{"id": "c113", "title": "C113 — Source admission and dependency audit of the 2116/4232 Terah–Moses Mirror", "filename": "490d_C113_2116_4232_Terah_Moses_Mirror_Intake_20260922.md", "role": "Research action", "step": 113, "sha256": "9bb3520135e7380f247c1e0804dd3eb473cca3ecf0eb34654a70fc61c3802d50", "bytes": 8576, "origins": ["C01–C479/reference/490d_C01_C265_Complete_Window_Archive_20260923.zip!/workspace/mirror_C113_2116_4232_intake_20260922/490d_C113_2116_4232_Terah_Moses_Mirror_Intake_20260922.md"], "download": "/sources/9bb3520135e7380f247c1e0804dd3eb473cca3ecf0eb34654a70fc61c3802d50.md", "format": "md", "derived": false, "tags": ["Regular", "Cumulative", "Inverse", "Covenant", "Mirror / 529"], "excerpt": "C113 — Source admission and dependency audit of the 2116/4232 Terah–Moses Mirror\n\n22 September 2026 · One authorized bounded step after C112.\n\nThe handoff's core 4232-year construction is reproducible in the declared frame. It supplies named patriarchal endpoints for an 8×529 comparison, while its 4×529 half-width is a", "content": "# C113 — Source admission and dependency audit of the 2116/4232 Terah–Moses Mirror\n\n22 September 2026 · One authorized bounded step after C112.\n\n**The handoff's core 4232-year construction is reproducible in the declared frame.** It supplies named patriarchal endpoints for an 8×529 comparison, while its 4×529 half-width is a generated local fulcrum. The compact Moses framework also checks. Its repeated 120-year increments reduce to **60×(21,23,25)**, with different operations producing the two increments. The transferred **1260+3.5** remains the next endpoint problem.\n\n## 1. Source settings and admission\n\nThe full handoff was read first. File_18 §§2.3–2.4 reproduces Abraham 2166, Isaac 2066 and Jacob 2006 BC by the stated +215/full-430 selection, while Moses 1526, Exodus 1446 and Moses' death/Conquest coordinate 1406 stay fixed. Moses aged 40 at 1486 is derived within that fixed biography. File_18 §1.3 and §4A.5 separately qualify Terah's firstborn **2226=2296−70** in the +60 Terah state. Identifying this firstborn as Haran follows the adopted reconstruction in the handoff.\n\nThe +60 qualification is local to that Terah row. It is not added to Abraham, Jacob or Moses. The common selected comparison frame does not erase native MT/SP/LXX sojourn distinctions. No regular Gear is applied to a patriarchal or Mosaic record here. The prior 1876 half-primer and 1446 thirds-primer campaigns remain inactive.\n\n| Source pair | Complementary sum | Offsets from 2116 |\n| --- | --- | --- |\n| Abram 2166 / Isaac 2066 | 4232 | +50 / −50 |\n| Terah firstborn 2226 / Jacob 2006 | 4232 | +110 / −110 |\n\nThe second sum is related to the first through opposite 60-year changes: 2226=2166+60 and 2006=2066−60. Their cancellation explains the repeated sum. Reversing each comparison through the Mirror likewise creates a dependent counterpart, rather than a fresh arithmetic witness.\n\n## 2. Three operations kept distinct\n\nFor the paired display `(b+1)t/b n BC`, ordinary paired reflection gives `AD b t/(b+1)n`. A **forward translation by W=4232** instead gives `AD (W−b)t/(W−b+1)n`. Both seasonal components obey the no-year-zero checks:\n\n\\[\n(b+1)+(W-b)-1=b+(W-b+1)-1=W.\n\\]\n\nThus the complementary pair-base rule is **C_W(b)=4232−b**, with local midpoint 2116. It is an involution on these pair-base labels. It does not replace the ordinary January AD 1 Mirror rule.\n\nThe own-mirror gap is `W−2b`; the crossed-event gap is `W−b−d`. These two formulas organize the handoff's repeated numbers without merging the events or the operators.\n\nThe 4232 interval has named-source realizations, for example **2167t/2166n BC → AD 2066t/2067n**, linking Abram to reflected Isaac. The central pair **2117t/2116n BC ↔ AD 2116t/2117n** is a generated fulcrum, not an independently identified event at 2116. Accordingly, C113 admits a provisional local **8-fold interval** and a **4-fold radius**; it does not add an unnamed historical event to the graph.\n\n| Converted width | Original | First ×25/23 | Second ×25/23 |\n| --- | --- | --- | --- |\n| Radius | 2116 = 4×529 | 2300 = 4×575 | 2500 = 4×625 |\n| Full width | 4232 = 8×529 | 4600 = 8×575 | 5000 = 8×625 |\n\nThese are converted widths. The original ±50/±110 event offsets remain in their original frame, and the converted widths do not automatically supply historical endpoint events.\n\n## 3. The compact Mosaic ledger\n\n| Fixed source boundary | Ordinary Mirror pair | Source translated by 4232 |\n| --- | --- | --- |\n| Birth 1527t/1526n BC | AD 1526t/1527n | AD 2706t/2707n |\n| Age 40: 1487t/1486n BC | AD 1486t/1487n | AD 2746t/2747n |\n| Exodus: 1447t/1446n BC | AD 1446t/1447n | AD 2786t/2787n |\n| Death/Conquest coordinate: 1407t/1406n BC | AD 1406t/1407n | AD 2826t/2827n |\n\nThe translated landings are generated coordinates attached to source boundaries; their dates are not independently named historical events. The paired seasonal display retains the model's precision and does not establish an unstated historical event month.\n\nWrite B=1526, E=1446, D=1406 and L=B−D=120. Then:\n\n\\[\nG_0=W-B-E=1260,\\qquad G_1=W-E-D=1380,\n\\qquad G_2=\\frac{25}{23}G_1=1500.\n\\]\n\nThe two 1260 descriptions—birth against Exodus, and age 40 against its own mirror—coincide because B+E=2×1486. The two crossed 1380 comparisons coincide because E+D is symmetric. Own-event comparisons remain different: Exodus gives 1340 and the death/Conquest coordinate gives 1420.\n\n## 4. The repeated 120 has a compact dependency structure\n\n\\[\n1260:1380:1500=21:23:25,\\qquad\n(1260,1380,1500)=60(21,23,25).\n\\]\n\nThe first increment is **G₁−G₀=B−D=120**: replace Moses' birth with his death while retaining the Exodus comparison. The second is **(25/23−1)×1380=120**: expand the 1380 width. These are distinct operations. In particular, `1260×25/23=31500/23`, which is **240/23 short of 1380**. The three terms must not be described as two successive 25/23 dilations.\n\nThe equality of the two gains is equivalently:\n\n\\[\nW=E+D+\\frac{L}{25/23-1}\n=1446+1406+1380=4232.\n\\]\n\nThis is a useful compatibility equation between the proposed bridge and the fixed Mosaic biography. It is a rearrangement of the same condition, not an additional independent witness. The 1500 remains an expanded width; this step assigns no historical event to an expanded endpoint.\n\n## 5. The generated 2706 counterpart\n\nThe inverse translation of Moses' ordinary paired reflection gives:\n\n\\[\n2707t/2706n\\ \\mathrm{BC}+4232\n=\\mathrm{AD}\\ 1526t/1527n.\n\\]\n\nThus 2706 is a **generated BC counterpart**, with the verified same-side sequence:\n\n\\[\n2706\\xrightarrow{1260}1446\\xrightarrow{40}1406\\ \\mathrm{BC}.\n\\]\n\nUsing the handoff's declared 6 BC comparison anchor, the same generated coordinate gives:\n\n\\[\n2706\\xrightarrow{1260}1446\\xrightarrow{1440}6,\n\\qquad2700=1260+1440=(3.5+4)\\times360.\n\\]\n\nBoth phase components verify these widths. The Exodus/Conquest meaning of the ordinary 1446→1406 segment is retained; the generated earlier endpoint gains no new historical identity from the equality. The 6 BC phase completion is a project comparison, not independent evidence for a birthday.\n\n## 6. Limited 3.5-year diagnostic and the next question\n\nFile_22 §6.2.5 and the handoff retain the harmonic **Aaron 1530t BC → Moses 1526n BC = 3.5 years** branch. With the handoff's fixed comparison endpoint **AD 1447n**:\n\n| Translated birth endpoint | Gap after AD 1447n |\n| --- | --- |\n| Moses: AD 2707n | 1260 |\n| Aaron: AD 2703t | 1256.5 = 1260−3.5 |\n\nThis reproduces the stated untransferred diagnostic. It does not execute Dean's additional transfer to the Exodus/witness comparison. To verify **1260+3.5=1263.5**, that transfer must supply its own start, end, direction and event roles. This step neither rejects the intended interpretation nor labels its additional boundary as already sourced. Aaron's 123-year and Moses' 120-year lifespans remain unchanged; their original death boundaries are not recast as 3.5 years apart.\n\nDean's Revelation 11–12 ordering and recurring-template interpretation are preserved as supplied, without expanding or adjudicating those interpretive claims in this arithmetic intake. Peleg/Joseph, covenant and Jared/conception comparisons remain for later bounded steps.\n\n## 7. Evidence and continuation state\n\n**32 exact arithmetic, source and phase checks passed.** Seven dependencies were frozen and hash-verified. The certificate, results and report body replayed byte for byte in isolation; the original files remained unchanged. No earlier campaign was executed.\n\nThe C112 graph remains frozen at **104 nodes, 193 durations, 35 reflections, rank 101**. The new local construction is certified separately, with its 8-fold named intervals and generated 4-fold fulcrum distinguished. Canonical files and the prior graph are unchanged. Regular Gears remain restricted to Noah/Shem/Flood.\n\n**Sources:** the complete 2116/4232 branch handoff, especially §§2–3 and 5–8; File_18 §§1.3, 2.3–2.4, 4A.5 and 6A; File_09 Appendix A.3; File_22 §6.2.5; File_62 §8.1; and the frozen C112 certificate/checkpoint. The new arithmetic is conditional on the supplied chronological model and is not a claim of independent historical dating or demonstrated literary intention.\n\n**Best next bounded step — High sufficient.** Resolve the transferred 3.5-year interval with explicit BC/AD endpoints, direction and event roles, preserving the intended 1260+3.5 reading while distinguishing an original death boundary from a generated or reversed-biography terminal. Stop at C113 pending the next instruction.\n", "evidenceLinks": [{"id": "d-be42daca1d82dac9", "title": "File 62"}, {"id": "d-68301ab760bfbe2e", "title": "File 18"}, {"id": "d-1c77fd504afbf59b", "title": "File 22"}, {"id": "d-45851004c5864229", "title": "File 09"}]}