{"id":"study-sothic-amendment-ledger","title":"The 365-Day Sothic Companion to the Key of 23 — Discussion and Amendment Ledger v0.3","filename":"365_Sothic_Key23_Discussion_and_Amendment_Ledger_v0_3_20260906.md","role":"Study document","step":null,"sha256":"81d5e80b3b81d2b28efb8315c24149b3ac4dc3f9e38e01b24582885cd40e0ed6","bytes":49249,"origins":["User-supplied supporting study edition; inclusion does not change its original claim level."],"download":"/study-documents/files/365_Sothic_Key23_Discussion_and_Amendment_Ledger_v0_3_20260906.md","format":"md","derived":false,"tags":["Calendar Keys","Cumulative","Regular","Covenant","Mirror / 529"],"excerpt":"Detailed Sothic–Mosaic selection discussion, Creation and Pillar applications, Long-SKL audit and prepared source amendments; companion to the Sothic Report V.","collection":"study-documents","date":"2026-09-06","dateLabel":"September 6, 2026 · v0.3","editionStatus":"Working amendment ledger · Finalization and central registration not claimed","storage":"study-files","downloadFilename":"365_Sothic_Key23_Discussion_and_Amendment_Ledger_v0_3_20260906.md","content":"# The 365-Day Sothic Companion to the Key of 23\n\n## The `1460/1460.5` pair, the `10220` Creation bridge, the divided seven, the SKL Mirror field, and the `AD 29465` Pillar\n\n**Date:** September 6 2026  \n**Working edition:** v0.3 — consolidated Sothic–Mosaic selection, Long-variant audit, and bounded source amendments  \n**Authorial proposals:** Dean, present discussion, points 1–9  \n**Status:** Consolidated discussion and amendment ledger; Report V is the recommended new-chat synthesis. Three separate full-replacement working amendments are prepared and verified; neither Finalization nor central registration is claimed.  \n**Verification:** Current consolidation audit: 116 exact scalar equalities checked in Fraction and SymPy; 141 phase/set/sensitivity/rejection assertions. Earlier 127/127 and v0.2 audit figures are preserved as historical records, not added to this count. Executable: `../03_Verification/verify_sothic_consolidation.py`. This is bounded verification, not a full repository pressure test.\n**Canonical source state:** Existing repository files and all four control files remain unchanged.  \n**Prepared source homes:** File_12 §5A for calendar definitions and the Sothic/Key-23 comparison; File_22 §§5A/9B for the cumulative–regular Creation and Pillar application; Supplement A §13/Appendix H for the finite-field and anchor-selection proof. Other reciprocal changes remain affected-only.  \n**Companions:** The earlier arithmetic and Mirror audits and v0.1/v0.2 ledgers are preserved in `../05_Frozen_Parents/`. The current executable is `../03_Verification/verify_sothic_consolidation.py`, with the current scalar manifest and phase/closure report in the same directory. The earlier script name `check_sothic_mirror_closure.py` is historical and is not required for this package.\n\n---\n\n# 0. Principal result\n\nThe proposed half-step Sothic ratio is mathematically coherent:\n\n\\[\nH_{365,23}=\\frac{1461.5}{1460.5}=\\frac{2923}{2921},\n\\qquad2921=23\\times127.\n\\]\n\nIt belongs to the broader one-year-completion grammar on a half-23 grid:\n\n\\[\nu=\\frac{23}{2}=11.5,\n\\qquad q_m=mu,\n\\qquad R_m=\\frac{q_m+1}{q_m}=\\frac{23m+2}{23m}.\n\\]\n\nThe original three ratios and the proposed companion are instances at:\n\n\\[\nm=1,6,26,127.\n\\]\n\nHowever, **the proposed Sothic companion does not preserve the original three Keys' exact common schematic year**:\n\n\\[\nK=\\frac{8400}{23}.\n\\]\n\nThe distinction is fundamental:\n\n\\[\n365H_{365,23}\n=365.25-\\frac1{11684}\n\\ne K.\n\\]\n\nThe exact 365-day continuation that does preserve `K` is a different ratio:\n\n\\[\nG_{365,K}=\\frac{K}{365}=\\frac{1680}{1679},\n\\qquad1679=23\\times73.\n\\]\n\nBoth are retained in this ledger, with separate meanings: `H` is Sothic/Julian-adjacent and half-23-aligned; `G` preserves the original common schematic day-volume. Neither is silently added to the canonical operator register. [F00; SG]\n\nThe strongest chronological result is:\n\n\\[\n\\boxed{9890+(460-130)=10220=7\\times1460.}\n\\]\n\nThis makes the two Cainan-bearing Creation fields uniformly seven ordinary Sothic blocks apart. The proposed half-step changes a seven-cycle carrier by `3.5` years and a ten-cycle carrier by `5`:\n\n\\[\n7\\times0.5=3.5,\n\\qquad10\\times0.5=5.\n\\]\n\nThese are exactly the half-week and Creation-head-to-Year-6 separations used in the proposed construction. This is a compact explanation of several coordinate results, not proof of ancient conscious design.\n\n---\n\n# 1. Source and state register\n\n| Key | Controlling source / use |\n|---|---|\n| DISC | Dean's September 6 2026 message, points 1–9, and subsequent twelve-node common-center clarification; original proposals and interpretive intent. |\n| R1 | Report I: regular Creation wrappers, `+130` Cainan, `4121/4116/4114`, `4251/4246/4244`. |\n| R3 | Report III: the actual cumulative–regular `9890` bridge; regular `130` versus cumulative `460` Cainan. |\n| R4 | Report IV: actual/Rounded and native/comparison-state distinctions; related harmonic-engine method. |\n| F00 | `File_00.Repository_Foundation_Axiom_Engine_Source_Map.md`, especially §3.24: exact common `K`, calibrated `S_K`, and Residue Protocol boundaries. |\n| SG | `490d_Repository_Style_Guide`, v2.5, §4.6: exact ratios, `K`, `S_K`, physical residue versus conceptual residual-display. |\n| CAP/REG | Restart Capsule v11.50 and State Vocabulary Register v1.51: existing state vocabulary and Mirror controls; neither is amended here. |\n| PROC | Project Procedures v3.5, §§6–7 and 18: staged amendments; no canonical rewrite before approved intake; exhaustive control-token novelty checks. |\n| F12 | `File_12.Calendrical_Physics.md`, §§5–7A and Mosaic reciprocal note: calendar registers, proposed Mosaic phases, `80.5→87.5`, and physical/schematic distinction. |\n| F17 | `File_17.Prophetic_Time_Span_Anatomy.md`: original exact Keys and the half-scale Mosaic applications. |\n| F09 | `File_09.Cumulative_Architecture.md`, §3A and Appendix A: cumulative Creation cell; phase-resolved paired Mirror; schematic Julian quarter-year coordinates. |\n| F18 | `File_18.Chronological_Data_Tables.md`: raw source and variant distinctions, cumulative Creation, SKL states. September 2 mounted edition. |\n| F22 | `File_22.Cumulative_MT_Harmonics.md`, §5 and cumulative-state registers: `9890`, restored Cainan, Year-6/Adam, actual Apparent Adam. |\n| F51a | `File_51a.Rounded_Scaffold_Mod5_Architecture.md`, §§4.5 and 6.2: Rounded Apparent Adam `4136`; Rounded Enoch ascension `3121−215=2906`, `2906→1446=1460`, and `2906→1526=1380`. |\n| F53 | `File_53.Jubilees_22Fold_Creation_Genealogy_Witness.md`, §14A: `294/293` Enochian side comparison and `70+294+1=365`. |\n| F69/F70 | Regular/cumulative Creation and subsequent seven-year cells, including `4251→4244→4237`, and schematic `AD 135` endpoint. |\n| F21/F34 | SKL source pair `2936/2906`, orthogonal `+30`, centered local `−2/0/+2`, and Pillar state. |\n| SA | File_70 Supplement A: four-node Enochian–SKL field; `2921` as an existing midpoint; `34.5` and `4.5` under their own operators. |\n| F33 | `File_33.Ordinal_Lock.md`, THEOREM P16: already published `16056→1446=14610=10×1461` Sothic comparison. Read-only novelty/context check; no prime proof is imported. |\n| CENS | Censorinus, *De die natali*, chapter 18, especially the Egyptian/canicular-year account: ancient witness to the 365-day civil year and 1461-year synchronism. |\n| AST | Observatoire de Paris educational source, Patrick Rocher, quoting P. Bretagnon's 2000 expression for mean tropical-year length. Used only for a bounded epoch calibration. |\n| BIB | Genesis 5:23; Acts 7:22; Exodus 40:17; Numbers 33:3. Biblical textual anchors, not independent proofs of the proposed ratio. |\n| DIO | Cassius Dio 69.12–14, Bar Kokhba war account: historical context of the AD 135 catastrophe, not derivation of a universal “end of Israel.” |\n\n## 1.1 Existing versus newly proposed relationships\n\nThe `365`, `1460`, `1380`, and Sothic-to-Exodus comparisons are not all new. File_51a already places the Rounded/`−215` Enoch ascension at `2906 BC`, followed by `1460` to Exodus and `1380` to Moses. File_33 already contains a ten-`1461` Sothic Exodus application.\n\nThe present candidate is the explicit **`1460.5/1461.5` half-23 companion**, together with its seven-cycle Creation bisection, ten-cycle head/Year-6 relation, declared SKL Mirror enumeration, and Pillar comparison. The searched controls do not contain the literal ratio; this is not a claim of exhaustive conceptual novelty throughout every historical repository edition.\n\n---\n\n# 2. Corrections and interpretations of the informal input\n\n| Original point | Input or wording requiring attention | Treatment in this ledger |\n|---|---|---|\n| 2 | `12.5/11.5 = about 4200/4200.3 days` | Read as a comparison of day-volumes, not as equality of those two quotients: `12.5×336 ≈ 11.5×solar year`. |\n| 4 | First listed Mirror example assigned ordinary Sothic, second assigned half-step Sothic “respectively” | Reverse those assignments: the first span is `5842=4×1460.5`; the second is `5840=4×1460`. |\n| 5 | Joshua birth `1437t BC` | Obvious intended reading assumed to be `1477t BC`, paired with the user's `1476n BC`. The original `1437t` does not fit the supplied birth anchor or subtraction. |\n| 7–8 | Regular Creation lower endpoint `4242 BC` | Assume `4244 BC` for the stated common Cainan-bearing Creation wrapper. `14464−4242=10222`, whereas `14464−4244=10220`. No independent Gear-1 `4242` state is silently substituted or destroyed. |\n| 6 | `80.5` beside `1527t/1526n` and `1446n/t` | Execute crossed phases explicitly. Same-phase `1526n→1446n` is `80`, not `80.5`. |\n| 9 | Total shift `34.5` suggests actual Apparent Adam `4146` | Arithmetic retained, but the fixed-Pillar endpoint is `4151t BC`; it stands `4.5` years earlier than `4146n BC`. An exact landing on `4146` is not established. |\n| 3 | `14466` as a tenfold resemblance of `1446` | Preserve “resemblance” / repository scale comparison; do not state the false literal multiplication `1446×10=14466`. |\n\nThese corrections preserve the evident intended structure. They are not unannounced emendations to the canonical sources.\n\n---\n\n# 3. The drift grammar and the three reference standards\n\n## 3.1 One extra calendar year\n\nLet `d` be a short calendar's year-length in days, `Y` a selected longer reference year, and `q` the reference-year count at which the short calendar accumulates one additional year:\n\n\\[\nqY=(q+1)d.\n\\]\n\nThen:\n\n\\[\nq=\\frac{d}{Y-d},\n\\qquad R=\\frac{q+1}{q}=\\frac{Y}{d}.\n\\]\n\nThis is the mathematical principle shared with idealized Sothic reckoning. It does not establish historical transmission from one named calendar to every other.\n\nWith the allowed half-23 measure `u=11.5`:\n\n| `m` | Reference count `q=11.5m` | Short-calendar count `q+1` | Reduced conversion |\n|---:|---:|---:|---:|\n| 1 | 11.5 | 12.5 | `25/23` |\n| 6 | 69 | 70 | `70/69` |\n| 26 | 299 | 300 | `300/299` |\n| 127 | 1460.5 | 1461.5 | `2923/2921` |\n\nThe first three reproduce the same `K` when multiplied by `336/360/364`. The fourth does not reproduce it when multiplied by `365`.\n\n## 3.2 Existing schematic and calibrated values\n\nThe unchanged definitions are:\n\n\\[\nK=\\frac{8400}{23}=365.217391304\\ldots,\n\\]\n\n\\[\nS_K=K+\\frac1{40}=\\frac{336023}{920}=365.242391304\\ldots.\n\\]\n\n`K` is the exact schematic equivalent; `S_K` is the repository's calibrated reference. Neither is silently replaced by the Julian mean `365.25`. [F00; SG]\n\nThe primitive Priestly comparison is:\n\n\\[\n12.5\\times336=4200,\n\\qquad11.5S_K=4200.2875.\n\\]\n\nThus the user's “about 4200 versus 4200.3 days” is correct as an approximate day-volume comparison.\n\n## 3.3 Enochian partners\n\n\\[\n299=23\\times13,\n\\qquad364=4\\times13\\times7,\n\\qquad294=6\\times7^2.\n\\]\n\nThe exact year implied by the side comparison is:\n\n\\[\nY_{294/293}=\\frac{294\\times364}{293}\n=\\frac{107016}{293}\n=365.242320819\\ldots.\n\\]\n\nAgainst the unchanged `S_K`:\n\n\\[\n293S_K-294\\times364=\\frac{19}{920}\\text{ day},\n\\]\n\nwhereas:\n\n\\[\n299S_K-300\\times364=\\frac{299}{40}=7.475\\text{ days}.\n\\]\n\nThe two ratios can therefore serve complementary purposes: closer physical calibration versus participation in the `23×13` architecture. That distinction already exists in the controls and File_53. It does not license switching ratios invisibly.\n\n**Source precision note:** File_53's printed `107016=293×365.2423` is rounded-display language. Strict multiplication gives `107015.9939`, a difference of `0.0061` day. This ledger uses `≈` for the rounded decimal and exact `107016/293` where needed. No File_53 rewrite is made here.\n\n## 3.4 Ordinary and half-step Sothic\n\nThe ideal ordinary equality is:\n\n\\[\n1461\\times365=1460\\times365.25=533265\\text{ days}.\n\\]\n\nCensorinus supplies an ancient witness to the underlying Egyptian drift account. The equality is a statement about ideal mean year-lengths; no observed Sirius-rising chronology is computed here. [CENS]\n\nThe proposed half-step ratio satisfies:\n\n\\[\nH=\\frac{2923}{2921},\n\\qquad365H=365.25-\\frac1{11684}.\n\\]\n\nConsequently:\n\n\\[\n1461.5\\times365-1460.5\\times365.25=-\\frac18\\text{ day}.\n\\]\n\nThe mismatch is only three hours in this mean-year calculation. This is not an assertion that a particular half Julian year contains exactly `182.625` calendar days.\n\nAgainst the common repository reference instead:\n\n\\[\n1461.5\\times365-1460.5S_K\n=\\frac{879}{80}\n=10.9875\\text{ days}.\n\\]\n\nThus `H` is extremely close to the Julian/Sothic standard, but not an equally close tropical-year realignment. Its structural coherence does not depend on pretending those standards coincide.\n\n## 3.5 A bounded check at the Exodus epoch\n\nThe Observatoire de Paris source gives the following P. Bretagnon (2000) mean tropical-year expression, in Julian millennia `T` from J2000:\n\n\\[\nY(T)=365.2421905166\n-0.0000615607T\n-0.0000000684T^2\n+0.0000002630T^3\n+0.0000000032T^4.\n\\]\n\nAt the approximate `1446 BC` epoch, `T≈−3.445`, it gives:\n\n\\[\nY\\approx365.2423914793\\text{ days}.\n\\]\n\nThis lies very close to the unchanged `S_K`. The new half-step block's mismatch is then approximately `10.98724` days. The physical conclusion remains the same. [AST]\n\nThis is a bounded mean-year calibration, not a calculation of a particular equinox-to-equinox year, heliacal visibility, ancient civil-calendar epoch, or a varying tropical-year integral across the entire deep-time chronology. File_00's wording associates `S_K` with the time of Christ; the numerical epoch check here instead demonstrates a close approximation at the proposed Exodus epoch. That wording discrepancy is recorded for source review, not silently rewritten.\n\nA strict “nearest half-23 realignment to this common tropical reference” criterion would give:\n\n\\[\nq=\\frac{365}{S_K-365}\n=\\frac{335800}{223}\n\\approx1505.8296.\n\\]\n\nThe nearest `11.5`-multiple is `1506.5=131×11.5`, giving the separate sensitivity candidate `3015/3013`, for which:\n\n\\[\n1507.5\\times365-1506.5S_K=-\\frac{13}{80}\\text{ day}.\n\\]\n\nThis is a diagnostic counter-test, not a new active repository ratio and not a substitute introduced to improve the date matches. It makes explicit that the choice `127`, rather than `131`, preserves Sothic/Julian adjacency rather than optimal common-tropical calibration.\n\n## 3.6 Exact continuation of the common `K`\n\nPreserving the original exact common schematic value instead forces:\n\n\\[\nG=\\frac{K}{365}=\\frac{1680}{1679},\n\\qquad365G=K.\n\\]\n\nHere `1679=23×73=146×11.5`. Thus `G` also belongs to the general half-23 one-year-completion form, but occupies a different point in it.\n\n**Three distinct questions must remain distinct:** nearest Julian/Sothic companion; closest common-tropical realignment; exact preservation of `K`.\n\n---\n\n# 4. SKL, Moses, Joshua, Exodus, and Tabernacle\n\nThe `1446 BC` Exodus is the repository's primary chronographic anchor, not an independently established Egyptian Sothic-reset date. Acts 7:22 supplies the Egyptian-wisdom context; it does not attest Moses' use of the proposed ratio. The Egypt–Sumer–Rome comparison is retained as a thematic/providential interpretation of the source-defined systems. [F05; BIB; CENS]\n\n## 4.1 Ordinary Sothic carrier\n\n\\[\n2906n\\to1446n\\text{ BC}=1460,\n\\]\n\n\\[\n1460\\times\\frac{1461}{1460}=1461,\n\\qquad2906n\\to1445n\\text{ BC}=1461.\n\\]\n\nThe parallel Joshua comparison is:\n\n\\[\n2936n\\to1476n\\text{ BC}=1460.\n\\]\n\nIts expanded terminal is `1475n BC`, a generated companion, not a replacement birth date.\n\nThe preceding Tishri states give:\n\n\\[\n2907t\\to1447t\\text{ BC}=1460,\n\\qquad2937t\\to1477t\\text{ BC}=1460.\n\\]\n\n`1447t` retains the plague-period comparison; `1477t/1476n` is the assumed intended Joshua pair. No new literal historical birth-day precision is asserted.\n\nExodus 40:17 places the Tabernacle on the first day of the first month in the second year. Accordingly, `1445n` is a year/phase-label correspondence. The equation does not assert that the Tabernacle was erected exactly one elapsed year after the Exodus departure on Nisan 15. The Tishri companion is not a second erection date. [BIB]\n\n## 4.2 Moses' `1380` and `120`\n\n\\[\n2907t/2906n\\to1527t/1526n\\text{ BC}=1380.\n\\]\n\nApplying the Priestly ratio:\n\n\\[\n1380\\times\\frac{25}{23}=1500,\n\\qquad1500-1380=120.\n\\]\n\nThe expanded endpoints are therefore:\n\n\\[\n2907t/2906n\\to1407t/1406n\\text{ BC}=1500.\n\\]\n\nThe `120` is the expansion gain, echoing Moses' lifetime; the calculation is not `120×25/23=120`.\n\n## 4.3 Moses' `80.5` and the half-step Sothic whole\n\nThe existing half-scale instance is:\n\n\\[\n80.5\\times\\frac{25}{23}=87.5,\n\\qquad87.5-80.5=7.\n\\]\n\nThe two explicitly crossed phase branches are:\n\n\\[\n1527t\\to1446n\\text{ BC}=80.5,\n\\]\n\n\\[\n1526n\\to1446t\\text{ BC}=80.5.\n\\]\n\nThe second is a Tishri comparison branch, not a claim that the historical Exodus took place in Tishri. Same-phase `1526n→1446n` remains `80`. [F12; F17]\n\nNow:\n\n\\[\n1380+80.5=1460.5,\n\\]\n\nand the half-23 structure is transparent:\n\n\\[\n1380=120u,\n\\quad80.5=7u,\n\\quad1460.5=(120+7)u=127u.\n\\]\n\nThe two complete Sothic-Key branches become:\n\n\\[\n2907t\\to1446n\\text{ BC}=1460.5\n\\xrightarrow{H}\n2907t\\to1445n\\text{ BC}=1461.5,\n\\]\n\n\\[\n2906n\\to1446t\\text{ BC}=1460.5\n\\xrightarrow{H}\n2906n\\to1445t\\text{ BC}=1461.5.\n\\]\n\nThe Priestly and half-step Sothic transformations are alternative measurements, not compounded here:\n\n\\[\n1460.5\\times\\frac{25}{23}=1587.5,\n\\qquad1460.5H=1461.5.\n\\]\n\n---\n\n# 5. The seven-cycle cumulative–regular Creation bridge\n\n## 5.1 Corrected component-wise field\n\nThe source-controlled Cainan-bearing wrappers are:\n\n\\[\nC=(14471,14466,14464)\\text{ BC},\n\\]\n\n\\[\nR=(4251,4246,4244)\\text{ BC}.\n\\]\n\nThe entries are respectively the Creation head, Year-6/Adam comparison, and Creation close. Each must retain its own node-class. [R1; F09; F18; F69]\n\nEvery corresponding difference is:\n\n\\[\nC_i-R_i=10220=7\\times1460.\n\\]\n\nIts derivation from Report III is:\n\n\\[\n\\underbrace{9890}_{\\text{Cainan-OFF Creation bridge}}\n+\\underbrace{460}_{\\text{cumulative Cainan}}\n-\\underbrace{130}_{\\text{regular Cainan}}\n=10220.\n\\]\n\nThis connects the proposed family directly to the earlier comparative engine rather than using two unexplained fitted dates.\n\n## 5.2 Seven ordinary cycles complete to the next week\n\n\\[\n7\\times1460=10220,\n\\qquad7\\times1461=10227.\n\\]\n\n| Cumulative Nisan source | Unexpanded terminal | Expanded terminal |\n|---:|---:|---:|\n| `14471n BC` | `4251n BC` | `4244n BC` |\n| `14466n BC` | `4246n BC` | `4239n BC` |\n| `14464n BC` | `4244n BC` | `4237n BC` |\n\nThe Creation envelope `4251–4244` is thus translated to the following seven-year envelope `4244–4237` in the repository's Creation/Fall interpretation.\n\n**Execution control:** This table applies the same seven-cycle carrier to each corresponding source node. It preserves the width of the source envelope. It is not one global dilation of every date about a single fixed anchor; such a dilation would also rescale the envelope's internal seven-year width.\n\n## 5.3 The AD 135 `7+3=10` closure\n\n\\[\n14466+135-1=14600=10\\times1460,\n\\]\n\n\\[\n4246+135-1=4380=3\\times1460.\n\\]\n\nTherefore:\n\n\\[\n14466\\text{ BC}\\to4246\\text{ BC}\\to\\text{AD }135\n\\]\n\ncarries:\n\n\\[\n7\\times1460+3\\times1460=10\\times1460.\n\\]\n\nAD 135 is retained as the chosen repository era-boundary and historical catastrophe comparison. Cassius Dio supplies the devastation context, not a claim that the Jewish people or every form of Israel's history ended then. [F69; DIO]\n\n---\n\n# 6. Seven half-step cycles and the divided week\n\n## 6.1 Head to midpoint\n\n\\[\n7\\times1460.5=10223.5,\n\\qquad7\\times1461.5=10230.5.\n\\]\n\nUnder the repository's explicitly opened schematic phase model:\n\n\\[\n14471n\\text{ BC}+10223.5\\text{ forward years}=4248t\\text{ BC},\n\\]\n\n\\[\n14471n\\text{ BC}+10230.5\\text{ forward years}=4241t\\text{ BC}.\n\\]\n\nThe target nodes are exactly:\n\n\\[\n4251n\\xrightarrow{3.5}4248t\\xrightarrow{3.5}4244n\\text{ BC},\n\\]\n\n\\[\n4244n\\xrightarrow{3.5}4241t\\xrightarrow{3.5}4237n\\text{ BC}.\n\\]\n\nThus seven half-step cycles lead from the cumulative head to the midpoint of the regular Creation week; expansion leads to the midpoint of the following week.\n\n## 6.2 Midpoint to close\n\nThe cumulative Creation midpoint is:\n\n\\[\n14471n\\xrightarrow{3.5}14468t\\xrightarrow{3.5}14464n\\text{ BC}.\n\\]\n\nFrom it:\n\n\\[\n14468t\\to4244n\\text{ BC}=10223.5,\n\\]\n\n\\[\n14468t\\to4237n\\text{ BC}=10230.5.\n\\]\n\nThis verifies the user's complementary midpoint-to-close description.\n\n## 6.3 Ten cycles and the five-year head displacement\n\n\\[\n14471+135-1=14605=10\\times1460.5.\n\\]\n\nTogether with the ordinary result:\n\n\\[\n14466+135-1=14600=10\\times1460,\n\\]\n\nthe five-year source displacement is explained by:\n\n\\[\n10(1460.5-1460)=5=14471-14466.\n\\]\n\nA generated companion follows if both complete ten-cycle spans are expanded with their respective ratios:\n\n\\[\n14466\\text{ BC}\\to\\text{AD }145=14610=10\\times1461,\n\\]\n\n\\[\n14471\\text{ BC}\\to\\text{AD }145=14615=10\\times1461.5.\n\\]\n\n`AD 145` is an arithmetic output only. No historical-event identification or prediction is attached to it.\n\n---\n\n# 7. The complete twelve-node SKL paired-Mirror test\n\n## 7.1 Declare the Mirror before calculating\n\nThe active Mirror is File_09's phase-resolved paired form:\n\n\\[\nYt/(Y-1)n\\text{ BC}\\mapsto\\text{AD }(Y-1)t/Y n.\n\\]\n\nIt is not Rounded Protocol 1, raw coordinate addition without state declaration, or the separate standalone same-numeric-year Mirror. [F09; REG]\n\nWrite the upper `+30` pair as `(U+1)t/U n BC` and the lower pair as `(D+1)t/D n BC`, with:\n\n\\[\nU\\in\\{2934,2936,2938\\},\n\\quad D\\in\\{2904,2906,2908\\}.\n\\]\n\nThe lower pair's Mirror is `AD D t/(D+1)n`. Both corresponding components have span:\n\n\\[\n(U+1)+D-1=U+(D+1)-1=U+D.\n\\]\n\n## 7.2 Exhaustive three-by-three span matrix\n\n| Upper Nisan member `U` | Lower `D=2904` | Lower `D=2906` | Lower `D=2908` |\n|---:|---:|---:|---:|\n| `2934` | `5838` | `5840` | `5842` |\n| `2936` | `5840` | `5842` | `5844` |\n| `2938` | `5842` | `5844` | `5846` |\n\nThe two four-cycle conversions are:\n\n\\[\n5840\\xrightarrow{1461/1460}5844,\n\\]\n\n\\[\n5842\\xrightarrow{2923/2921}5846.\n\\]\n\nThe two examples in the original message therefore have their cycle labels reversed:\n\n| Source pair to the Mirror of the other source pair | Span | Correct input family |\n|---|---:|---|\n| `2935t/2934n` to Mirror of `2909t/2908n` | `5842` | four half-step Sothic cycles |\n| `2935t/2934n` to Mirror of `2907t/2906n` | `5840` | four ordinary Sothic cycles |\n\n## 7.3 Explicit coverage routes\n\nFor ordinary Sothic, two anchored routes cover all six source pairs:\n\n\\[\n(U,D):(2936,2904)\\to(2936,2908),\n\\]\n\n\\[\n(U,D):(2934,2906)\\to(2938,2906).\n\\]\n\nThe first holds the upper pair fixed and moves the AD endpoint forward four years. The second holds the AD endpoint fixed and moves the BC source four years earlier. Both transform `5840` to `5844`.\n\nFor the half-step family:\n\n\\[\n(2938,2904)\\to(2938,2908),\n\\]\n\n\\[\n(2934,2908)\\to(2938,2908),\n\\]\n\n\\[\n(2936,2906)\\to(2938,2908).\n\\]\n\nThe first two are fixed-end routes. The third explicitly distributes the four-year gain bilaterally as `2+2`; it is not a hidden fixed-anchor operation. All transform `5842` to `5846`.\n\nAcross these declared routes, all three upper pairs and all three lower pairs occur: six phase pairs, or twelve distinct source phase nodes. The Mirror targets are their defined counterparts, not another twelve independent source witnesses.\n\n**Strengthened result (v0.2, superseding the former affine qualification):** In addition to the selected-route coverage, one fixed translation by `5842=4×1460.5` maps all twelve source phase-nodes onto exactly their paired-Mirror target set. Following that translation by inverse Mirror gives the affine involution `R(x)=−5842−x`, which permutes all twelve original nodes in six transpositions. This does not assert self-correspondence of each individually named node, global closure under each of the other three four-cycle translations, or identical `1476/1446` interior landings on every route. See §§7.5–7.9 for the complete proof and the conditional uniqueness statement.\n\nThe selected central one-cycle links do remain exact:\n\n\\[\n2936n\\to1476n=1460,\n\\quad2906n\\to1446n=1460,\n\\]\n\n\\[\n2937t\\to1476n=1460.5,\n\\quad2907t\\to1446n=1460.5.\n\\]\n\n## 7.4 Compressed explanation\n\nLet the upper and lower Gear offsets be `g,h∈{−2,0,2}`. Then:\n\n\\[\nD(g,h)=2936+2906+g+h=5842+g+h.\n\\]\n\nThe central cross-Mirror span is:\n\n\\[\n5842=4\\times1460.5.\n\\]\n\nThe ordinary and half-step input/output cells occupy this constrained matrix. This explains why a four-year expansion is compatible with the existing two-year Gear spacing. Matrix repetitions should not be counted as independent probabilities.\n\n## 7.5 The common center and the complete coordinate set\n\nThis section records Dean's clarification and replaces the v0.1 stopping point at selected-route coverage. It uses File_09 Appendix A.3, not Rounded A-space or the standalone same-number Mirror. Define `x` as elapsed schematic years from January 1, AD 1:\n\n\\[\nx(Bn\\text{ BC})=-B+\\frac14,\\qquad\nx(Bt\\text{ BC})=-B+\\frac34,\n\\]\n\\[\nx(\\text{AD }An)=A-\\frac34,\\qquad\nx(\\text{AD }At)=A-\\frac14.\n\\]\n\nThe phase model is schematic. It does not assert literal equal Gregorian/Julian month lengths or observed ancient month starts. The paired Mirror is `M(x)=−x` on this point set, with its outputs displayed in chronological `t/n` order. Pointwise reflection reverses that order; it is not the separate same-numeric-year standalone Mirror. [F09; REG]\n\nThe outer coordinates are:\n\n\\[\nx(2939t\\text{ BC})=-2938.25,\\qquad\nx(2904n\\text{ BC})=-2903.75.\n\\]\n\nThus:\n\n\\[\n\\boxed{W=34.5=3\\times11.5,\\qquad\nc=\\frac{-2938.25-2903.75}{2}=-2921.}\n\\]\n\nThe center is the boundary December 31, 2922 BC / January 1, 2921 BC. Its distance to January 1, AD 1 is exactly `2921` years. Its reflected center is January 1, AD 2922, not January 1, AD 2921.\n\nAll twelve nodes are exactly:\n\n\\[\n\\boxed{\n\\mathcal X=\\left\\{-2921+15r+2g+\\frac p4:\n r,p\\in\\{-1,1\\},\\ g\\in\\{-1,0,1\\}\\right\\}.\n}\n\\]\n\nThe factors represent the two `30`-separated rails, three local Gears, and two half-year phase endpoints. The full width is `30+4+0.5=34.5`; each node is a distinct quarter-coordinate.\n\nThe already registered Short-ladder center-pair `2922t/2921n BC` brackets this January instant. The pair's individual endpoints remain distinct from the exact center between them. [SA; REG]\n\n## 7.6 One affine involution and one uniform four-cycle translation\n\nThe offset set around `c` is closed under sign reversal. Therefore:\n\n\\[\nR(x)=2c-x=-5842-x\n\\]\n\nsatisfies:\n\n\\[\n\\boxed{R(\\mathcal X)=\\mathcal X,\\qquad R^2=\\mathrm{id}.}\n\\]\n\nThis is an actual affine permutation of the twelve coordinates, not only participation in different routes. Its pointwise transpositions are:\n\n| First BC node | Partner BC node under `R` |\n|---|---|\n| `2939t` | `2904n` |\n| `2938n` | `2905t` |\n| `2937t` | `2906n` |\n| `2936n` | `2907t` |\n| `2935t` | `2908n` |\n| `2934n` | `2909t` |\n\nWriting `T_L(x)=x+L`, the chronological four-cycle map is:\n\n\\[\n\\boxed{T_{5842}(\\mathcal X)=M(\\mathcal X),\\qquad\nM\\circ T_{5842}=R.}\n\\]\n\nSince `5842=4×1460.5`, exactly four equal half-step input cycles carry every original node to one of the twelve paired-Mirror target nodes, with no output outside that set:\n\n| Source BC phase pair | After `5842` years | BC source of that target under inverse paired Mirror |\n|---|---|---|\n| `2939t/2938n` | `AD 2904t/2905n` | `2905t/2904n` |\n| `2937t/2936n` | `AD 2906t/2907n` | `2907t/2906n` |\n| `2935t/2934n` | `AD 2908t/2909n` | `2909t/2908n` |\n| `2909t/2908n` | `AD 2934t/2935n` | `2935t/2934n` |\n| `2907t/2906n` | `AD 2936t/2937n` | `2937t/2936n` |\n| `2905t/2904n` | `AD 2938t/2939n` | `2939t/2938n` |\n\nEach row has two equal component spans. For example, `2939+2904−1=2938+2905−1=5842`. Pair-display ordering must not be mistaken for a pointwise phase-preserving reflection: `T` preserves phase, whereas `M` and `R` reverse it.\n\nThe affine self-maps of this fixed finite set that are bijections are exactly the identity and `R`. Proof: a bijective affine map `ax+b` preserves the set's nonzero diameter, hence `|a|=1`. For `a=1`, the fixed extrema force `b=0`. For `a=−1`, exchanging the extrema forces `b=−5842`; the interior sign symmetry establishes sufficiency. The accompanying script also enumerates all possible images of the extrema and obtains exactly these two maps.\n\nThe Sothic ratio itself remains a different operator: a dilation with factor greater than one cannot preserve the nonzero diameter of this same finite set. The global permutation is translation plus inverse Mirror, not the claim that `2923/2921` alone permutes all dates.\n\n## 7.7 The exact roles of all four cycle lengths\n\nFour equal cycles per route are intended. No arbitrary mixing of the four periods within a route is introduced.\n\n| Cycle length `q` | Translation `4q` | Original nodes landing within the exact twelve-node Mirror target set | Outside target set |\n|---:|---:|---:|---:|\n| `1460` | `5840` | `8` | `4` |\n| `1460.5` | `5842` | `12` | `0` |\n| `1461` | `5844` | `8` | `4` |\n| `1461.5` | `5846` | `4` | `8` |\n\nThe counts assume the same translation is attempted from every source node, with no wrapping or state-dependent reassignment. The former selected-route constructions remain valid. The table specifies why those constructions are not four independent global permutations of one fixed finite set.\n\nFor example, `2939t BC + 5846 years = AD 2908t` remains within the target set, but `2935t BC + 5846 years = AD 2912t` is outside it. Therefore an unrestricted assertion that all four periods land only on the twelve targets from every possible source node is false.\n\nThe overlapping maps reduce to:\n\n\\[\nM T_L(\\mathcal X)=\\mathcal X+(5842-L).\n\\]\n\nThe offsets are respectively `+2,0,−2,−4` in forward-running phase coordinates. Their intersections with `\\mathcal X` explain the `8/12/8/4` counts through the three-Gear spacing. No modular wraparound is licensed.\n\n## 7.8 What is unique\n\nWithin the already fixed `30`-rail, local `±2`, and half-year paired-phase template, a uniform `5842`-year all-node closure pins the center uniquely:\n\n\\[\n\\mathcal X(c)=c+E,\\quad E=-E,\n\\qquad\nT_L(\\mathcal X(c))=M(\\mathcal X(c))\n\\iff c=-\\frac L2.\n\\]\n\nAt `L=5842`, `c=−2921`. Since `E` is already fixed by the SKL template, this produces exactly Dean's twelve date/phase coordinates. Any nonzero uniform displacement of this fixed template destroys the `5842` all-node closure against the unchanged BC/AD datum.\n\nThis is uniqueness of placement of the prescribed template, not derivation of that template from cycle periods alone. A symmetric field with a different rail separation can have the same center and the same `5842` closure. Merely requiring all four durations to occur somewhere is also weaker: shifting the full prescribed field one BC label earlier gives center January 1, 2922 BC and intersection counts `4/8/12/8`; all four durations still occur, but `5842` no longer closes all twelve. This counter-test does not dispute the result with the original center and `5842` closure explicitly held fixed.\n\nThus the valid strengthened claim is: **the fixed SKL template has a unique placement under the central half-step four-cycle closure.** Global uniqueness across every possible node pattern or weaker selected-route test is not established.\n\n## 7.9 Opposed `±720` continuation is exact\n\nThe source controls explicitly permit the nested local wheel on each admitted macro member. Opening that comparison here adds the coordinate offsets `k∈{−720,0,720}` without identifying those offsets with the local two-year unit. [F21/F34; REG §D.38]\n\nIn forward-running coordinates:\n\n\\[\n\\boxed{T_{5842}(\\mathcal X+k)=M(\\mathcal X-k).}\n\\]\n\nHence the earlier macro copy crosses to the Mirror of the later copy, and vice versa. The central copy crosses to its own paired-Mirror set. The union of the three explicitly opened copies has `36` phase-nodes and obeys the same all-node closure:\n\n\\[\n\\mathcal X_{\\mathrm{macro}}\n=c+\\{-720,0,720\\}+E,\n\\qquad\nR(\\mathcal X_{\\mathrm{macro}})=\\mathcal X_{\\mathrm{macro}}.\n\\]\n\nThese `36` are comparison-overlay coordinates, not new raw textual rows or independent witnesses.\n\nFor paired cross-axis spans using BC Nisan labels `U,D`, the simpler invariant is:\n\n\\[\n\\boxed{(U+k)+(D-k)=U+D.}\n\\]\n\nBoth phase components retain that exact span. Thus every valid `5840/5842/5844/5846` relation in the original field has an opposed macro counterpart with the same span; this is a theorem of the declared translations, not a coincidence checked separately at each node.\n\n| Original labels `(U,D)` | Opposed macro labels `(U+720,D−720)` | Unchanged four-cycle span |\n|---|---|---:|\n| `(2936,2904)` | `(3656,2184)` | `5840` |\n| `(2936,2906)` | `(3656,2186)` | `5842` |\n| `(2936,2908)` | `(3656,2188)` | `5844` |\n| `(2938,2908)` | `(3658,2188)` | `5846` |\n\nFor the central row:\n\n\\[\n3657t/3656n\\text{ BC}\\to\\text{AD }2186t/2187n\n\\]\n\nhas `3657+2186−1=3656+2187−1=5842`, and the target is the paired Mirror of `2187t/2186n BC`.\n\nThe same-sign shift of both BC-label endpoints would instead change the span by `2k`; it is the opposed, crisscrossed assignment that preserves the four-cycle carrier. Fixed `1476/1446` internal landmarks are not consequences of this endpoint identity and remain route-specific.\n\n---\n\n\n# 7A. Final discussion refinement: anchored selection and the Long family\n\nThe following supersedes the final assistant reply where its qualifications were incomplete. Full source context and proof remain in Report V.\n\n## 7A.1 Why this center: the Sothic–Mosaic selection mechanism\n\nInternal symmetry alone would allow many shapes. Dean's subsequent refinement supplies the missing placement rationale: the principal flanks stand one ordinary Sothic cycle before Joshua's birth and the plague/Exodus packet.\n\nThe corresponding January centers are:\n\n\\[\n2936\\rightarrow1476=1460,\n\\qquad2906\\rightarrow1446=1460.\n\\]\n\nThus the source midpoint is:\n\n\\[\n\\boxed{1460+\\frac{1476+1446}{2}=2921.}\n\\]\n\nThe previously controlled source anchors and target packet co-register. The `1380→1500` Priestly route supplies another operator-based compatibility check, not independent source testimony.\n\n### 7A.1.1 The twenty-year calendar interchange\n\nAt the fixed Exodus target:\n\n\\[\n2906-1446=1460=4\\times365,\n\\]\n\n\\[\n2886-1446=1440=4\\times360.\n\\]\n\nTherefore:\n\n\\[\n\\boxed{2906-2886=20=4(365-360).}\n\\]\n\nThe inherited `30|20|30` SKL corridor contains exactly the displacement required to interchange these two fourfold calendar-body counts without moving Exodus. `720+720=1440` is the 360-based realization; `1460` is the 365-based realization. They are structurally comparable counts, not equal elapsed durations or an unannounced calendar conversion. [F21/F34; SA]\n\n### 7A.1.2 A smaller reconstruction of the corridor\n\nLet `e=1446`, `Q=4×365=1460`, and `F=4×360=1440`. With the inherited 30-year rail:\n\n\\[\n\\boxed{(e+Q+30,\\ e+Q,\\ e+F,\\ e+F-30)=(2936,2906,2886,2856).}\n\\]\n\nIts spacings are `30`, `Q−F=20`, and `30`. The Moses/Joshua comparisons become:\n\n\\[\n(e+Q)-(e+80)=Q-80=1380,\n\\]\n\n\\[\n(e+F-30)-(e+30)=F-60=1380.\n\\]\n\nTheir 50-year rectangle is consequently compatible with:\n\n\\[\n80-30=30+(Q-F)=50.\n\\]\n\nThis clarifies evidence accounting. The corridor, both `1380` differences, the `20`, and the `50` are not independent after the listed inputs are fixed. The explanatory advance is that a small input packet reconstructs all of them. A probability claim would have to charge for the choices of calendar bodies, anchors, rail, and endpoint classes.\n\n\n## 7A.2 Joshua to the paired Mirror of Exodus\n\nThe paired target is `AD 1446t/1447n`. Writing that set in reverse order does not change its members, but component-wise pairing must be stated.\n\n| Span | Length |\n|---|---:|\n| `1477t BC→AD 1446t` | 2922 |\n| `1476n BC→AD 1447n` | 2922 |\n| Outer cross-phase `1477t BC→AD 1447n` | 2922.5 |\n| Inner cross-phase `1476n BC→AD 1446t` | 2921.5 |\n\nHence:\n\n\\[\n2922=2\\times1461=1460.5+1461.5,\n\\]\n\n\\[\n2922.5=1461+1461.5=\\frac{2\\times1461+2\\times1461.5}{2},\n\\]\n\n\\[\n2921.5=1460.5+1461.\n\\]\n\nDean's average intuition is correct when interpreted as the average of the **two doubled completed totals**; the ordinary one-period average is `1461.25`.\n\nThe exact outer-span midpoint is `x=−15`, January 1, 15 BC. The corresponding-phase midpoints are `16t BC` and `15n BC`, straddling that January center. The interval `1t BC→AD 1n` does straddle the epoch datum, but it is not automatically the midpoint or an internal-cycle landing of these Joshua/Exodus paths. The prior assistant's loose suggestion that the epoch straddle had been established is superseded by this phase calculation.\n\n\n## 7A.3 The Long SKL family and the Moses–Joshua fifty\n\nThe Long branch has its own legitimate roles:\n\n\\[\n2888n\\text{ BC}\\rightarrow\\text{AD }33n=2920=2\\times1460,\n\\]\n\n\\[\n2886n\\text{ BC}\\rightarrow\\text{AD }35n=2920,\n\\]\n\n\\[\n2856n\\text{ BC}\\rightarrow\\text{AD }65n=2920.\n\\]\n\nAD 33n retains its preferred Passion comparison, AD 35 its separate comparison role, and AD 65 the schematic Christ-generation terminus—not the literal duration of Jesus' earthly life. [F13; F43; F54; F68]\n\nThe reversed 50-year relation is exact:\n\n\\[\n2905t/2904n\\text{ BC}\\rightarrow\\text{AD }1476t/1477n=4380,\n\\]\n\n\\[\n2855t/2854n\\text{ BC}\\rightarrow\\text{AD }1526t/1527n=4380.\n\\]\n\nMoving the BC source forward 50 and its mirrored target forward 50 preserves the span. In source-year magnitudes, the source labels decrease while the target AD labels increase. This is the appropriate reversed orientation of the Moses–Joshua birth separation.\n\nThe complete fixed-field test, assuming the obvious typo `2859t/2558n` intended `2859t/2858n`, is:\n\n| Source | To AD 1526t | To AD 1527n |\n|---|---:|---:|\n| 2859t BC | 4384 | 4384.5 |\n| 2858n BC | 4383.5 | 4384 |\n| 2857t BC | 4382 | 4382.5 |\n| 2856n BC | 4381.5 | 4382 |\n| 2855t BC | 4380 | 4380.5 |\n| 2854n BC | 4379.5 | 4380 |\n\nThe matrix contains `3×1460`, `3×1460.5`, and `3×1461.5`, but **not `3×1461=4383`**. The earlier suggestion that adjacent/single-date variants could supply the missing member was not accompanied by a fixed alternative endpoint declaration. It is not promoted to a result. A future extended test may specify such a field before calculation; the fixed matrix remains unchanged.\n\nThe Long twelve-node field is centered at January 1, 2871 BC. Its own self-Mirror translation is `5742`, not `5842`. Its genuine Sothic paths are not evidence that both variants separately satisfy the same four-cycle whole-field theorem.\n\n\n# 8. The AD 29465 Pillar and Apparent Adam\n\n## 8.1 Inherited square and the ordinary Sothic product\n\n\\[\n2936+29465-1=32400=180^2.\n\\]\n\nFrom actual regular MT Year 6, Cainan OFF:\n\n\\[\n4116+29465-1=33580=23\\times1460.\n\\]\n\nThe Priestly conversion gives:\n\n\\[\n33580\\times\\frac{25}{23}=36500,\n\\]\n\n\\[\n36500-33580=2920=2\\times1460.\n\\]\n\nThe arithmetic in point 9 is correct through this step. The factor is Priestly `25/23`, not the ordinary Sothic ratio itself.\n\n## 8.2 Half-step product and the `34.5` displacement\n\n\\[\n23\\times1460.5=33591.5=33580+11.5,\n\\]\n\n\\[\n33591.5H=23\\times1461.5=33614.5.\n\\]\n\nHence:\n\n\\[\n33614.5-33580=11.5+23=34.5=30+4.5.\n\\]\n\nFixing the Pillar at `AD 29465n` makes the phases explicit:\n\n\\[\n4128t\\text{ BC}\\to\\text{AD }29465n=33591.5,\n\\]\n\n\\[\n4151t\\text{ BC}\\to\\text{AD }29465n=33614.5.\n\\]\n\nActual Apparent Adam is `4146n BC`, whose Pillar span is `33610`. The proposed output differs by:\n\n\\[\n33614.5-33610=4.5.\n\\]\n\nThus the `34.5` construction is exact, while its identification with the `30` Apparent-Age shift is incomplete by `4.5`. The existing Supplement A uses `34.5/4.5` under its own operators, but shared numbers do not automatically license the missing operation in this Pillar construction. [F22; SA]\n\n## 8.3 Exact common-`K` companion reaches Rounded Apparent Adam\n\nA distinct consequence of the forced `G=1680/1679` continuation is:\n\n\\[\n33580=20\\times1679,\n\\]\n\n\\[\n33580G=33600,\n\\]\n\n\\[\n4136+29465-1=33600.\n\\]\n\nTherefore, with the Pillar fixed:\n\n\\[\n4116n\\text{ BC}\\xrightarrow{G\\text{ on the Pillar span}}4136n\\text{ BC}.\n\\]\n\n`4136 BC` is already the Rounded Apparent-Adam state controlled by File_51a. It is not the actual `4146 BC` Apparent-Adam state. The two resulting calendar counts have identical schematic day-volume:\n\n\\[\n36500\\times336=33600\\times365=12264000.\n\\]\n\nThis comparison follows from the same seed and common `K`; it is not an independent second physical synchronization or a reason to redefine either Adam state. [F51a; F00; SG]\n\n---\n\n# 9. What this family contributes to the unification strategy\n\nThe new analysis has both a positive result and a useful constraint.\n\nThe positive result is that much of the family compresses to:\n\n\\[\nq_0=1460,\n\\quad\\delta=\\frac12,\n\\quad R_\\delta=\\frac{q_0+\\delta+1}{q_0+\\delta},\n\\]\n\nwith:\n\n\\[\n9890+(460-130)=7q_0,\n\\]\n\n\\[\n7\\delta=3.5,\n\\qquad10\\delta=5,\n\\qquad23\\delta=11.5.\n\\]\n\nThe `7`, `10`, and `23` applications then produce the observed half-week, Creation head/Year-6, and Pillar offsets. The Mirror adds the already admitted local Gear field:\n\n\\[\n5842+g+h,\n\\qquad g,h\\in\\{-2,0,2\\}.\n\\]\n\nThe constraint is that a shared *grammar* is broader than a shared *calibration*. The original three exact Keys share `K`. The proposed `H` shares the half-23 completion grammar and the Sothic/Julian neighborhood, not the same `K`. The forced `G` shares `K` but not optimal tropical calibration.\n\nUnder the author's providential premise, different scribal/calendrical traditions could preserve different compatible features of this grammar. The mathematical investigation does not require every participant to know the complete cross-tradition field. Direct historical dependence, statistical rarity, and a claim that ancient scribes explicitly used `2923/2921` remain unproved.\n\nThe principal source-placement burden is now narrow: explain why the received Cainan-adjusted Creation separation is `7×1460`, why the selected terminal occurs at `10×1460`, and whether additional previously bounded families follow without adding discretionary operators. The week bisections are then consequences of one half-year displacement rather than separate discoveries requiring separate mechanisms.\n\n---\n\n# 10. Executed bounded amendment preparation\n\nThe author authorized consolidation and necessary repository updates with discretion over implementation. The following three additive replacements are prepared in `../02_Repository_Amendments/`, with frozen parents, reconstructible patches, and separate verification. No live source, existing control document, archive, or publication manifest is overwritten.\n\n| File | Prepared scope | Preserved boundary |\n|---|---|---|\n| File_12 | New §5A: completion grammar, H/G distinction, calibration, Enochian companion, scope guards | Original three Keys and all inherited proof text remain unchanged. |\n| File_22 | New §5A: matched-Cainan Creation bridge; new §9B: Pillar comparisons | Existing `9890`, source nodes, actual/Rounded states, and inherited equations are protected. |\n| File_70 Supplement A | New §13: SKL whole-field symmetry, Mosaic–Joshua selection, Long branch; new Appendix H | Prior 446-row manifest, evidence weights, 53 guards, and earlier Enoch-centered proof remain unchanged. |\n\nThe detailed Mirror/SKL proof now belongs with Supplement A rather than becoming an oversized appendix to File_22. This is the only substantive routing change from v0.2.\n\nTaxonomy is resolved for these working amendments: `H=2923/2921` is a locally opened **Sothic-adjacent Key-of-23 companion**; `G=1680/1679` is a locally opened **exact common-K 365-day extension**. The default original three-Key inventory is not silently enlarged.\n\nThe candidate additions remain verification-complete working text pending explicit author Finalization. Proposed central entries and exact new guards are supplied separately in `../04_Registration_Proposals/`; existing Register and Capsule editions remain unchanged. Reports I–IV remain unchanged; Report V and Strategy v0.2 provide the current research checkpoint.\n\n## 10.1 Open issues retained\n\nThe Pillar half-step remains `4.5` years from actual Apparent Adam. The fixed Long–Moses matrix does not contain `4383`. The Joshua/Mirrored-Exodus outer interval has its midpoint at January 1, 15 BC, not the epoch datum. The full remote SKL Creation/Flood continuation is still untested. No heliacal-reset epoch or historical proof of scribal use of H/G is claimed.\n\nThe pre-existing File_00 solar-epoch wording and File_53 rounded-decimal equality are recorded for separate source review, not silently rewritten. Optional adjacent-date/Mirror variants are not added to repair the fixed-field misses.\n\n---\n\n# 11. Portable external references\n\nRetrieved September 6 2026. The repository supplies the chronographic anchors; outside sources provide only the historical/calendar context named above.\n\n- Censorinus, *De die natali*, chapter 18, Egyptian/canicular-year discussion: https://topostext.org/work/741\n- Observatoire de Paris, Patrick Rocher, *Soleil Terre Lune — Phénomènes*, historical tropical-year section, P. Bretagnon (2000) formula: https://media4.obspm.fr/public/ressources_lu/pages_stlp/impression.html\n- Exodus 40:17, official ESV text: https://www.esv.org/Exodus%2B40%3A17%3BExodus%2B40%3A34/\n- Cassius Dio 69.12–14, translated account of the Bar Kokhba war: https://www.livius.org/sources/content/cassius-dio/cassius-dio-on-bar-kochba/\n- File_33 read-only Sothic precedent: https://490d.com/source/490d-unified-chronology/File_33.Ordinal_Lock.md\n- Canonical raw-source index: https://490d.com/source/490d-unified-chronology/\n\nThe epoch calculation uses an approximate epoch argument; its printed digits identify the calculation, not a claim of observational accuracy to those digits. No modern paper's proposed new calendar or historical reconstruction has been adopted.\n\n---\n\n# Appendix A. Exact-token novelty check and parent identity\n\nAn exhaustive literal-token scan of the complete three mounted vocabulary controls was executed before recording the proposed ratios as absent from their literal vocabulary. Absence of a literal ratio is not proof of conceptual novelty. `2921` already occurs as the SKL Short midpoint; its new use as a denominator must not replace that state.\n\n| Token | Capsule occurrences | Register occurrences | Style Guide occurrences |\n|---|---:|---:|---:|\n| `1460.5` | 0 | 0 | 0 |\n| `1,460.5` | 0 | 0 | 0 |\n| `1461.5` | 0 | 0 | 0 |\n| `1,461.5` | 0 | 0 | 0 |\n| `2923/2921` | 0 | 0 | 0 |\n| `2923 / 2921` | 0 | 0 | 0 |\n| `2923` | 0 | 0 | 0 |\n| `2,923` | 0 | 0 | 0 |\n| `2921` | 1 | 2 | 0 |\n| `2,921` | 0 | 0 | 0 |\n| `1680/1679` | 0 | 0 | 0 |\n| `1680 / 1679` | 0 | 0 | 0 |\n| `1679` | 0 | 0 | 0 |\n| `1,679` | 0 | 0 | 0 |\n| `Sothic` | 2 | 0 | 0 |\n| `3015/3013` | 0 | 0 | 0 |\n\nThe scan includes plain, comma-grouped, and spaced-ratio forms. The literal `Sothic` already occurs in the Capsule; the existing source-defined residual nomenclature must not be overwritten by the new operator symbol.\n\n## Read-only mounted-source fingerprints\n\n| Source | SHA-256 |\n|---|---|\n| `File_12.Calendrical_Physics(5).md` | `89e3af8692c36cb3251880bc62db013441668dd3eabb3b8fd7770be96b6208fe` |\n| `File_22.Cumulative_MT_Harmonics(10).md` | `bb722b0df2161a74911097f81c30e8cb51cc6a3e4ec76d0ca22f9d3112befc7c` |\n| `File_09.Cumulative_Architecture(8).md` | `a7910c13c2d1f471fbdc47d46ad0494c5f8f8c78951f74feb804173f04d40594` |\n| `File_18.Chronological_Data_Tables(20260902-184631).md` | `58e5ae1a36f4753c0a133ca7fcdf1b6efd1697ae29c7dbfa09e76466a32d07cc` |\n| `File_51a.Rounded_Scaffold_Mod5_Architecture(6).md` | `31dfe17ef8b50bf583503af256cbae4e29a75b30613548047f4dc233473bacb4` |\n| `Restart_Capsule(20260829-155229).md` | `ca54da57bc46487d6cf0ef5cb07bac7c517df79fdb9d5039f122df528fe0f398` |\n| `State_Vocabulary_Register(20260829-155229).md` | `0b927f7a9268138f1c06412b0ad11c05cb2e753a456531c170fd95898c5b493a` |\n| `490d_Repository_Style_Guide(20260829-155221).md` | `bbdd87290ed995534f9ba1bc4e36fcbecda96c971d1f2340a310d5c6a834727e` |\n| `Project_Procedures(20260829-155229).md` | `aafb0106954107345fdbe33d3f5e94122fb9b2e67c8201605d3078945c4637fe` |\n\n\n# Appendix C. v0.2 bounded revision record\n\nSeptember 6 2026: Dean identified the January 1, 2921 BC common center and challenged the former affine qualification. The new whole-field proof supersedes that qualification while retaining the prior selected-route calculations, calendar-calibration distinctions, and all Creation/Pillar material. No canonical file or control document is changed.\n\nPreserved v0.1 parent: `365_Sothic_Key23_Discussion_and_Amendment_Ledger_v0_1_20260906.md`\n\nSHA-256: `9f69f73da84e9a5dd13f8ab87a2344902a841c347d15bf689576559d9edc4a75`\n\nNew executable verification: `check_sothic_mirror_closure.py`. Its scope is the new mathematical module, not recertification of the whole inherited ledger.\n\n# Appendix D. v0.3 consolidation record\n\nSeptember 6 2026: incorporated Dean's Mosaic–Joshua location argument, the `30|20|30` fourfold-calendar corridor, and the Long-SKL comparisons; added exhaustive six-by-two phase audit; corrected assistant overstatements about independent witnesses, `4383`, and the epoch straddle; prepared Report V, Strategy v0.2, three bounded source amendments, and registration proposals. All prior source and research parents remain preserved. New canonical Final status is not claimed.\n"}