diff --git a/qma_coulomb_hardness_v2.txt b/qma_coulomb_hardness_v2.txt
index bec9a4a..bc1ca73 100644
--- a/qma_coulomb_hardness_v2.txt
+++ b/qma_coulomb_hardness_v2.txt
@@ -16,11 +16,11 @@ What makes the statement sharp: nuclei are genuine point charges of charge one,
 
 Schuch-Verstraete (2009) proved QMA-completeness for a Hubbard model with local magnetic fields and gave a continuum realization via designed scalar and spin-dependent potentials. O'Gorman, Irani, Whitfield, Fefferman (2022) proved QMA-completeness for electronic structure in a supplied finite orbital basis, which fixes the Hilbert space in advance. Cubitt, Montanaro, Piddock (2019) proved QMA-hardness of the signed exchange problem on finite square-lattice graphs, providing the starting point. Each relaxation is removed at once, giving the free continuum with real unit point nuclei from the same signed-exchange source.
 
-Schuch, N. and Verstraete, F., "Computational complexity of interacting electrons and fundamental limitations of density functional theory", Nature Physics 5 (2009), 732-735. local: 0712.0483.pdf
+Schuch, N. and Verstraete, F., "Computational complexity of interacting electrons and fundamental limitations of density functional theory", Nature Physics 5 (2009), 732-735. local: ./pdf/0712.0483.pdf
 
 O'Gorman, B., Irani, S., Whitfield, J., and Fefferman, B., "Intractability of electronic structure in a fixed basis", PRX Quantum 3 (2022), 020322.
 
-Cubitt, T., Montanaro, A., and Piddock, S., "Universal quantum Hamiltonians", PNAS 115 (2018), 9497-9502. local: 1701.05182v4.pdf
+Cubitt, T., Montanaro, A., and Piddock, S., "Universal quantum Hamiltonians", PNAS 115 (2018), 9497-9502. local: ./pdf/1701.05182v4.pdf
 
 Electrons in R^3. Each carries a spin in C^2, so one electron lives in L^2(R^3) tensor C^2 and N electrons live in the N-fold antisymmetric tensor power
 
@@ -99,7 +99,7 @@ Couplings J_e can be positive or negative; the orbital construction yields only
 The mechanism is Piddock-Montanaro Lemma 5: eliminate excited states, keep second order. A quantitative form with fewer hypotheses than the standard Schrieffer-Wolff theorem (no first-order-block vanishing required) follows.
 
 Schrieffer, J. R. and Wolff, P. A., "Relation between the Anderson and Kondo Hamiltonians", Phys. Rev. 149 (1966), 491-492.
-Bravyi, S., DiVincenzo, D. P., and Loss, D., "Schrieffer-Wolff transformation for many-body systems", Ann. Physics 326 (2011), 2793-2823. local: 1105.0675.pdf
+Bravyi, S., DiVincenzo, D. P., and Loss, D., "Schrieffer-Wolff transformation for many-body systems", Ann. Physics 326 (2011), 2793-2823. local: ./pdf/1105.0675.pdf
 
 Lemma 1 (second-order bottom energy).
   Let A and B be self-adjoint operators on a finite-dimensional Hilbert
@@ -391,7 +391,7 @@ which is a smooth nonnegative bump supported in the unit disk, positive
 inside, and vanishing to order 16 at the boundary. Define
 
     phi = (-Delta_r + 1)^{-1} f ,   so  -Delta_r phi + phi = f,
-    varphi = phi / ||phi||_2 ,
+    phi = phi / ||phi||_2 ,
     W(r) = - f(r) / (2 phi(r)) .      (11)
 
 Then phi > 0, radial, exponentially decaying, and W is nonpositive and
@@ -400,7 +400,7 @@ compactly supported (inside the unit disk). Check the eigen-relation:
     -Delta phi + phi = f   =>   -Delta phi / 2 = (f - phi)/2 ,
     -Delta phi / 2 + W phi = (f - phi)/2 - f/2 = -phi/2 .
 
-So (-Delta_r/2 + W) phi = -phi/2, i.e. varphi is the ground mode with energy
+So (-Delta_r/2 + W) phi = -phi/2, i.e. phi is the ground mode with energy
 exactly -1/2. Derivatives of phi through order six are bounded. The
 representation
 
@@ -419,16 +419,16 @@ bound on the unit disk, so W and all its derivatives are bounded there, and
 W is zero outside.
 
 Isolated gap. The planar operator -Delta_r/2 + W has the unique ground state
-varphi and a fixed positive gap above it. Proof: the shifted quadratic form
+phi and a fixed positive gap above it. Proof: the shifted quadratic form
 on a test function u is int phi^2 |nabla(u/phi)|^2 / 2 (nonnegativity by
 closure and local positivity, and the kernel is exactly the multiples of
-phi). If a unit sequence perpendicular to varphi had shifted form tending
+phi). If a unit sequence perpendicular to phi had shifted form tending
 to zero, it would be bounded in H^1 and have a weakly and locally L^2
 convergent subsequence; by compact support of W the limit would have to lie
 in the kernel (multiples of phi), so the limit would be perpendicular to and
-parallel to varphi at once, hence zero; but then the 1/2 shift precludes the
+parallel to phi at once, hence zero; but then the 1/2 shift precludes the
 form values from tending to zero. So a fixed gap c_pl > 0 separates the
-ground mode varphi from the rest.
+ground mode phi from the rest.
 
 The vertical mode. For the z direction use the normalized Gaussian
 
@@ -441,7 +441,7 @@ gap omega above its ground mode.
 The three-dimensional mode. Per site i, centered at planar position u_i
 (from the contact-gadget layout, at scale D):
 
-    psi_i(y) = varphi(r - u_i) g(z),        e_* = -1/2 + omega/2,   (12)
+    psi_i(y) = phi(r - u_i) g(z),        e_* = -1/2 + omega/2,   (12)
 
 the energy of the (planar ground) tensor (vertical ground). psi_i is
 smooth, decaying exponentially at infinity with rate controlled by
@@ -621,12 +621,12 @@ v_{ij} = v(d). So the calibration of one link is a one-dimensional problem.
 
 The modes supply the hopping profile
 
-    T(d) = - int_{R^2} varphi(r) W(r) varphi(r - d e_1) dr
+    T(d) = - int_{R^2} phi(r) W(r) phi(r - d e_1) dr
          = ( 1 / (2 ||phi||_2^2) ) int f(r) phi(r - d e_1) dr .       (25)
 
 The second form follows from W = -f/(2 phi):
-    -varphi(r) W(r) = (phi(r)/||phi||) * f(r)/(2 phi(r)) = f(r)/(2 ||phi||).
-Multiply by varphi(r - de_1) = phi(r - de_1)/||phi|| and integrate:
+    -phi(r) W(r) = (phi(r)/||phi||) * f(r)/(2 phi(r)) = f(r)/(2 ||phi||).
+Multiply by phi(r - de_1) = phi(r - de_1)/||phi|| and integrate:
    T(d) = (1/(2 ||phi||^2)) int f(r) phi(r - d e_1) dr .
 This is manifestly positive (f, phi > 0), uniformly Lipschitz, and by the
 tail bound exp(-|r|) of phi it satisfies, for some absolute C,
@@ -728,7 +728,7 @@ superexchange calculation requires a one-body diagonal term -s_i/lambda on
 site i, where
 s_i = sum_{j!=i} v_{ij}. In the mode basis, the diagonal entry from
 -s_i/lambda must be supplied by a small deepening of well i. Because
-<psi_i, W_i psi_i> = int varphi^2 W < 0 (W nonpositive), increasing the
+<psi_i, W_i psi_i> = int phi^2 W < 0 (W nonpositive), increasing the
 depth of well i lowers its diagonal energy, so the required sign is correct
 and the size is tunable. Let
 
@@ -738,12 +738,12 @@ Fix a smooth cutoff zeta with 0 <= zeta <= 1, supported inside (-1,1),
 equal to 1 for |z| <= 1/2, with piecewise polynomial rational data. Then
 put
 
-    b_i = s_i / ( - int varphi^2 W ) >= 0 ,
+    b_i = s_i / ( - int phi^2 W ) >= 0 ,
     V_ell(r,z) = zeta(z/S) sum_i (1 + b_i/lambda) W_i(r) .       (35)
 
 The b_i are nonnegative and polynomially bounded independently of D,
 depending only on the geometry of the wells through v_{ij} and the fixed
-integral -int varphi^2 W. Hence 0 <= b_i/lambda < 1 at the scales. The
+integral -int phi^2 W. Hence 0 <= b_i/lambda < 1 at the scales. The
 functions V_ell are supported in disjoint vertical cylinders around the u_i,
 inside Omega.
 
@@ -860,7 +860,7 @@ bounded everywhere, L_c is at least the separable operator
 minus an error O(S^3/H) + O(p(n,D)/lambda) that is uniform in all states
 (as a form inequality). Call the first bracket (planar) A_pl and the second
 (vertical) A_v, each shifted so its ground energy is near zero:
-A_pl has ground energy -1/2 (mode varphi at each site) and A_v has ground
+A_pl has ground energy -1/2 (mode phi at each site) and A_v has ground
 energy omega/2 (mode g).
 
 Step 2: the planar gap. Use a quadratic partition of unity in the plane:
@@ -872,15 +872,15 @@ The IMS localization identity (product rule with kinetic coefficient 1/2)
 then costs O(1/D^2) in the form. On each site term use the isolated ground
 state and gap of -Delta_r/2 + W; on the exterior term use the
 free kinetic lower bound and the fact that no well sits on its support. With
-site cutoffs theta_i and varphi_i = varphi(.-u_i), the site term evaluated
+site cutoffs theta_i and phi_i = phi(.-u_i), the site term evaluated
 on theta_i u is at least
 
-    (-1/2 + c_1) ||theta_i u||^2 - c_1 |<theta_i varphi_i, u>|^2 ,   (42)
+    (-1/2 + c_1) ||theta_i u||^2 - c_1 |<theta_i phi_i, u>|^2 ,   (42)
 
 where c_1 > 0 may be taken below both the isolated gap and 1/2. The exterior
 term also absorbs its share of the (-1/2 + c_1) mass, because its support
-carries no well. The sum of rank-one operators |theta_i varphi_i><...| over
-i differs from P_r = sum_i |varphi_i><varphi_i| by at most
+carries no well. The sum of rank-one operators |theta_i phi_i><...| over
+i differs from P_r = sum_i |phi_i><phi_i| by at most
 O(m e^{-c' D}) + O(p(n,D) lambda^{-0.8}) (mode tails and Gram correction).
 Hence
 
@@ -888,7 +888,7 @@ Hence
 
 Simon, B., "Semiclassical analysis of low lying eigenvalues. I,
 non-degenerate minima: asymptotic expansions", Ann. Inst. H. Poincare A
-38 (1983), 295-308. local: AIHPA_1983__38_3_295_0.pdf
+38 (1983), 295-308. local: ./pdf/AIHPA_1983__38_3_295_0.pdf
 
 Step 3: the vertical gap. Localize the z problem with an inner cutoff equal
 to 1 on |z| <= S/2 (supported in |z| <= S) and an exterior function. On the
@@ -951,7 +951,7 @@ background and cutoff errors already bounded in the one-particle-gap step, from
     ( sum_{k != j} W_k  +  lambda^{-1} sum_k b_k W_k )  psi_j .        (48)
 
 Row j (diagonal). The depth-deepening b-term contributes diagonally as
-follows: with I = <psi_j, W_j psi_j> = int varphi^2 W < 0, the j-th piece
+follows: with I = <psi_j, W_j psi_j> = int phi^2 W < 0, the j-th piece
 of
 lambda^{-1} sum_k b_k W_k on psi_j is lambda^{-1} b_j I = lambda^{-1}
 ( s_j / (-I) ) I = - s_j / lambda. Since s_j = sum_{i != j} v_{ij}, this is