Independent review of C502–C511
Reviewer: grammar-review agent, independently assigned by the root researcher. Date: 27 September 2026.
Read all ten journal entries, their step scripts, and the C502–C511 Markdown report. Checked the relevant File18, latest File52c, Strategy, and prior C480/C481 inputs. Replayed all ten scripts with in-memory replacements for begin and finish: all 25 supplied assertions passed, and results, findings, reassessments, inputs, sources, and checks matched the journal. The replay did not invoke the journal writers. No numerical correction is required.
Affine laws and pivot theorem
Independently expanded five identities as exact formal polynomials: anchor difference, translation conjugacy, same-anchor composition, different-anchor order, and reflection compatibility. All reduce identically to zero. In particular, C509 has the correct sign:
The pivot theorem is correct for the stated integer inputs and integer pivots. One E stage is integral exactly when the source and pivot agree modulo23. Two stages about the same pivot are integral exactly when their original displacement belongs to529Z. Independently checked all529 displacement residues as a finite diagnostic of these two conditions; the general result also follows from the stated coprime-denominator argument.
An original529-multiple width becomes a575-multiple width after the first stage, so integral first endpoints share a residue modulo23. This guarantees a common residue condition for a second pivot, but does not license a pivot. C480 supplies the required residue19; the fixed12026 construction instead has endpoint residue22 against pivot20 and therefore the stated common4/23 fractional part. Both final widths are1250.
Coordinates and source states
C510 correctly distinguishes civil B+A−1 from Rounded B+A−2. C511 correctly gives Rounded coordinates1445,525,−475, displayed as AD1446, AD526,476BC with AD12026 held. As an independent contrast, using the civil chart with the same printed positive-side anchor and start would give AD1446,AD526,475BC. The initial same-side width remains10580 in both charts; the difference appears at the crossing. The Rounded origin is not a civil year zero.
C503–C504 preserve the current LXX182/753 main chain, native second Cainan ON in the full-430 comparison frame, and the SP equalized primary rail. Jared remains an unshifted upstream source node; only the selected NoahG1/FloodG2 stations use the local Gear comparison. The LXX Jared4534 and SP Jared3954 are their File18 minimum/native values4319 and3739 plus215. The SP−1 companion is not applied.
C508 correctly keeps the Strategy rectangle separate from C483's completion comparison. Current File18 also makes the node/frame distinction concrete:4206 is the native SP Creation-week opening, whereas4414 is the equalized preferred chain head;13406 is the cumulative implied Day1 display, whereas13396 is its Day10 terminus. Thus:
Consequently the rectangle's9200 gap differs from the completion-pair gap8982 by215+3=218. This is a declared frame and node-class change, not an error or interchangeable pair. Independently verified both held-head expansions end at1406:4206−(70/69)2760=1406 and13406−(300/299)11960=1406.
Two small synthesis qualifications
- C503's phrase “the complete14/15/16 pattern and its three-Key integrality” can be made more precise: the MT trio has integral E/J outputs, while its central Noah member alone has integral outputs under all three Keys. The cross-tradition negative result is correct.
- State Rounded reflection's same-number BC/AD display rule for nonzero coordinates. File52c explicitly displays q=0 as the comparison origin1BC; the general statement must not introduce an extra civil year-zero label. None of the reviewed calculations reaches zero.
Citation refinement only: C509's direct File52c source for the uniform1280 anchor-switch relation is §3.7.3, with the Shem example in §3.8.2; §3.11 is a related later application.
The review checks arithmetic, operation domains, and the stated source selections. Its assertions are not independent historical or statistical witnesses. No journal, step script, or canonical source was modified.