/* Part II extends the same Clarity layout and local fonts as Part I. */
html, body { max-width: 100%; overflow-x: clip; }
.hero { padding-bottom: 28px; }
.hero .title { max-width: 960px; font-size: 38px; line-height: 1.45; }
.hero .title .subtitle { display: inline-block; max-width: 820px; font-size: 28px; line-height: 1.45; margin-top: 10px; }
.contents { border-bottom: 1px solid #e9e9e9; gap: 10px 25px; padding-top: 20px; padding-bottom: 20px; }
#blog-main > section.container.blog.main { min-width: 0; padding-top: 34px; }
#blog-main h3 { margin-top: 22px; margin-bottom: 10px; font-size: 20px; font-weight: 500; }
#blog-main .post-purpose { margin: 22px 0 24px; padding: 4px 0 4px 18px; border-left: 3px solid #4279a3; background: transparent; }
#blog-main .dynamics-summary { margin: 18px 0 22px; padding: 14px 18px; border: 1px solid #d9e4ed; border-left: 3px solid #4279a3; border-radius: 4px; background: #f8fbfe; }
#blog-main .dynamics-summary p { margin: 0; font-size: 18px; line-height: 1.6; }
#blog-main .equation { width: 100%; max-width: 100%; box-sizing: border-box; padding: 6px 12px; margin: 8px auto; border: 0; border-radius: 0; background: transparent; font-size: 18px; overflow-x: auto; overscroll-behavior-inline: contain; }
#blog-main p:has(+ .equation) { margin-bottom: 8px; }
#blog-main .equation + p { margin-top: 8px; }
.equation .katex-display { margin: 0; padding: 2px 0; }
.equation .katex-display > .katex { white-space: nowrap; }
.katex { font-size: 1.05em; }
.equation .katex { font-size: 1.1em; }
.equation:focus-visible { outline: 2px solid #777; outline-offset: 3px; }
#blog-main details { margin: 22px 0; padding: 16px 22px; background: #fdfdfd; }
#blog-main details summary { font-size: 17px; line-height: 1.55; }
#blog-main details p { font-size: 17px; line-height: 1.65; }
#blog-main details .equation { font-size: 16px; }
#blog-main p.text:has(+ .pg19-figure) { margin-bottom: 8px; }
#blog-main .pg19-figure { max-width: 440px; margin: 8px auto 24px; }
.pg19-figure img { display: block; }
.pg19-figure a:focus-visible { outline: 2px solid #777; }
#blog-main .longbench-results { width: min(1040px, calc(100vw - 48px)); max-width: none; position: relative; left: 50%; transform: translateX(-50%); margin: 24px 0 12px; overflow-x: auto; scrollbar-width: thin; }
.longbench-results::-webkit-scrollbar { height: 6px; }
.longbench-results::-webkit-scrollbar-thumb { background: #bbb; border-radius: 3px; }
.longbench-results table { min-width: 900px; table-layout: fixed; font-variant-numeric: tabular-nums; }
.longbench-results caption { position: sticky; left: 0; width: min(1040px, calc(100vw - 48px)); }
#blog-main .longbench-results th, #blog-main .longbench-results td { padding: 10px 5px; font-size: 11px; text-align: center; }
#blog-main .longbench-results th:first-child { width: 108px; min-width: 108px; text-align: left; position: sticky; left: 0; z-index: 1; background: #fff; }
.longbench-results thead th { white-space: normal; overflow-wrap: anywhere; }
#blog-main .longbench-results tbody tr { background: #fff; }
.longbench-results tr > :last-child { font-weight: 600; border-left: 1px solid #d6d6d6; }
.table-wrapper caption { padding-bottom: 12px; }
#blog-main .dynamics-comparison { max-width: 820px; margin: 16px auto; }
.dynamics-comparison table { table-layout: fixed; }
#blog-main .dynamics-comparison table td, #blog-main .dynamics-comparison table th { text-align: left; padding: 8px 12px; font-family: Charter, Georgia, serif; font-size: 14px; line-height: 1.45; white-space: normal; overflow-wrap: anywhere; vertical-align: top; }
.dynamics-comparison th:first-child { width: 32%; min-width: 0; }
.dynamics-comparison caption { padding-bottom: 6px; }
.dynamics-comparison .katex { white-space: nowrap; }
.closing-thought { padding-top: 12px; }
#blog-main .resources { margin-top: 32px; }
.references { list-style: none; padding-left: 0; }
.references li { font-size: 16px; line-height: 1.65; margin: 0 0 14px; padding-left: 18px; text-indent: -18px; overflow-wrap: anywhere; }
.source-note { overflow-wrap: anywhere; }
.citation pre { margin: 0 0 12px; }
.citation pre code { margin: 0; padding: 18px 20px !important; border-radius: 4px; background: transparent !important; font: 13px/1.7 ui-monospace, SFMono-Regular, Consolas, monospace; font-size: 13px !important; color: var(--ink); white-space: pre-wrap; overflow-wrap: anywhere; }
/* A shared decay makes the difference in state trajectories visible. */
.state-demo { max-width: 680px; margin: 20px auto; padding: 18px; border: 1px solid #dce3e6; border-radius: 8px; background: #fff; }
.state-demo-heading { display: flex; align-items: baseline; justify-content: space-between; gap: 12px 20px; flex-wrap: wrap; }
#blog-main .state-demo h3 { margin: 0; font-size: 19px; line-height: 1.5; }
.state-demo-norm, .state-demo-time { font: 12px/1.5 Poppins, sans-serif; color: #52616a; font-variant-numeric: tabular-nums; }
.state-demo-norm > span { color: #222; font-weight: 600; }
.state-demo-intro { margin: 8px 0 14px; font-size: 16px; line-height: 1.5; }
.state-demo-panels { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); }
.state-demo-panel { min-width: 0; padding: 0 10px; text-align: center; }
.state-demo-panel + .state-demo-panel { border-left: 1px solid #e5eaed; }
.state-demo-decay { --state-color: #4279a3; }
.state-demo-oscillation { --state-color: #b96946; }
.state-demo-panel h4 { margin: 0; color: var(--state-color); font: 500 16px/1.5 Poppins, sans-serif; }
.state-demo-panel p { margin: 3px 0 8px; color: #60666b; font-size: 14px; line-height: 1.4; }
.state-demo-panel svg { display: block; width: 100%; height: auto; max-width: 240px; margin: 0 auto; overflow: visible; color: var(--state-color); }
.state-demo-guide { fill: none; stroke: #dce3e6; stroke-width: 1; stroke-dasharray: 3 5; }
.state-demo-axis { fill: none; stroke: #dce3e6; stroke-width: 1; }
.state-demo-trail { fill: none; stroke: currentColor; stroke-width: 2; opacity: 0.45; }
.state-demo-origin { fill: currentColor; }
.state-demo-arrow { fill: none; stroke: currentColor; stroke-width: 3; stroke-linecap: round; }
.state-demo-arrowhead { fill: currentColor; stroke: none; }
.state-demo-controls { margin-top: 14px; padding-top: 12px; border-top: 1px solid #e5eaed; }
.state-demo-controls[hidden] { display: none; }
.state-demo-actions { display: flex; align-items: center; flex-wrap: wrap; gap: 10px; }
.state-demo-actions button { min-width: 76px; min-height: 40px; padding: 8px 16px; border: 1px solid #cbd6dc; border-radius: 5px; background: #fff; color: #304b5b; font: 500 12px/1.5 Poppins, sans-serif; cursor: pointer; }
.state-demo-actions button:first-child { background: #304b5b; border-color: #304b5b; color: #fff; }
.state-demo-actions button:hover { border-color: #304b5b; box-shadow: 0 0 0 1px #304b5b; }
.state-demo-actions button:focus-visible { outline: 2px solid #4279a3; outline-offset: 3px; }
.state-demo-time { margin-left: auto; white-space: nowrap; }
.state-demo-sliders { display: grid; grid-template-columns: 1fr 1fr; gap: 18px; margin-top: 12px; }
.state-demo-sliders label { color: #304b5b; font-size: 12px; font-weight: 500; }
.state-demo-sliders output { font-size: 12px; }
.state-demo-sliders input { width: 100%; height: 22px; margin: 8px 0 0; accent-color: #4279a3; cursor: pointer; }
.state-demo .state-demo-hint { margin: 12px 0 0; color: #637078; font-size: 13px; line-height: 1.5; }
.state-demo figcaption { margin-top: 12px; font-size: 14px; font-style: italic; }
/* Two different target frequencies expose the limit of one oscillatory pair. */
.pair-demo { max-width: 820px; margin: 24px auto; padding: 22px; border: 1px solid #dce3e6; border-radius: 8px; background: #fff; }
#blog-main .pair-demo h3 { margin: 0; font-size: 19px; line-height: 1.5; }
.pair-demo-intro { margin: 8px 0 16px; font-size: 16px; line-height: 1.55; }
.pair-demo-controls { margin: 0 0 20px; }
.pair-demo-controls[hidden], .pair-demo-speed-controls[hidden] { display: none; }
.pair-demo-modes { display: flex; gap: 8px; flex-wrap: wrap; margin-bottom: 16px; }
.pair-demo button { min-height: 38px; padding: 8px 13px; border: 1px solid #cbd6dc; border-radius: 5px; background: #fff; color: #304b5b; font: 500 12px/1.5 Poppins, sans-serif; cursor: pointer; }
.pair-demo button[aria-pressed="true"] { background: #304b5b; border-color: #304b5b; color: #fff; }
.pair-demo button:hover { border-color: #304b5b; }
.pair-demo button:focus-visible, .pair-demo input:focus-visible { outline: 2px solid #4279a3; outline-offset: 3px; }
.pair-demo-speed-label { display: flex; justify-content: space-between; flex-wrap: wrap; gap: 6px 14px; font: 500 12px/1.5 Poppins, sans-serif; color: #304b5b; }
.pair-demo-speed-controls input { display: block; width: 100%; height: 24px; margin: 8px 0; accent-color: #4279a3; cursor: pointer; }
.pair-demo-presets { display: flex; gap: 8px; }
.pair-demo-presets button { min-height: 32px; padding: 5px 10px; }
.pair-demo-legend { display: flex; flex-wrap: wrap; gap: 8px 22px; margin-bottom: 16px; font: 12px/1.5 Poppins, sans-serif; color: #52616a; }
.pair-demo-legend span { display: inline-flex; align-items: center; gap: 7px; }
.pair-demo-swatch { width: 24px; border-top: 2px solid #7458b0; }
.pair-demo-swatch-b { border-top-color: #b96946; }
.pair-demo-swatch-readout { border-top: 2px dashed #4279a3; }
.pair-demo-plots { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); gap: 22px; }
.pair-demo-plot { min-width: 0; --target-color: #7458b0; }
.pair-demo-plot[data-signal="B"] { --target-color: #b96946; }
.pair-demo-plot-heading { display: flex; justify-content: space-between; flex-wrap: wrap; gap: 4px 10px; align-items: baseline; }
.pair-demo-plot h4 { margin: 0; color: var(--target-color); font: 500 13px/1.5 Poppins, sans-serif; }
.pair-demo-match { color: #4279a3; font: 11px/1.5 Poppins, sans-serif; }
.pair-demo-plot[data-matching="true"] .pair-demo-match { color: #42745c; }
.pair-demo-plot svg { display: block; width: 100%; height: auto; margin-top: 6px; }
.pair-demo-axis { fill: none; stroke: #dce3e6; stroke-width: 1; }
.pair-demo-zero { stroke-dasharray: 3 4; }
.pair-demo-target, .pair-demo-readout { fill: none; stroke-width: 2; stroke-linecap: round; stroke-linejoin: round; }
.pair-demo-target { stroke: var(--target-color); }
.pair-demo-readout { stroke: #4279a3; stroke-dasharray: 6 4; }
.pair-demo-plot svg path { vector-effect: non-scaling-stroke; }
.pair-demo-plot svg text { fill: #637078; font: 11px Poppins, sans-serif; }
#blog-main .pair-demo-status { margin: 12px 0 0; font-size: 15px; line-height: 1.5; color: #304b5b; }
.pair-demo figcaption { margin-top: 10px; font-size: 13px; }
/* Rows are coordinate systems. Columns compare no shift with cyclic shift. */
.transport-demo { max-width: 820px; margin: 24px auto; padding: 22px; border: 1px solid #dce3e6; border-radius: 8px; background: #fff; }
.transport-demo-heading { display: flex; align-items: baseline; justify-content: space-between; flex-wrap: wrap; gap: 8px 16px; }
#blog-main .transport-demo h3 { margin: 0; font-size: 19px; line-height: 1.5; }
.transport-demo-norm { font: 12px/1.5 Poppins, sans-serif; color: #52616a; font-variant-numeric: tabular-nums; }
.transport-demo-norm > span { font-weight: 600; color: #222; }
.transport-demo-intro { margin: 8px 0 16px; font-size: 16px; line-height: 1.55; }
.transport-demo-controls { margin: 0 0 16px; }
.transport-demo-controls[hidden] { display: none; }
.transport-demo-actions { display: flex; gap: 8px; }
.transport-demo button { min-height: 38px; padding: 8px 16px; border: 1px solid #cbd6dc; border-radius: 5px; background: #fff; color: #304b5b; font: 500 12px/1.5 Poppins, sans-serif; cursor: pointer; }
.transport-demo button:first-child { background: #304b5b; border-color: #304b5b; color: #fff; }
.transport-demo button:hover { border-color: #304b5b; }
.transport-demo button:focus-visible, .transport-demo input:focus-visible { outline: 2px solid #4279a3; outline-offset: 3px; }
.transport-demo-sliders { display: grid; grid-template-columns: 1fr 1fr; gap: 22px; margin-top: 12px; }
.transport-demo-sliders label { display: flex; align-items: baseline; justify-content: space-between; flex-wrap: wrap; gap: 4px 8px; color: #304b5b; font: 500 12px/1.5 Poppins, sans-serif; }
.transport-demo-sliders input { display: block; width: 100%; height: 24px; margin: 8px 0 0; accent-color: #4279a3; cursor: pointer; }
.transport-demo-grid { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); }
.transport-demo-panel { min-width: 0; padding: 12px; }
.transport-demo-panel:nth-child(even) { border-left: 1px solid #e5eaed; }
.transport-demo-panel:nth-child(n+3) { border-top: 1px solid #e5eaed; }
.transport-demo-panel h4 { display: flex; align-items: center; justify-content: center; min-height: 2.8em; margin: 0; text-align: center; color: #304b5b; font: 500 14px/1.4 Poppins, sans-serif; }
.transport-demo-panel svg { display: block; width: 100%; height: auto; max-width: 300px; margin: 0 auto; }
.transport-demo-panel svg text { fill: #637078; font: 12px Poppins, sans-serif; }
.transport-demo-axis { fill: none; stroke: #e5eaed; stroke-width: 1; }
.transport-demo-zero { stroke: #cbd6dc; }
.transport-demo-guide { fill: none; stroke: #cbd6dc; stroke-width: 1; stroke-dasharray: 3 4; }
.transport-demo-bar { fill: #526f87; }
.transport-demo-mode-1 { color: #4279a3; }
.transport-demo-mode-2 { color: #b96946; }
.transport-demo-trail { fill: none; stroke: currentColor; stroke-width: 1.5; opacity: 0.4; }
.transport-demo-vector { stroke: currentColor; stroke-width: 3; stroke-linecap: round; }
.transport-demo-endpoint { fill: currentColor; }
.transport-demo-mode-2 .transport-demo-vector, .transport-demo-mode-2 .transport-demo-trail { stroke-dasharray: 4 3; }
.transport-demo-mode-2 .transport-demo-vector { stroke-width: 2; }
.transport-demo-mode-2 .transport-demo-endpoint { fill: none; stroke: currentColor; stroke-width: 1.5; }
.transport-demo-origin { fill: #52616a; }
.transport-demo-panel svg path, .transport-demo-panel svg line, .transport-demo-guide { vector-effect: non-scaling-stroke; }
.transport-demo-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 8px 18px; margin-top: 12px; font: 12px/1.5 Poppins, sans-serif; color: #52616a; }
.transport-demo-legend span { display: inline-flex; align-items: center; gap: 6px; }
.transport-demo-swatch { width: 22px; border-top: 2px solid #4279a3; }
.transport-demo-swatch-2 { border-top: 2px dashed #b96946; }
.transport-demo figcaption { margin-top: 12px; font-size: 13px; }
@media (max-width: 700px) {
  .state-demo { padding: 14px 12px; }
  .state-demo-panels { grid-template-columns: 1fr; }
  .state-demo-panel { display: grid; grid-template-columns: 108px minmax(0, 1fr); align-items: center; gap: 4px; padding: 6px 0; text-align: left; }
  .state-demo-panel + .state-demo-panel { border-left: 0; border-top: 1px solid #e5eaed; }
  .state-demo-panel h4 { font-size: 14px; }
  .state-demo-panel p { font-size: 13px; }
  .state-demo-panel svg { max-width: 180px; }
  .state-demo-intro { margin-bottom: 8px; }
  .state-demo-sliders { gap: 14px; }
  .pair-demo { padding: 18px 16px; }
  .pair-demo-plots { grid-template-columns: 1fr; gap: 16px; }
  .pair-demo-legend { gap: 8px 16px; }
  .transport-demo { padding: 18px 12px; }
  .transport-demo-sliders { gap: 12px; }
  .transport-demo-panel { padding: 10px 6px; }
  .transport-demo-panel h4 { font-size: 12px; }
  .transport-demo-panel svg text { font-size: 18px; }
}
@media (max-width: 380px) {
  .state-demo-panel { grid-template-columns: 90px minmax(0, 1fr); }
  .state-demo-sliders { grid-template-columns: 1fr; }
}
@media (max-width: 600px) {
  .hero { padding-bottom: 24px; }
  .hero .title { font-size: 29px; }
  .hero .title .subtitle { font-size: 21px; margin-top: 9px; }
  .hero .info { margin-top: 26px; gap: 9px; }
  .hero .button { font-size: 12px; padding: 10px 13px; }
  .contents { gap: 10px 18px; }
  .contents a { font-size: 11px; }
  #blog-main h2 { font-size: 25px; line-height: 1.4; }
  #blog-main h3 { font-size: 19px; line-height: 1.5; }
  #blog-main .equation { font-size: 16px; padding: 6px 10px; }
  #blog-main .equation[tabindex="0"]::after { content: "↔ Scroll to read the full equation"; display: block; margin-top: 10px; text-align: left; color: #777; font: 10px/1.4 Poppins, sans-serif; }
  #blog-main details { padding: 14px; }
  #blog-main .longbench-results { width: calc(100vw - 40px); }
  .longbench-results caption { width: calc(100vw - 40px); }
  #blog-main .dynamics-comparison table td, #blog-main .dynamics-comparison table th { font-size: 13px; padding: 6px 8px; }
  .dynamics-comparison th:first-child { width: 36%; }
  .references li { font-size: 15px; }
  .citation pre code { padding: 14px !important; font-size: 12px !important; }
}
@media (max-width: 380px) {
  .dynamics-comparison th:first-child { width: 40%; }
}
@media print {
  .state-demo-controls { display: none; }
  .state-demo { break-inside: avoid; }
  .state-demo-panels { grid-template-columns: repeat(2, minmax(0, 1fr)); }
  .state-demo-panel { display: block; text-align: center; }
  .pair-demo-controls { display: none; }
  .pair-demo { break-inside: avoid; }
  .transport-demo-controls { display: none; }
  .transport-demo { break-inside: avoid; }
  .hero { padding: 20px 0; }
  #blog-main .equation { overflow: visible; font-size: 14px; }
  #blog-main .longbench-results { width: 100%; left: auto; transform: none; overflow: visible; }
  #blog-main .longbench-results table { min-width: 0; }
  .longbench-results caption { position: static; width: 100%; }
  #blog-main .longbench-results th, #blog-main .longbench-results td { padding: 5px 2px; font-size: 7px; }
  #blog-main .longbench-results th:first-child { position: static; width: 60px; min-width: 0; }
  #blog-main h2, #blog-main h3 { break-after: avoid; }
  details { break-inside: auto; }
}