diff --git a/min_uncut_hardness_v2.txt b/min_uncut_hardness_v2.txt
index 696d3dd..90bed8f 100644
--- a/min_uncut_hardness_v2.txt
+++ b/min_uncut_hardness_v2.txt
@@ -1,13 +1,13 @@
 For a finite undirected graph G = (V,E) and a subset S of V, uncut_G(S) counts edges with both endpoints in S or both endpoints outside S, that is, edges not crossing the cut between S and its complement. Set OPT_uncut(G) equal to the minimum of uncut_G(S) over all 2^|V| subsets. Both parts of a partition may be empty; only the edge count appears in the objective. Then OPT_uncut(G) is the smallest number of edges whose deletion leaves a bipartite spanning subgraph. Deleting the uncut edges of any minimizing S leaves G bipartite with bipartition (S, V minus S). Conversely, if an edge set D is deleted so that G minus D is bipartite, the proper two-coloring of G minus D yields a subset S with every edge of D uncut, so uncut_G(S) <= |D|. Taking minima on both sides identifies OPT_uncut(G) with the minimum edge-deletion-to-bipartite number.
 
 Deciding whether OPT_uncut(G) equals zero is two-coloring, hence in P. Computing OPT_uncut exactly is NP-hard, by reduction from Max-Cut. A randomized polynomial-time algorithm attains factor O((log |V|)^(1/2)).
-Agarwal, Charikar, Makarychev, Makarychev 2005, O(sqrt(log n)) approximation algorithms for Min UnCut, Min 2CNF deletion, and directed cut problems: ./acmm-2005.pdf
+Agarwal, Charikar, Makarychev, Makarychev 2005, O(sqrt(log n)) approximation algorithms for Min UnCut, Min 2CNF deletion, and directed cut problems: ./pdf/acmm-2005.pdf
 
 Four sources bound the achievable constant factor. Under the Unique Games Conjecture, the near-satisfiable Max-Cut gap of Khot, Kindler, Mossel, ODonnell yields arbitrarily large constant factors for weighted Min-UnCut. Unconditionally, Hastad, Huang, Manokaran, ODonnell, Wright ruled out every factor below 11/8 for the weighted minimum-deletion form of Max-Cut; Wiman improved to below 1.45685; Martinsson improved to below 73139148/49096883, approximately 1.48969, for the minimum weighted violated two-variable parity-equation problem. Replacing each equality or inequality constraint by a fresh path of length four or three, respectively, transfers that construction to weighted Min-UnCut: with fixed endpoint bits each path has minimum uncut weight zero when the constraint is satisfied and one when it is violated, so absolute cost is preserved up to a common integer denominator.
-Khot, Kindler, Mossel, ODonnell 2007, Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?: ./kkmo-2007.pdf
-Hastad, Huang, Manokaran, ODonnell, Wright 2017, Improved NP-inapproximability for 2-variable linear equations: ./hhmow-2017.pdf
-Wiman 2018, Improved inapproximability of Max-Cut through Min-Cut: ./wiman-2018.pdf
-Martinsson 2024, On the NP-hardness approximation curve for Max-2Lin(2): ./martinsson-2024.pdf
+Khot, Kindler, Mossel, ODonnell 2007, Optimal inapproximability results for MAX-CUT and other 2-variable CSPs?: ./pdf/kkmo-2007.pdf
+Hastad, Huang, Manokaran, ODonnell, Wright 2017, Improved NP-inapproximability for 2-variable linear equations: ./pdf/hhmow-2017.pdf
+Wiman 2018, Improved inapproximability of Max-Cut through Min-Cut: ./pdf/wiman-2018.pdf
+Martinsson 2024, On the NP-hardness approximation curve for Max-2Lin(2): ./pdf/martinsson-2024.pdf
 
 Theorem. Fix an integer K >= 2. There is a deterministic polynomial-time algorithm sending a 3SAT formula phi to a pair (G, k), where G is a simple finite undirected unweighted graph and k >= 1 is a positive integer coded in binary, such that (i) satisfiable phi gives OPT_uncut(G) <= k, and (ii) unsatisfiable phi gives OPT_uncut(G) > K k. For each fixed K the running time, the number of vertices and edges of G, and the number of bits of k are polynomial in the bit length of phi. Every constant is effective; the algorithm uses no advice, no oracle, no unproved hypothesis.
 
@@ -26,7 +26,7 @@ An affine space A over F_2 is a translate of a linear subspace. In coordinates A
 For a in A define ev_a: D(A) -> F_2 by ev_a(b) = b(a). Then ev_a is a frequency, ev_a(1) = 1, and a -> ev_a is a bijection from A to the set of odd frequencies. If p: A -> A' is affine, its pullback p^*: D(A') -> D(A) has dual (p^*)^*(ev_a) = ev_{p(a)}. Odd frequencies therefore index hidden labels, and Fourier data at odd frequencies is exactly label data.
 
 A folded bit proof on A is a function f from Boolean tables P: A -> {plus or minus 1} to {plus or minus 1} with f(-P) = -f(P). For a in A the evaluation proof f_a(P) = P(a) is folded. Every test is evaluated against arbitrary folded f. The evaluation encoding is the long code, and the condition f(-P) = -f(P) is the folding symmetry standard in PCP analysis.
-Bellare, Goldreich, Sudan 1998, Free bits, PCPs, and nonapproximability: ./bgs-1998.pdf
+Bellare, Goldreich, Sudan 1998, Free bits, PCPs, and nonapproximability: ./pdf/bgs-1998.pdf
 
 Fix integers n, m >= 2. Put X = [n]^m and N = |X|. Let R be the set of pairs (i, y) with i in [m] and y in [n]^m having the i-th coordinate deleted. Then |R| = M = m n^{m-1}. A face array B assigns to each row (i, y) an independent uniform affine function B^i_y in D(A), and sets B(x) = sum_{i=1}^m B^i_{x_{-i}} in D(A) for each x in X, with x_{-i} denoting x with coordinate i deleted. Thus B(x)(a) is a bit for each a in A.
 
@@ -43,14 +43,14 @@ Test 3 samples a codeword z in C and forces its entry to +1 in one table and to
 Write eps_j(f) for the failure probability of Test j under the joint law of (B, c, g, lambda). Let b_1, b_2, b_3, b_4 be positive rational budgets, set by the construction as functions of the parameters sigma, delta, eta, |C|. The folded proof f has cost at most J if eps_j(f) <= J b_j for j = 1, 2, 3 and similarly for the fourth test.
 
 Evaluation proofs. For every a in A the evaluation proof f_a satisfies eps_1 <= 2 sigma, eps_2 <= 2 delta + 2 eta, and eps_3 = |C|^{-1}. The first two bounds follow from the random-hyperplane sign identity of Goemans and Williamson: adding an independent centered Gaussian of standard deviation s to a standard Gaussian changes its sign with probability arctan(s)/pi, which is at most s. Under Test 1 the perturbation has standard deviation (sigma^2 + eta^2)^{1/2} <= 2 sigma; under Test 2 the row-resampling channel preserves the queried bit with probability at least 1 - 2 delta - 2 eta. Under Test 3 exactly one of the |C| codewords matches the query point, giving eps_3 = |C|^{-1}.
-Goemans, Williamson 1995, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming: ./gw95.pdf
+Goemans, Williamson 1995, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming: ./pdf/gw95.pdf
 
 Set b_1 = 2 sigma, b_2 = 2 delta + 2 eta, b_3 = |C|^{-1}. Evaluation proofs are the cost-1 calibration and every other folded proof pays at least as much, so a NO-case proof must cost more than J.
 
 Define the smoothed field F_B from R^X to R by F_B(c) = E_{g, lambda} f(P_{c + sigma g, eta lambda} circ B), and the gradient field h_x(B, c) = sqrt(N) partial_{c_x} F_B(c). Gaussian integration by parts gives
 h_x(B, c) = (sqrt N / sigma) E_{g, lambda} g_x f(P_{c + sigma g, eta lambda} circ B).
 The Fourier-Hermite expansion in c and the Gaussian integration-by-parts identity are standard tools of noise stability.
-Mossel, ODonnell, Oleszkiewicz 2010, Noise stability of functions with low influences: invariance and optimality: ./moo10.pdf
+Mossel, ODonnell, Oleszkiewicz 2010, Noise stability of functions with low influences: invariance and optimality: ./pdf/moo10.pdf
 Bessel inequality for the orthonormal family {g_x}_{x in X} in the joint Gaussian space of (g, lambda) gives, for every B, c and every x in X,
 |h_x(B, c)| <= sqrt N / sigma, and E_x |h_x(B, c)|^2 <= sigma^{-2}.
 
@@ -84,7 +84,7 @@ holds for every nonzero frequency, where k denotes the same codeword and x is an
 Localisation. Fix a subbox Y = product_{i=1}^m Y_i of X of side length ell (each Y_i a subset of [n] of size ell containing x_i). The low-degree field L_x depends on B only through rows whose coordinates lie in Y. Write L^{ij}_x for the part of L_x whose Hermite degree has I_x = 0 and whose row-degree distribution loads frequency components on rows B^i_{x_{-i}} and B^j_{x_{-j}} for some fixed pair i < j; write L^0_x for the part whose Hermite degree has I_x >= 1. These parts together account for all of L after fixing pairs (i, j) exhaustively if m is large. For each pair (i, j) and each point x in Y define the slice function V_x on D(A) by summing over frequency components with I_x = 0 and no other on-subbox rows in tables i and j; the equality V_x(b) = sum_{alpha: alpha(1) = 1} hat V_x(alpha) chi_alpha(b) recovers the one-row restriction after averaging over the free local row.
 
 Box Cauchy-Schwarz. For any real array v: Y -> R and any face multipliers a_j: Y_{-j} -> [-1, 1], the iterated Cauchy-Schwarz inequality gives |E_{u in Y} v(u) prod_j a_j(u_{-j})|^{2^m} <= E_{u^0, u^1} prod_{omega in {0,1}^m} v(u^omega), where u^omega is the interleaved point (u_i^{omega_i}). The inequality is the standard iterated Cauchy-Schwarz bound from hypergraph regularity theory.
-Gowers 2007, Hypergraph regularity and the multidimensional Szemeredi theorem: ./gowers-2007.pdf
+Gowers 2007, Hypergraph regularity and the multidimensional Szemeredi theorem: ./pdf/gowers-2007.pdf
 Applying this to v = V and then conditioning on the independent slice functions, the face multipliers drop out and each surviving cube of points has an expected fourth-moment product that can be evaluated with the same row functions on two independent cubes. The pair-correlation inequalities
 E d_Y(L^{ij}) <= 2 A_0 (m/ell)^{1/2^m} + sqrt(H (gamma + H^2/A_0)),
 E d_Y(L^0)    <= 2 A_0 (m/ell)^{1/2^m},
@@ -123,28 +123,28 @@ E d_X(L) <= E d_X(L^0) + sum_{i < j} E d_X(L^{ij}) < 1/(2T).
 This contradicts the first direction. The no-odd-coefficient hypothesis must fail: the event q_x >= theta holds with probability at least p at some class with i in [m] and x in Y. By the bijection between odd frequencies and labels, this gives an odd frequency of the one-row restriction of h of magnitude at least theta, which is the conclusion of inner decoding.
 
 From parity to a two-player game. Let E be a uniform list of M_0 parity equations x_{v_1} + x_{v_2} + x_{v_3} = tau in F_2 over variables x_j, with each entry j carrying an equation E^{(j)} that may repeat variable names. Hastad 2001, Theorem 5.4, proves that for every fixed rational zeta > 0 it is NP-hard to distinguish lists in which some assignment satisfies at least (1 - zeta) M_0 equations from lists in which no assignment satisfies more than (1/2 + zeta) M_0 equations. The base game soundness below uses the weaker consequence that for zeta <= 1/4 no assignment satisfies more than 3 M_0 / 4 equations in the NO case.
-Hastad 2001, Some optimal inapproximability results: ./hastad-2001.pdf
+Hastad 2001, Some optimal inapproximability results: ./pdf/hastad-2001.pdf
 
 The list is made uniform by replicating each entry a number of times proportional to Q times its weight, with Q large enough that satisfaction proportions change by at most epsilon; the NO-case bound persists up to 3/4 + epsilon. All constants are effective in zeta and Q.
 
 The outer game. Fix integers t >= t_0 >= 1. A first question is a tuple U = (E_1, ..., E_t) of t independent uniform list entries. Its label alphabet A_U = product_j A(E_j) is a nonempty affine space of dimension at most 2t (each A(E) is contained in F_2^3). The second question V, given U and a uniform size-t_0 subset H of [t], is a length-t tuple whose coordinate j is a variable question v(E_j, p_j) for a uniform p_j in [3] when j in H, and the full equation E_j when j not in H. Its label alphabet A_V = product_j A_{V,j} with A_{V,j} = F_2 for j in H and A_{V,j} = A(E_j) for j not in H. Acceptance is coordinatewise: the pullback pi_e: A_U -> A_V sends (a_j) to (a_j[p_j])_{j in H} and to a_j for j not in H, and the two labels must agree under pi_e. The use of smooth equation-variable games with affine hints for decoding is standard in the literature.
-Khot, Safra 2013, A two-prover one-round game with strong soundness: ./ks13.pdf
+Khot, Safra 2013, A two-prover one-round game with strong soundness: ./pdf/ks13.pdf
 
 Base game soundness. Take t = 1 and H = {1}. The single-coordinate game accepts when the first-player label a at its queried position p equals the second-player bit b. Supposing no assignment satisfies more than 3/4 of the equations, the ordinary game has value at most 11/12.
 
 Fix any deterministic second-player strategy; the bit for each variable name defines a global assignment. On at least 1/4 of the sampled entries this assignment violates the equation, and for every valid first-player answer to such an entry a uniform position p in [3] detects disagreement with probability at least 1/3. So the failure probability is at least (1/4)(1/3) = 1/12, giving value at most 11/12.
 
 Iterated repetition. Raz amplification gives an effective universal constant c < 1 such that the ordinary r-fold repetition of the base game has value at most c^r for every r >= 0.
-Raz 1998, A parallel repetition theorem: ./raz-1998.pdf
-Holenstein 2009, Parallel repetition: simplifications and the no-signaling case: ./holenstein-2009.pdf
+Raz 1998, A parallel repetition theorem: ./pdf/raz-1998.pdf
+Holenstein 2009, Parallel repetition: simplifications and the no-signaling case: ./pdf/holenstein-2009.pdf
 
 Hint soundness. Suppose both players receive q affine forms L_1, ..., L_q sampled uniformly from D(A_V). The value of the hinted game is at most
 (1 - 2^{-q} (1 - c))^{t_0}.
 Call a hidden coordinate j in H active if every coefficient beta_{l, j} of z_j in every L_l vanishes. Independence gives |Active| distributed as Binomial(t_0, 2^{-q}) conditional on t_0 and q. For fixed active set, the active coordinates in H are independent of all inactive coordinates and sample fresh equation-position pairs. Restricted to active coordinates the q hints have zero coefficient, so the game value there is at most c^{|Active|}. Averaging over the binomial distribution gives
 E c^{|Active|} = (1 - 2^{-q} (1 - c))^{t_0}.
 Choosing t_0 large makes this value below any prescribed positive threshold s.
-Khot, Minzer, Safra 2017, On independent sets, 2-to-2 games and Grassmann graphs: ./kms17.pdf
-Dinur, Khot, Kindler, Minzer, Safra 2025, Towards a proof of the 2-to-1 games conjecture: ./dkkms-2025.pdf
+Khot, Minzer, Safra 2017, On independent sets, 2-to-2 games and Grassmann graphs: ./pdf/kms17.pdf
+Dinur, Khot, Kindler, Minzer, Safra 2025, Towards a proof of the 2-to-1 games conjecture: ./pdf/dkkms-2025.pdf
 
 Joint smoothness of pulled-back hints. Beyond soundness of the hinted game, the decoding analysis needs the joint distribution of the pulled-back hints to be close to uniform.