diff --git a/singular_free_tangent_sheaf_v2.txt b/singular_free_tangent_sheaf_v2.txt
index e19f99d..84f0577 100644
--- a/singular_free_tangent_sheaf_v2.txt
+++ b/singular_free_tangent_sheaf_v2.txt
@@ -41,7 +41,7 @@ and Peternell (Publ. Math. IHES 114, 2011, 87-169), by Druel (Bull.
 London Math. Soc. 46, 2014, 827-835), and by Graf and Kovacs (Doc.
 Math. 19, 2014, 815-830).
 
-./gkkp-1003.5340-differential-forms-log-canonical.pdf
+./greb-kebekus-kovacs-peternell-2011-1003.2913-diff-forms-lc.pdf
 ./druel-1304.6000-log-canonical-spaces.pdf
 ./graf-kovacs-1301.7315-optimal-extension-1forms.pdf
 
@@ -174,7 +174,7 @@ isotropic precisely when q is a ramification point of F|_Gamma. On
 every two-dimensional quadratic space the polar form is x . y =
 (Q(x+y) - Q(x) - Q(y))/2, and x^2 abbreviates Q(x).
 
-The next lemma produces six vectors in H^0(Gamma, Phi)^* with
+A lemma produces six vectors in H^0(Gamma, Phi)^* with
 prescribed sum and normalization. If w = sum_j w_j and w_j^2 + w_j .
 w = 1 at each marked point, then
 
@@ -281,13 +281,11 @@ section s of Gamma + 4F on Sigma maps to
 with the normal differential first. This fixes the scalar in the
 canonical-root isomorphism for subsequent residue computations.
 
-The next lemma computes the section spaces that transfer from Sigma to
+A lemma computes the section spaces that transfer from Sigma to
 C and to Gamma. It uses the comparison theorem of Serre (Ann. Inst.
 Fourier 6, 1956, 1-42): algebraic and analytic section spaces of
 coherent sheaves on projective complex curves agree.
 
-./serre-1956-gaga.pdf
-
 Lemma (adjoint jets). For 0 <= j <= 3, put A_j = Gamma + (4-j)F =
 (6-j, 2) on Sigma and N_j = A_j|_Gamma = (8-j)F + Delta on Gamma.
 Restriction identifies H^0(Sigma, A_j) with H^0(C, K_C - jH) and
@@ -576,7 +574,7 @@ frames gm of O_Sigma(Gamma), fF of F, and m of M on Gamma with
   kappa = k(y, z) gm^2 fF^4,
   beta = b(z) m,   m^4 = gm^2 fF^4|_Gamma,
 
-so omega = dz on Gamma. Here k(0, z) = b(z)^4 and
+so omega = dz on Gamma, with k(0, z) = b(z)^4 and
 b'(0) k_y(0, 0) != 0. Put K(z) = k_y(0, z). Solving y = 0 on C gives
 the contact expansion
 
@@ -686,7 +684,7 @@ fourth root of a unit). Set
   a_j = xi / z_j,   fF_j = l_j^fr / a_j,   tau_j = (l_j^fr)^2 fF_j.
 
 These frame O_C(Z), H, and Lambda respectively. With r = xi u, the
-coefficient row of r in l_j^fr is z_j u, where u here denotes the
+coefficient row of r in l_j^fr is z_j u, where u denotes the
 coefficient row in fF_j. Let t_j be the fiber-linear function on
 L^{-1} corresponding to l_j^fr, giving compatible split coordinates
 (t_j, z_j). Let l_j in W^* be coefficient evaluation in tau_j. Since
@@ -1099,12 +1097,12 @@ frame (d_t, d_z), so matching them is matching modulo I^9 F. The
 determinant equation with G = 1 + O(t) gives
 v_1 /\ v_2 = t^4(1 + O(t)) E_t /\ d_z = t^5(1 + O(t)) d_t /\ d_z. []
 
-Analytic realization and Grauert contraction. The finite jets of
-the previous section live in overlapping charts, and are realized
+Analytic realization and Grauert contraction. The finite jets live
+in overlapping charts, and are realized
 on a single Hausdorff complex surface Y containing C; the vector
 fields are then lifted from their jets by a cohomology vanishing
 argument; and the curve C is contracted to a singular point.
-Throughout this section, powers of an ideal denote ordinary ideal
+Throughout, powers of an ideal denote ordinary ideal
 powers, and cohomology is analytic sheaf cohomology.
 
 Coherence of analytic structure and ideal sheaves, and the Hartogs
@@ -1112,8 +1110,6 @@ extension property for normal surfaces, are taken from Grauert and
 Remmert, Coherent Analytic Sheaves, Grundlehren 265 (Springer 1984),
 and from Demailly, Complex Analytic and Differential Geometry (2012).
 
-./demailly-2012-complex-analytic-differential-geometry.pdf
-
 Lemma (Hausdorff neighborhood). The overlap maps of the finite-jets
 proposition define, after shrinking their domains, a smooth Hausdorff
 complex surface Y containing C. Its conormal bundle is L, and its
@@ -1141,7 +1137,7 @@ finitely many flows. Shrinking successively gives their compositions
 on neighborhoods of the same compact annular bands. Denote the
 resulting inside-to-outside maps by Phi_j for 1 <= j <= 6.
 
-Here is a quotient construction that also verifies the separation
+A quotient construction also verifies the separation
 property. Choose mutually disjoint coordinate disks D_j about the
 six points, and in each radii
 
@@ -1216,7 +1212,7 @@ Restriction to C gives the exact sequence
 
   0 -> O_C -> F|_C -> T_C -> 0.
 
-Here the first map sends 1 to the class of the normal Euler field
+The first map sends 1 to the class of the normal Euler field
 t d_t, and the second is restriction of a tangent vector field to C.
 The Euler class is unchanged when the local equation of C is
 multiplied by a unit. The sequence is intrinsic; a splitting is
@@ -1282,7 +1278,8 @@ single exponent, and shrinking the representative makes
   I^{ar} subset J^r subset I^r  for r >= 1.
 
 The proper analytic direct-image theorem makes R^1 pi_* E coherent.
-The theorem on formal functions identifies its completed stalk with
+The theorem on formal functions (Grauert, Publ. Math. IHES 5, 1960,
+5-64) identifies its completed stalk with
 
   (R^1 pi_* E)_x completed = inverse limit over r of H^1(Y, E / J^r E).
 
@@ -1295,6 +1292,8 @@ zero completion implies that the stalk itself is zero, by Nakayama's
 lemma. Away from x the map pi is an isomorphism, so the same sheaf
 vanishes there. Thus R^1 pi_* E = 0.
 
+./grauert-1960-theorem-garbentheorie.pdf
+
 The sheaf pi_* E is also coherent. Cartan's theorem B on the Stein
 space X, plus the Leray spectral sequence for pi, gives
 H^1(Y, E) = 0. The cohomology sequence of
@@ -1382,6 +1381,8 @@ curves and rational singularities" (2001; arXiv:math/0109221), and
 Serre, "Un theoreme de dualite", Comment. Math. Helv. 29 (1955),
 9-26.
 
+./flenner-zaidenberg-2001-math0109221-rational-curves-singularities.pdf
+
 By the ordinary determinant formula, the pullback of omega^o is
 
   pi^* omega^o = t^{-5} u(t, z)^{-1} d_t /\ d_z.
@@ -1432,6 +1433,8 @@ local rings", Publ. Math. IHES 36 (1969), 23-58. The finite-
 determinacy statement is proved below, with fixed estimates and no
 complete-intersection hypothesis.
 
+./artin-1969-algebraic-approximation.pdf
+
 Put P = C[[x_1, ..., x_e]], n = (x_1, ..., x_e), I = (f_1, ...,
 f_s), R = P / I, where f = (f_1, ..., f_s) in n P^s is a row.
 Write m_R = n R, and let an overbar denote reduction modulo I. Choose
@@ -1775,8 +1778,6 @@ normal affine surface X smooth, contradicting the Main Theorem.
 The only remaining value of logarithmic Kodaira dimension for a
 surface is two. []
 
-./bgk-1403.5613-zariski-lipman-normal-surfaces.pdf
-
 Derivation blowups. For a finite A-module M of generic rank r, its
 blowup is universal among proper birational morphisms from
 integral varieties to X for which the pullback of M modulo torsion
@@ -1785,8 +1786,6 @@ Barajas, Chavez-Martinez, and Romano-Velazquez, "The blow-up of a
 singularity at the module of derivations" (2026;
 arXiv:2510.07607v2), section 1.6.
 
-./barajas-chavez-romano-2510.07607-blowup-derivations.pdf
-
 Corollary (derivation blowups). Starting with the singular
 surface X of the Main Theorem, every iteration of blowing up at
 the derivation module is isomorphic to X. The same holds if each
@@ -1808,8 +1807,6 @@ which exceeds the bound p_g - g - b <= 2 of Bergner and Graf
 (Forum Math. Sigma 8, 2020, paper e21). The surface is not log
 canonical.
 
-./bergner-graf-2020-lipman-zariski-genus-one-higher.pdf
-
 The surface X stands outside every positive result on the
 Lipman-Zariski conjecture for normal surfaces. Its tangent sheaf
 is free, but no frame can be made commuting at the singular point.
@@ -1822,11 +1819,6 @@ Kovacs, because its canonical discrepancy is -5, and it is not
 covered by the geometric-genus criteria of Graf or of Bergner and
 Graf, because p_g - g - b >= 12.
 
-./jorder-1311.5141-weak-lipman-zariski.pdf
-./gkkp-1003.5340-differential-forms-log-canonical.pdf
-./druel-1304.6000-log-canonical-spaces.pdf
-./graf-kovacs-1301.7315-optimal-extension-1forms.pdf
-
 Derivation blowups at the tangent module, and derivation blowups
 followed by normalization, leave X unchanged and do not resolve
 its singular point, so the Lipman-Zariski conjecture fails in
@@ -1834,4 +1826,3 @@ characteristic zero for normal surfaces, and the analogous question
 of Barajas, Chavez-Martinez, and Romano-Velazquez about derivation
 blowups has a negative answer in characteristic zero.
 
-./barajas-chavez-romano-2510.07607-blowup-derivations.pdf