.site-header{
  position:sticky; top:0;
  background:rgba(255,255,255,.92);
  z-index: 1000;
  backdrop-filter:blur(10px);
  border-bottom:1px solid var(--line);
}

.site-header .container{
  display:flex; align-items:center; justify-content:space-between;
  padding:14px 18px;
}

.abstract {
  font-weight:700;
}

.brand{
  font-family:var(--ui);
  font-weight:700;
  text-decoration:none;
  color:var(--fg);
}

/* Navigation bar */
.nav a{
  font-family:var(--ui);
  text-decoration:none;
  color:var(--muted);
  margin-left:14px;
}

.nav a:hover{ color:var(--fg); }

.nav {
  display: flex;
  gap: 1.5rem;
}

.nav-item {
  position: relative;
  display: inline-block; /* important: makes the hover area stable */
}

.submenu {
  display: none;
  position: absolute;
  top: calc(100% - 5px); /* keep it flush; no gap */
  left: -12px;
  min-width: 220px;
  background: #fff;
  border: 1px solid #ddd;
  padding: 0.4rem 0;
  z-index: 1000;
  box-shadow: 0 6px 18px rgba(0,0,0,0.2);
}

.submenu li {
  list-style: none;
}

.submenu a {
  display: block;
  padding: 0.4rem 0.8rem;
  white-space: nowrap;
}

.submenu::before {
  content: "";
  position: absolute;
  left: 0;
  right: 0;
  top: -20px;
  height: 20px;
}

.has-submenu > a::after {
  content: " ↓";
  font-size: 0.8em;
}

.has-submenu:hover .submenu {
  display: block;
}

.has-submenu:focus-within .submenu {
  display: block;
}

.page-title.has-external{
  display: flex;
  align-items: center;
  gap: .6rem;
}


.page-navigation {
  display: grid;
  grid-template-columns: 1fr 1fr;
  margin: 8px 0 0 0;
}

.nav-col {
  display: flex;
  flex-direction: column;
  gap: 0.5rem;
}

.nav-left {
  align-items: flex-start;
  text-align: left;
}

.nav-right {
  align-items: flex-end;
  text-align: right;
}

.nav-link {
  text-decoration: none;
  color: var(--text-muted);
}

.nav-link:hover {
  opacity: 1;
  text-decoration: underline;
}


.page-title-text{
  flex: 1;
}

.external-icon img{
  width: 32px;
  height: 32px;
  object-fit: contain;
  vertical-align: middle;
  opacity: .75;
}

.external-icon:hover img{
  opacity: 1;
}

.page{ padding:16px 0 16px; }

/* Footer */
.site-footer .container {
  display: flex;
  align-items: center;
  gap: 1rem;
}

.site-footer .container .kofi-widget {
  margin-left: auto;
}

.site-footer{
  border-top:1px solid var(--line);
  background:rgba(255,255,255,.92);
  margin-top:36px;
  padding:22px 0;
  color:var(--muted);
  font-family:var(--ui);
  font-size:0.9rem;
}