Independent review of C984–C1007

Result: PASS, with one nonblocking source-pointer clarification. All 212 exact checks pass. No arithmetic or whole-field discrepancy was found. This review does not add numbered research actions or alter completed journal records.

The reproducible evidence is INDEPENDENT_C984_C1007.json. Run the independent script from any directory:

python /workspace/scratch/1b40da62dcbd/c932_c1131/prep/key_constraints/review_C984_C1007.py

It uses only Python's standard library. Rank is calculated from determinant minors, and each two-stage affine domain is enumerated over a complete guaranteed period. It imports neither the root algebra helper nor the preparation calculations. It also checks all eight frozen source hashes, ten literal excerpts, and the completed block's referenced artifact hashes and lengths.

Constraint dependencies and partial operations

The two backward systems have determinants −1656 and −8372 and recover E=25/23, P=70/69 and J=300/299. The four-equation system has coefficient rank three and augmented rank three. Its primitive left dependency is

including the right-hand constants. Each choice of three equations is independent. The two calendar equalities alone have rank two and leave the common scale K free. The completion identity fixes K=8400/23. These are equivalent constraint descriptions of inherited identities; neither the partitions alone nor reversing the equations independently establishes the historical Keys. C984–C990 explicitly preserve that distinction.

The selection fractions 1/6, 3/13 and 1/26 are correct, including their product law. Nested selection gives J, while whole P then whole J gives 7000/6877. The computed 3/13 does not authorize a chronological cut. The 1/25 negative control gives E=312/287, differing from 25/23 by 1/6601.

The C993 theorem is valid for the stated partition-summing incidence map: column i of the conversion/coarsening commutator is $(k_i-k_{B(i)})e_{B(i)}$. It vanishes for every input exactly when each block has one common factor. The source 483 example instead agrees only in total: its partial and uniform images differ by $(-35/6,35/6)$. The selected-first general formula and selected-last source example use opposite signs consistently.

The retained-part measurement matrix has rank two, native/P minor −1/69, and left dependency (5,−6,1). Both the inverse and the third dependent measurement were checked on all four declared rows: (690,0), (690,30), (690,60) and (9660,2940). Numerical recovery still does not recover order, named interval, anchor or route authorization, as C997 states.

Complete fixed-pivot domain

For integer pivots a,b and reduced positive ratios p₁/q₁,p₂/q₂, requiring the input and both successive outputs to be integers gives

Thus the domain is empty unless gcd(p₁,q₂) divides b−a. Otherwise it is exactly one residue class of period q₁q₂/gcd(p₁,q₂). The second numerator disappears from this condition because its ratio is reduced. This theorem concerns stagewise integer membership; fractional images remain valid rational comparisons.

Independent exhaustive enumeration over q₁q₂ confirms the entire fixed-pivot diagnostic at a=14006,b=4836:

For J→P, gcd(300,69)=3 does not divide −9170. Every nonempty class also passes three exact two-stage substitutions, including negative representatives. These classes are diagnostic domains, not nine source-authorized chronological routes or event dates.

The whole-field placement criterion is correct. Both inherited examples have differences divisible by 529, but only C480 occupies its required residue. Translating all points and both pivots by 215 translates the residue and both outputs by 215 without changing the period or obstruction; independently checked for all eight nonempty pairs. This covariance does not by itself authorize a historical translation.

The entire File46 head field survives on mesh 250/23 with unchanged indices (92,89,46,43,0). Its exact images match the stored model, and only indices 92,46,0 are integral. No source points were removed or repaired.

Conditional matching-unit volume

Every one of the nine fixed assignments to the 299|161 parts has the stored exact outputs and units. The common component volumes are (109200,58800), giving total168000. Algebraically, with U=diag(336,360,364) and D=diag(E,P,J), the calibration is UD=K I. The nine rows instantiate that one identity; they are not independent confirmations.

For the inherited J/E comparison, 300×364+175×336=168000. Swapping its unit labels gives164500 while the numerical sum remains475. Common-unit remeasurement gives500,1400/3,6000/13, exactly the uniform E/P/J images of460. C1004–C1006 correctly keep this realization conditional and do not establish a literal mixed-calendar elapsed chronology.

Source attribution to carry forward

1. C995–C996: cite Supplement A §10.3 for the retained-lower family. The controlling source is project_sources/14-file_70-supplement-a-key-of-23-fine-resolution-720-30-rail-2-.md, lines2130–2185, SHA256 7a3a2b42ad70a08f9b44b087106b4f6517924c13a00817ecfadf1326da11b968. It explicitly supplies the fixed2940 lower segment and the complete12600/12740/13440 table. Latest File52c's9660 passages concern other mirror/span contexts; they should not be presented as the controlling source for this table. Arithmetic is unchanged. Root has acknowledged carrying the clarification into C1031 and the final synthesis.
2. C1005: identify the assembled475 comparison as inherited C533, built from File60's component branches. File60 §5 supplies299|161 and299→300, with161→175 supplied in its broader reconciliation discussion. The expression300+175=475 is already recorded in C533. Naming that inherited comparison avoids implying that File60 directly appoints a literal475-year mixed-calendar timeline. The present conditional qualifications are adequate and should be retained.

The block advances explanatory compression without enlarging the source chronology: calendar scale, source partition, retained component roles, pivot and grid assumptions remain visible premises. No new discovery claim is needed for the inherited490/12600 completions,529 ladder or earlier placement witnesses.