** result are prior checkpoints; the new audit is not a claim to reproduce either campaign’s frozen files or certificate.\n\nThe package contains the integrated report, SVG/PNG figure, audit script and results, machine-readable source/landing rows, source hashes, and the unchanged original handoff. Rerun the arithmetic with:\n\n```bash\npython evidence/audit_axis_report.py\n```\n\nThe remaining bounded questions are:\n\n| Item | Exact content already retained | Still needed |\n|---|---|---|\n| Adam/Jared “4600/5100 to Christ” shorthand | Correct W=8464 and W=9200 landings, §8 | Additional source state or operation for that particular claim |\n| Shem-birth/Noah-death Christ-generation comparisons | Q₅₉₀₆/Q₆₃₅₆ and their direct Q₆ spans | Exact AD 35/95 or BC counterpart endpoints and phases |\n| Joseph 1875 | Exact complement with Peleg birth | Independent event/seasonal identification of the famine transaction |\n| 1150/1152 and Peleg ±2 relation to Gears | Numerical offsets and exact local spans | An admitted, source-specific Gear operation |\n| Full 5+1+1+6(+1) cross-tradition sequence | Verified constituent families and background examples | One complete state-labeled endpoint chain |\n| Proposed 3D effect | Exact translations and composed local reflections | Definition of z and any metric or incidence claims |\n\n## Appendix C. Coverage of the attached 2116/4232 handoff\n\n| Original handoff content | Integrated location |\n|---|---|\n| Receiving brief, selected frame, Gears/primer boundaries, January mean, 4232 rule | Receiving brief; §§1–3; §18 |\n| 2116→2300→2500 and doubled widths | §2 |\n| Abram/Isaac, firstborn/Jacob, Isaac 180, Jared/Sodom/conception and 11×529 | §3.2–3.3 |\n| Peleg/Nahor ±2/±1 and corrected landings | §3.4 |\n| Entry/Joseph/Peleg, nations, central famine year and limits | §3.5 |\n| Covenant 35+35, 400/70 themes, Hebrew root qualifications | §3.6 |\n| Mosaic biography, secondary age 40, generated 2706, 2700 to 6 BC | §4 |\n| Crossed 1380, own-event 1340/1420, distinct +120 operations | §5 |\n| Divine authorship, chiastic/fractal Revelation reading and narrative order | §6.1 |\n| Calendar and day-for-year scales; full 2520 construction | §6.2 |\n| Exact Aaron/Moses components and all six track endpoints | §6.3 |\n| Transferred witness roles, explicit plus interval, valid C113 minus interval | §6.4 |\n| BC reflected tracks, exchanged partitions, separate centers | §6.5 |\n| Dependency ledger and source/evidence distinctions | §§1.3, 18; Appendices B–D |\n\n## Appendix D. Sources and execution settings\n\n**[S1] Attached source handoff:** *490d_Branch_Handoff_2116_4232_Terah_Moses_Mirror_20260922 (2).md*. Read in full; original preserved unchanged in the evidence package. Its post-C113 §7 controls the resolved witness transfer.\n\n**[S2] Chronological source tables:** *File_18.Chronological_Data_Tables(20260919-141048).md*, especially the regular source frames and §§6A–6B cumulative MT OFF/ON tables. Controlling for the full seven-year units and Shelah convergence.\n\n**[S3] Mirror/phase control:** *File_09.Cumulative_Architecture(9).md*, especially Appendix A.3 and the Creation/Conquest 5520 discussion. Controlling for the January origin, quarter-year proof coordinates, suffix inversion, and distinction between paired and standalone mirrors.\n\n**[S4] Cumulative harmonic and birth-phase controls:** *File_22.Cumulative_MT_Harmonics(20260906-202427).md* and *File_62.Half_Clutch_Birth_Law_Interface (1).md*, as referenced by the original handoff. The later explicit lifespan/phase decisions remain controlling.\n\n**[S5] Bounded audit:** *490d_1380_Exchange_Joint_Bounded_Audit_20260923.md*. Read for the split 322/138 completion, preserved envelopes, 26/27 distinction, exact crossed midpoints, optional AD 30 Temple comparison, and 1380 factor exchange.\n\n**[S6] Generation and cumulative comparison controls:** *File_69.Enoch_Centered_Genealogical_Accordion(20260823-145801).md*, together with File_22 and *File_61.Jacob_Moses_Cumulative_Regular_Root_System(6).md*, as cited and checked in S5.\n\n**[S7] Prior integrated Mirror study:** *490d_Mirror_Cumulative_Regular_MT_LXX_SP_Comprehensive_Handoff_20260920 (1).md*, especially §§4.2, 5, 10, and 12; and *490d_Mirror_Bilateral_Integration_and_8395_Correspondence_20260920 (1).md*. These preserve the 115 background, 6900’s two exact continuations, fixed-landing central-gap distinction, and MT/LXX Creation-to-Conquest comparisons.\n\n**[S8] Creation and theological controls:** *File_07.Creation_Seed_Decimal_Root (1)(1).md* and *File_70.Genesis_Toledot_Atonement_Weave(10)(1).md*, especially File_70 §8 on Nisan 14/15. Dean’s latest Year 14/15 clarification is recorded explicitly in §15.3 as the current branch interpretation.\n\n**[S9] Temple-state controls:** *File_00.Repository_Foundation_Axiom_Engine_Source_Map(9).md* and *File_05.Exodus_Target_Fulcrum_Anchor(4).md*, as retained in S5’s phase and Passion-state audit. The report does not undertake a new historical redating of Herod’s construction or Jesus’ ministry.\n\n**[S10] Biblical textual checks:** [Numbers 1:3](https://www.biblegateway.com/verse/en/Numbers%201%3A3), [Numbers 1](https://www.biblegateway.com/passage/?search=Numbers+1&version=KJV), [Numbers 14:29](https://www.biblegateway.com/verse/en/Numbers14%3A29), and [John 2:20](https://www.biblegateway.com/verse/en/John%202%3A20). The textual census-age correction and construction wording were checked for this synthesis. The other biblical/lexical correspondences are retained from S1: Genesis 10:25; 15; 21:22–34; 47:13–26; Exodus 1:22; Daniel 9:24–27; Ezekiel 29:3; Revelation 11–12; and the BDB שבע note. First Kings 6:1, 37–38 supplies the Temple’s biblical dating language.\n\n**[S11] Related branch:** *490d_Branch_Handoff_3plus7x529_Flood_Noah_Christ_20260921 (2).md*. Its source-state qualifications remain separate from the current Gear-2 core.\n\n**Execution settings:** no astronomical year-zero relabeling; normal Gear 2 in the core; regular Cainan insertion +130 upstream; cumulative insertion +460 upstream through Arphaxad, with Shelah onward fixed; full seven-year cumulative envelopes; original and reflected phase pairs distinguished; source event, generated coordinate, converted width, and theological role recorded separately. No canonical source file or main-window checkpoint was changed.\n\n**Best next bounded step:** assemble the single state-labeled MT/SP/LXX cumulative-Flood→Creation **5+1+1+6(+1)** endpoint ledger, using this report’s verified operators and retaining both the **7000/Year-14** and **7500/Year-15** interpretations.\n\n## Appendix E. SKL precession square: 25921 and the 24+25 partition\n\n**Added:** 25 September 2026. **Frame:** normal Gear 2; the parent report’s t/n and no-year-zero conventions. The SKL also retains declared local **−2/0/+2-year** companions, distinct from its **−720/0/+720** macro field. The calculations below hold the normal central SKL state fixed. [E2, §2.2]\n\n### E.1 The established 259210 basis\n\nFile_21 already documents **262086 BC → 2876 BC = 259210 = 490×529 = 10×161²**, and **25921 = 161² = 49×529**. These precede the present axis comparison. [E1]\n\nWith full phases, **262087t/262086n BC → 2877t/2876n BC** gives:\n\n$$262087-2877=262086-2876=259210=10\\times25921.$$\n\n### E.2 One precessional Great Year, then the additional year\n\nHold the SKL Long Flood at **27367t/27366n BC**. Its interval to Exodus **1447t/1446n BC** is the repository’s **25920-year precessional Great Year**. One further year reaches the Tabernacle pair **1446t/1445n BC**, giving **25921 = 161²**. [E1, §15.2; E2, §5.4]\n\nApplying the report’s previously selected **12696 = 24×529** forward translation leaves the generated point **14671t/14670n BC**:\n\n| Interval, all endpoints BC | Tishri calculation | Nisan calculation | Years |\n|---|---:|---:|---:|\n| SKL Flood → Exodus | 27367−1447 | 27366−1446 | **25920** |\n| SKL Flood → Tabernacle | 27367−1446 | 27366−1445 | **25921 = 49×529** |\n| SKL Flood → generated point | 27367−14671 | 27366−14670 | **12696 = 24×529** |\n| Generated point → Tabernacle | 14671−1446 | 14670−1445 | **13225 = 25×529 = 115²** |\n\nThus:\n\n$$\\boxed{25920+1=25921=12696+13225=(24+25)\\times529.}$$\n\nThe complementary square admits two exact **25/23** expansions, replacing one factor of 23 at each step:\n\n$$13225=25\\times23^2\n\\xrightarrow{\\times25/23}14375=25^2\\times23\n\\xrightarrow{\\times25/23}15625=25^3=125^2=5^6.$$\n\nThe same generated point is **13224** years before Exodus and **13225** before the Tabernacle endpoint; the one-year distinction is retained.\n\n### E.3 The existing 13×529 Mirror connection\n\nWithin the MT cumulative Shem-birth seven-year field, select **5433t/5432n BC**, whose ordinary reflection is **AD 5432t/5433n**. This is the **Shem-birth / Noah-death boundary**, not Noah’s birth. [E3; E4]\n\nFrom the same Tabernacle pair, both components give **6877 = 13×529**:\n\n$$1446t\\text{ BC}\\rightarrow\\text{AD }5432t:\n\\quad1446+5432-1=6877,$$\n$$1445n\\text{ BC}\\rightarrow\\text{AD }5433n:\n\\quad1445+5433-1=6877.$$\n\nConsequently, SKL Flood → Tabernacle → reflected Shem birth spans **(49+13)×529**:\n\n$$27367+5432-1=27366+5433-1=32798=62\\times529.$$\n\nThe adjacent Shem reflection **AD 5431t/5432n**, compared with reflected Conquest **AD 1406t/1407n**, supplies the related factor pattern:\n\n$$5431-1406=5432-1407=4025=161\\times25\n\\xrightarrow{\\times25/23}4375=7\\times5^4.$$\n\nIt belongs to **3703 → 4025 → 4375**, precisely one seventh of **25921 → 28175 → 30625**, with each arrow applying 25/23. These nested factor relationships motivate further comparison of the dated endpoints.\n\n**Scope:** the new finding connects the already documented SKL square to the report’s established 12696 width and the MT Mirror field. The proposed 126960/253920 Creation-scale extensions remain deferred. Appendix E’s arithmetic was checked separately; Appendix B’s 855-check count belongs to the original report.\n\n**Existing repository references**\n\n- **[E1] File_21 — SKL Unified Protocol:** §14.1 (259210); §25, Note A (25920+1, 161², and the tenfold relation); §15.2 (1445 BC Tabernacle endpoint).\n- **[E2] File_34 — Unified Chronology: SKL, Berossus, Bible:** §5.4 (27366 BC → 1446 BC = 25920); §2.2 (local ±2 and macro ±720 Gear fields).\n- **[E3] File_18 — Chronological Data Tables:** §6A, MT cumulative trunk; Shem’s **5436–5429 BC** envelope and Noah’s preceding 950-year lifespan.\n- **[E4] File_09 — Cumulative Architecture:** Appendix A.3, phase-preserving reflection and civil cross-axis arithmetic **BC+AD−1** for matching seasonal components.\n"}