/* =========================
   Color Variables
   ========================= */
:root {
    --purple-dark: #6b2c91;
	--purple-light: #863fb0;
    --white: #fff;
    --light-grey: #ececed;
    --yellow-contrast: #ff9;
}

/* =========================
   Global
   ========================= */
body {
    background-color: var(--white);
    color: #2b2b2b;
    font-family: "Inter", system-ui, sans-serif;
}

/* =========================
   Header
   ========================= */
.site-header {
    position: relative;
    overflow: hidden;               /* keeps the background tidy */
    background-color: #863fb0;      /* fallback if image missing */
    border-bottom: 1px solid #ddd;
    padding: 1.2rem 0 0.8rem;       /* keeps header height as-is */
}

/* Tiled, 50% opacity background image */
.site-header::before {
    content: "";
    position: absolute;
    inset: 0;
    background-image: url("headerbackground.png");
    background-repeat: repeat;      /* seamless tiling */
    background-size: auto;          /* keep original tile size */
    opacity: 0.10;                   /* 15% opacity */
    z-index: 0;
}

/* Ensure header content sits above the background */
.site-header .container {dark
    position: relative;
    z-index: 1;
}

.site-title {
    font-family: "Source Serif 4", Georgia, serif;
    letter-spacing: 0.02em;
}

.site-title .caps {
    color: var(--white);
    font-weight: 700;
}

/* =========================
   Navbar
   ========================= */
.custom-navbar {
    background-color: var(--purple-dark);
}

.custom-navbar .nav-link {
    color: #e0dde6;
    padding: 0.75rem 1rem;
    position: relative;
}

.custom-navbar .nav-link:hover {
    color: var(--yellow-contrast);
}

/* Active tab */
.custom-navbar .nav-link.active {
    color: var(--white);
    font-weight: 600;
}

.custom-navbar .nav-link.active::after {
    content: "";
    position: absolute;
    bottom: 0.3rem;
    left: 15%;
    width: 70%;
    height: 3px;
    background-color: var(--white);
    border-radius: 2px;
}

/* Toggler */
.navbar-toggler {
    border-color: rgba(255, 255, 255, 0.4);
}

.navbar-toggler-icon {
    filter: invert(1);
}

/* =========================
   Content
   ========================= */

h1 {
    color: var(--yellow-contrast);
    font-family: "Inter", system-ui, sans-serif;
    font-weight: 100;              /* thin */
    line-height: 1.05;             /* tight but readable */

}

h2 {
    color: var(--purple-light);
    font-family: "Inter", system-ui, sans-serif;
    font-weight: 100;              /* thin */
    line-height: 1.05;             /* tight but readable */

    /* Responsive very-large size:
       roughly ~5 lines of body text on desktop */
    font-size: clamp(3.5rem, 8vw, 6rem);

    margin: 2.5rem 0 1.5rem;
}



 h3 {
    font-family: "Source Serif 4", Georgia, serif;
}

a {
    color: var(--purple-dark);
    text-decoration: underline;
    text-decoration-thickness: 1px;
    text-underline-offset: 2px;
}

a:hover,
a:focus {
    color: var(--yellow-contrast);
}

.abstract {
  border: 1px outset black;
  padding: 10px;
}

.abstract-toggle {
    background: none;
    border: none;
    padding: 0;

    color: var(--purple-dark);
    text-decoration: underline;
    text-decoration-thickness: 1px;
    text-underline-offset: 2px;

    font: inherit;
    cursor: pointer;
}

/* Hover / focus */
.abstract-toggle:hover,
.abstract-toggle:focus {
    color: var(--white);
    background: none;
    outline: none;
}

.hline {
    border: none;
    border-bottom: 2px solid var(--purple-dark);
    margin: 2rem 0;
}

.vcenter {rk
    display: flex;
    align-items: center;     /* vertical centering */
}

p.lead {
    font-weight: 400;
}

p.p-bord{border: 2px solid var(--purple-dark); padding: 1em;}