.brand-logo {
  display: block;
  position: fixed;
  left: 9px;
  top: 6px;
  z-index: 80;
  width: 114px;
  height: 114px;
  border-radius: 50%;
  object-fit: contain;
}

.presentation-brand-logo {
  position: fixed;
  left: 9px;
  top: 6px;
  z-index: 80;
  width: 114px;
  height: 114px;
  border-radius: 50%;
  pointer-events: none;
  user-select: none;
  filter: drop-shadow(0 7px 18px rgba(0,0,0,.34));
}
.presentation-brand-logo::before,.presentation-brand-logo::after {
  content:"";
  position:absolute;
  z-index:2;
  border-radius:50%;
  border:1px dashed rgba(217,170,60,.29);
}
.presentation-brand-logo::before { inset:9%; }
.presentation-brand-logo::after { inset:21%; border-color:rgba(49,216,210,.24); }
.presentation-brand-logo .presentation-logo-image {
  position:absolute;
  left:11%;
  top:11%;
  z-index:1;
  width:78%;
  height:78%;
  border-radius:50%;
  object-fit:cover;
}
.presentation-brand-logo .presentation-logo-nineteen {
  position:absolute;
  left:50%;
  top:69%;
  z-index:3;
  display:grid;
  place-items:center;
  width:15%;
  aspect-ratio:1.08;
  transform:translate(-50%,-50%);
  border-radius:50%;
  background:#06142d;
  color:#f5d77f;
  font:800 18px/1 Georgia,serif;
  text-shadow:0 0 6px rgba(245,215,127,.52);
  animation:presentationLogoPulse 19s ease-in-out infinite;
}
.presentation-brand-logo .presentation-logo-lightning {
  position:absolute;
  inset:0;
  z-index:4;
  width:100%;
  height:100%;
  overflow:visible;
}
.presentation-brand-logo .presentation-logo-bolt {
  fill:none;
  stroke-linecap:round;
  stroke-linejoin:round;
  stroke-dasharray:1;
  stroke-dashoffset:1;
  animation:presentationLightning 1.45s ease-out forwards;
  filter:drop-shadow(0 0 1.2px currentColor) drop-shadow(0 0 5px currentColor);
}
.presentation-brand-logo .presentation-logo-orbit {
  position:absolute;
  inset:3%;
  z-index:5;
  animation:presentationLogoSpin 19s linear infinite;
}
.presentation-brand-logo .presentation-logo-orbit i {
  position:absolute;
  left:50%;
  top:-6px;
  width:14px;
  height:14px;
  border-radius:50%;
  background:#31d8d2;
  box-shadow:0 0 24px #31d8d2;
}

/* Presentation-wide collision guard: numbers and operators always own
   separate layout space, including while values are animating. */
.air-sum {
  max-width: 100%;
  column-gap: clamp(9px, 2.2vw, 14px) !important;
  flex-wrap: nowrap;
}

.air-sum .air-slot {
  box-sizing: content-box;
  width: auto !important;
  min-width: max(1.35em, 34px) !important;
  padding-inline: clamp(2px, .65vw, 5px) !important;
  flex: 0 0 auto;
  white-space: nowrap;
}

.air-sum .air-sign {
  display: inline-flex;
  min-width: .9em;
  padding-inline: clamp(2px, .55vw, 4px);
  align-items: center;
  justify-content: center;
  flex: 0 0 auto;
  line-height: 1;
  white-space: nowrap;
}

.division-line > *,
.multiple-proof > *,
.sum-row > *,
.sum-line > * {
  flex-shrink: 0;
}

.division-line,
.multiple-proof {
  column-gap: clamp(5px, 1.15vw, 9px);
}
@keyframes presentationLogoSpin { to { transform:rotate(360deg); } }
@keyframes presentationLightning { 0%{opacity:0;stroke-dashoffset:1}8%{opacity:1;stroke-dashoffset:0}20%{opacity:.18}31%{opacity:1}45%{opacity:.12}58%{opacity:.92}100%{opacity:0;stroke-dashoffset:0} }
@keyframes presentationLogoPulse { 0%,90%,100%{color:#f5d77f;text-shadow:0 0 6px rgba(245,215,127,.52);filter:brightness(1)}95%{color:#43fff6;text-shadow:0 0 7px #31d8d2,0 0 15px #31d8d2,0 0 25px rgba(49,216,210,.9);filter:brightness(1.7)} }

.presentation-nav-hints {
  position: fixed;
  inset: 54px 0 16px;
  z-index: 24;
  pointer-events: none;
  opacity: 0;
  visibility: hidden;
  transition: opacity .35s ease, visibility .35s ease;
  font-family: Aptos, "Segoe UI", Arial, sans-serif;
}

.presentation-nav-hints.is-visible {
  opacity: 1;
  visibility: visible;
}

.presentation-nav-zone {
  position: absolute;
  top: 0;
  bottom: 0;
  transition: background-color .18s ease, box-shadow .18s ease;
}

.presentation-nav-zone::after {
  content: attr(data-label);
  position: absolute;
  bottom: 18px;
  padding: 5px 10px;
  border: 1px solid rgba(255,255,255,.07);
  border-radius: 999px;
  color: rgba(245,241,232,.4);
  background: rgba(5,13,28,.24);
  font-size: clamp(9px,2vw,11px);
  font-weight: 800;
  letter-spacing: .08em;
  line-height: 1;
  text-transform: uppercase;
  white-space: nowrap;
}

.presentation-nav-zone.is-previous {
  left: 0;
  width: var(--previous-width, 50%);
  border-right: 1px solid rgba(242,214,117,.055);
  background: linear-gradient(90deg,rgba(242,214,117,.032),transparent 76%);
}

.presentation-nav-zone.is-previous::after {
  left: 14px;
}

.presentation-nav-zone.is-next {
  right: 0;
  width: calc(100% - var(--previous-width, 50%));
  background: linear-gradient(270deg,rgba(53,224,208,.032),transparent 76%);
}

.presentation-nav-zone.is-next::after {
  right: 14px;
}

.presentation-nav-hints.is-forward-only .presentation-nav-zone.is-next {
  left: 0;
  width: 100%;
}

.presentation-nav-hints[data-hover="previous"] .is-previous,
.presentation-nav-hints.is-pressed[data-hover="previous"] .is-previous {
  background: linear-gradient(90deg,rgba(242,214,117,.075),transparent 78%);
  box-shadow: inset 3px 0 rgba(242,214,117,.13);
}

.presentation-nav-hints[data-hover="next"] .is-next,
.presentation-nav-hints.is-pressed[data-hover="next"] .is-next {
  background: linear-gradient(270deg,rgba(53,224,208,.075),transparent 78%);
  box-shadow: inset -3px 0 rgba(53,224,208,.13);
}

@media (max-width: 520px) {
  .brand-logo,.presentation-brand-logo { left:6px; top:5px; }
  .presentation-nav-zone::after { bottom: 16px; padding: 4px 8px; }
  .presentation-nav-zone.is-previous::after { left: 8px; }
  .presentation-nav-zone.is-next::after { right: 8px; }
}

@media (prefers-reduced-motion: reduce) {
  .presentation-nav-hints,.presentation-nav-zone { transition: none; }
  .presentation-brand-logo .presentation-logo-orbit,.presentation-brand-logo .presentation-logo-nineteen { animation:none; }
  .presentation-brand-logo .presentation-logo-lightning { display:none; }
}