C113 — Source admission and dependency audit of the 2116/4232 Terah–Moses Mirror

22 September 2026 · One authorized bounded step after C112.

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.

1. Source settings and admission

The 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.

The +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.

The 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.

2. Three operations kept distinct

For 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:

Thus 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.

The 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.

The 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.

These 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.

3. The compact Mosaic ledger

The 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.

Write B=1526, E=1446, D=1406 and L=B−D=120. Then:

The 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.

4. The repeated 120 has a compact dependency structure

The 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.

The equality of the two gains is equivalently:

This 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.

5. The generated 2706 counterpart

The inverse translation of Moses' ordinary paired reflection gives:

Thus 2706 is a generated BC counterpart, with the verified same-side sequence:

Using the handoff's declared 6 BC comparison anchor, the same generated coordinate gives:

Both 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.

6. Limited 3.5-year diagnostic and the next question

File_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:

This 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.

Dean'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.

7. Evidence and continuation state

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.

The 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.

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.

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.