Re-check V1 · Re-check by V1

Correction X1.1 (holds): I re-derived the lattice form of Lemma A (M=g^{-T}O^4 has invariant -w0λ), the condition M^∨=ϖM giving c=(a,b,-1-b,-1-a), the GSp4 coset bijection and Macdonald's count (⟨2ρ,c⟩=4a+2b+3, W_c={1,s} only when a=b), and the values 1 and q(q+1) at J''. My own BFS enumeration of t-stable Lagrangians (script V1/lag.py, different from S1's Hermite-normal-form method) agrees. At ϖJ with q=2 and box t^{-3}, the nonzero λ are exactly (1+a,1+b,-b,-a) with a≤2, values 15, 360, 960, 5760, 23040, 61440; with q=3 and box t^{-2}, values 40, 4320, 29160; (2,0,0,0) gives 0. At J'' the values are 1, q(q+1), q(q+1) for (1,1,0,0), (2,0,0,0), (1,1,1,-1), and both translates vanish at the labels (3,-1) and (4,-2), so their support is exactly {ν1, μ}. The cancellation, the swap of Corollary C for Proposition B and the conclusion (SG) over every F hold; the claim that the counts are field-independent rests on hand proofs that are uniform in F, since the machine checks are only over F_q[[t]].

Correction X1.2 (holds): I re-proved Lemmas 1–3; they use no table entry. I re-derived every hand count in step 4: P^1 and GL2 coset counts, the cyclic-submodule double counts q^4(q+1)^2/q and q^5(q+1)^2(q^2+1)/q^2, the anti-isometry graphs q(q^2-1), and the R_2-points of LG(2,4). Lagrangian enumeration matches every polynomial: |b|≤5 complete at q=2 and 3; |b|≤4 at q=5 (e.g. 4500, 117000, (q+1)^2=36); and the |b|=5 columns (5,0,0), (4,1,0), (3,2,0) at q=5. A5-6's two diagonal cells are confirmed wrong (72 and 360 at q=2, against its 36 and 90), and the zero pattern of Lemma 3 holds. I stopped my q=5 run of column (3,1,1) after 5 min, and S1 itself did not run (2,2,1) at q=5; S1 labels the |b|=5 closed forms heuristic for other q, as it should.

Correction X1.3 (holds): I enumerated the Lagrangians of U/U^# (U=t^{-1}O^6) at the labels c1–c4 for q=2, 3, 5. The results are R1=(1,15,0,0), R2=(30,360,9,0), R3=(120,0,6,1) at q=2; (1,40,0,0), (120,4320,16,0), (1080,0,24,1) at q=3; and S1's stated q=5 values. All twelve polynomials hold. I re-derived the reduction (only c1–c4 occur; a_p>2 is impossible), the H1H1 · Finite orbit filtration: each orbit closure is the union of the finitely many orbits below it, and every object lives on finitely many orbit closures.⊥H2H2 · Equivariant recollement: restriction and extension by zero along orbit embeddings exist and are exact. split at c3, the R_2^4 count at c1, and the anti-isometry-graph count at c2. A4-10 has exactly four false cells (R2(c1), R2(c2), R3(c1), R3(c3)). Eliminating c4, then c3, then c1 correctly shows e2 is not in the span. T_(2,0,0,0,0,0)φ0=q(q+1)1_{c1}: values 6, 12, 30 and zero at (1,1,0) at q=2, 3, 5. So the formula for 1_{O_{c2}} holds.

Proposition X1.4 (holds): Since Pf(tω)=t^m Pf ω, σ maps component s to s+m and reaches component 0 only when m divides s. In Chen–Yi v4 I checked that §7.2 assumes LX connected for Prop. 64 and that Thm 18 (§3) does not. I recomputed the stabilizer Lie algebra dimension (2m^2+m)N+Σ(4j-3)a_j over F_3 and F_5: 80 cases, m≤3, a_1<N, no mismatch. The Cayley transform argument is valid in characteristic ≠2 (2(XD+DX^T)=0; injective on the open set det(1-X) a unit; dim Lie ≥ dim S_a ≥ dim Lie), and so is the reduction to the finite-type model. I checked the identity def(ν)=n_1(ν) for m≤8 (148 cases), with ν^top=φ(ω_k) the unique minimizer. S1-4's description of C-2 (characteristic 0, and almost all p only) is accurate. I did not re-verify Chen–Yi's own proofs.

Re-derivation X1.5 (holds): I re-derived A5-7. The slices S_{d,c} are finite; Lemma 3 keeps the support inside the slice and above b in dominance; the central shift sends b'' to b''+2c; Lemma 2 makes the diagonal entry ≥1; the downward induction works inside each finite slice (the per-b choice c=⌊b_m/2⌋ also stays in the slice); and the SL corollary follows by the degree-0 coset bijection and Pf=1. A5-7 does not use the false table entries, and the S_{4,0} matrix is lower triangular with nonzero diagonal (checked at q=2, 3, 5). Its verdicts are right: A5-7 holds as stated, and A4-13 holds with its symplectic cells updated. 'Under A4-6's hypotheses' correctly covers D0–D4The standing inputs of the sheaf–function dictionary over F̄_q, p ≠ 2: D0 Chen–Yi's orbit geometry; D1 traces of Frobenius and the perverse t-structure; D2 decomposition of Satake objects into shifted IC sheaves; D3 Lang's theorem; D4 unitriangularity of Satake traces; D5 comparison of F̄_q with C. and q odd.

Re-derivation X1.6 (holds): I checked every path from the errors to the inputs. A7-6's table matches my enumeration (including T_(1,1,1,-1): 0 at ϖJ and q(q+1) at J''). The text of A7-19 (item 6) contains the σ one-line reduction. The text of A7-25 (item 3) says 'the table for m=3 was recomputed', which overstates what A7-22 did (two rows). A7-32's use of Prop. 64 concerns E6/F4 with E6 simply connected (families/e6-f4.html; Chen–Yi Example 88), so it does not rest on A7-11. The A1-9 verdict is right for this cluster only; S1-6 says correctly that A1-9's other error-graded defects (the false blocked-route remark and the stale cells) are outside it. All four verdicts are right.