/* Figure 2. Weak contacts add: n contacts of 3° in one window, multiplied as matrices, against one contact of the summed angle.
   Every class is prefixed cat2- and every token is scoped to the figure. */
.cat2 {
  --k-paper: var(--cat-paper, #faf8f3); --k-ink: var(--cat-ink, #1d1d1b); --k-body: var(--cat-body, #2a2926); --k-soft: var(--cat-soft, #3c3a36);
  --k-hair: var(--cat-hair, #8a8a8a); --k-zero: var(--cat-zero, #6f6d68); --k-rule: var(--cat-rule, color-mix(in srgb, var(--k-ink) 16%, var(--k-paper)));
  --k-c: #009fe3; --k-m: #e6007e; --k-c-text: #0072b5; --k-m-text: #c4006b;
  --k-text: var(--cat-text, "InterVariable", "Inter", -apple-system, "Helvetica Neue", Arial, sans-serif);
  --k-display: var(--cat-display, "Inter Display", "InterVariable", "Inter", -apple-system, "Helvetica Neue", Arial, sans-serif);
  --k-mono: var(--cat-mono, "JetBrains Mono", ui-monospace, "SF Mono", Menlo, monospace);
  margin: 0; padding: clamp(.85rem, 2vw, 1.5rem); background: var(--k-paper); color: var(--k-body);
  border: 1px solid var(--k-ink); font-family: var(--k-text); font-weight: 420; line-height: 1.42;
  font-optical-sizing: auto; box-sizing: border-box; position: relative;
}
@media screen and (prefers-color-scheme: dark) {
  .cat2 { --k-paper: var(--cat-paper, #141413); --k-ink: var(--cat-ink, #faf8f3); --k-body: var(--cat-body, #e9e6df); --k-soft: var(--cat-soft, #c9c5bc);
    --k-c: #2bb3f0; --k-m: #ff3d9e; --k-c-text: #2bb3f0; --k-m-text: #ff6fb6; --k-zero: var(--cat-zero, #8a8a8a); }
}
.cat2 *, .cat2 *::before, .cat2 *::after { box-sizing: border-box; }
.cat2-label { margin: 0; font: 700 .72rem/1.3 var(--k-mono); letter-spacing: .14em; text-transform: uppercase; color: var(--k-soft); }
.cat2-head { display: flex; flex-wrap: wrap; justify-content: space-between; gap: .5rem 1rem; align-items: center;
  padding-bottom: .75rem; border-bottom: 1px solid var(--k-rule); }
.cat2-head .cat2-live { color: var(--k-ink); }
.cat2-live::before { content: ""; display: inline-block; width: .5rem; height: .5rem; margin-right: .45rem; background: var(--k-m); vertical-align: .05rem; }
.cat2[data-paused="true"] .cat2-live::before { background: transparent; border: 1px solid var(--k-ink); }
.cat2-btns { display: flex; flex-wrap: wrap; gap: .4rem; }
.cat2 button { appearance: none; border: 1px solid var(--k-ink); border-radius: 0; background: transparent; color: var(--k-ink); cursor: pointer;
  display: inline-flex; align-items: center; justify-content: center; min-height: 36px; padding: 0 .7rem;
  font: 700 .64rem/1 var(--k-mono); letter-spacing: .1em; text-transform: uppercase; }
.cat2 button:hover { background: color-mix(in srgb, var(--k-ink) 8%, transparent); }
.cat2 button:focus-visible { outline: 2px solid var(--k-ink); outline-offset: 2px; }
.cat2-grid { display: grid; grid-template-columns: minmax(0, .8fr) minmax(0, 1.5fr); gap: clamp(1rem, 2.6vw, 2.25rem); padding-top: 1rem; align-items: start; }
.cat2-stage { min-width: 0; }
.cat2-svg { display: block; width: 100%; max-width: 360px; height: auto; margin: 0 auto; overflow: visible; }
.cat2-bigsum { margin: .5rem 0 0; text-align: center; font-family: var(--k-display); font-weight: 860; font-size: clamp(1.6rem, 3vw, 2.2rem); line-height: 1; letter-spacing: -.04em; color: var(--k-ink); font-variant-numeric: tabular-nums; }
.cat2-svg text { font-family: var(--k-mono); font-weight: 700; font-size: 6px; letter-spacing: .1em; fill: var(--k-soft); }
.cat2-svg .t-ink { fill: var(--k-ink); } .cat2-svg .t-c { fill: var(--k-c-text); } .cat2-svg .t-m { fill: var(--k-m-text); }
.cat2-svg .t-num { font-family: var(--k-display); font-weight: 820; letter-spacing: -.02em; font-size: 15px; }
.cat2-svg .ax { stroke: var(--k-ink); stroke-width: .9; fill: none; }
.cat2-svg .arc { stroke: var(--k-hair); stroke-width: .8; fill: none; }
.cat2-svg .seg { stroke: var(--k-paper); stroke-width: .9; }
.cat2-svg .seg-a { fill: var(--k-ink); } .cat2-svg .seg-b { fill: var(--k-soft); }
.cat2-svg .vec { stroke: var(--k-ink); stroke-width: 1.6; }
.cat2-svg .vec-head { fill: var(--k-ink); }
.cat2-svg .leg-c { stroke: var(--k-c); stroke-width: 3; } .cat2-svg .leg-m { stroke: var(--k-m); stroke-width: 3; }
.cat2-svg .drop { stroke: var(--k-ink); stroke-width: .6; stroke-dasharray: 1.6 1.6; }
.cat2-tiles { margin: .15rem 0 .3rem; text-align: center; font: 400 .7rem/1.3 var(--k-mono); color: var(--k-soft); }
.cat2-dial { display: grid; grid-template-columns: minmax(0, 1fr) auto; gap: .1rem .6rem; align-items: center; max-width: 360px; margin: .4rem auto 0;
  font: 700 .66rem/1.3 var(--k-mono); letter-spacing: .12em; text-transform: uppercase; color: var(--k-soft); }
.cat2-dial output { font: 400 .9rem/1 var(--k-mono); letter-spacing: .02em; color: var(--k-ink); font-variant-numeric: tabular-nums; }
.cat2-dial input { grid-column: 1 / -1; width: 100%; margin: .2rem 0 0; accent-color: var(--k-ink); min-height: 32px; }
.cat2-panel { min-width: 0; display: flex; flex-direction: column; gap: .9rem; }
.cat2-say { margin: 0; font-size: 1.05rem; font-weight: 450; line-height: 1.32; color: var(--k-ink); max-width: 40rem; }
.cat2-say b { font-weight: 700; }
.cat2-mats { display: grid; grid-template-columns: minmax(0, 1fr) auto minmax(0, 1fr); gap: .5rem; align-items: center; }
.cat2-eq { font: 400 1.6rem/1 var(--k-display); color: var(--k-ink); text-align: center; }
.cat2-mat { min-width: 0; }
.cat2-mat .cat2-label { font-size: .62rem; margin-bottom: .35rem; }
.cat2-grid6 { display: grid; grid-template-columns: repeat(6, minmax(0, 1fr)); border-left: 2px solid var(--k-ink); border-right: 2px solid var(--k-ink); padding: .15rem .25rem; }
.cat2-grid6 span { padding: .3rem .1rem; text-align: center; font: 400 .74rem/1.15 var(--k-mono); color: var(--k-zero); font-variant-numeric: tabular-nums; white-space: nowrap; overflow: hidden; }
.cat2-grid6 span.d { color: var(--k-c-text); font-weight: 700; } .cat2-grid6 span.x { color: var(--k-m-text); font-weight: 700; }
.cat2-form { margin: .35rem 0 0; font: 400 .74rem/1.35 var(--k-mono); color: var(--k-soft); }
.cat2-form b { color: var(--k-ink); font-weight: 700; }
.cat2-diff { margin: 0; font: 400 .76rem/1.4 var(--k-mono); color: var(--k-soft); border-top: 1px solid var(--k-rule); padding-top: .55rem; }
.cat2-diff b { color: var(--k-ink); }
.cat2-weights { display: grid; grid-template-columns: 1fr 1fr; gap: .8rem 1.2rem; border-top: 1px solid var(--k-ink); padding-top: .7rem; }
.cat2-w { min-width: 0; }
.cat2-w .cat2-label { color: var(--k-c-text); min-height: 2.6em; } .cat2-w.m .cat2-label { color: var(--k-m-text); }
.cat2-num { display: block; margin: .25rem 0 .1rem; font-family: var(--k-display); font-weight: 860; font-size: clamp(1.9rem, 3.4vw, 2.6rem); line-height: .9;
  letter-spacing: -.05em; color: var(--k-ink); font-variant-numeric: tabular-nums lining-nums; }
.cat2-sub { margin: 0; font: 400 .74rem/1.35 var(--k-mono); color: var(--k-soft); }
.cat2-fine { margin: .9rem 0 0; padding-top: .7rem; border-top: 1px solid var(--k-rule); font-size: .86rem; line-height: 1.4; color: var(--k-soft); max-width: 60rem; }
.cat2-sr { position: absolute; width: 1px; height: 1px; margin: -1px; padding: 0; overflow: hidden; clip: rect(0 0 0 0); white-space: nowrap; border: 0; }
@media (max-width: 860px) {
  .cat2-grid { grid-template-columns: minmax(0, 1fr); }
  .cat2-svg { max-width: 300px; }
  .cat2-svg text { font-size: 7.5px; }
  .cat2-mats { grid-template-columns: minmax(0, 1fr); }
  .cat2-eq { font-size: 1.2rem; }
}
@media (max-width: 420px) { .cat2-grid6 span { font-size: .64rem; padding: .28rem 0; } }
@media (prefers-reduced-motion: reduce) { .cat2 * { transition: none !important; animation: none !important; } }
@media (forced-colors: active) {
  .cat2 { forced-color-adjust: none; --k-paper: Canvas; --k-ink: CanvasText; --k-body: CanvasText; --k-soft: CanvasText; --k-hair: GrayText; --k-zero: GrayText;
    --k-c: Highlight; --k-m: LinkText; --k-c-text: CanvasText; --k-m-text: CanvasText; --k-rule: GrayText; }
}
@media print { .cat2 { --k-paper: #fff; --k-ink: #000; --k-body: #000; --k-soft: #222; --k-zero: #555; print-color-adjust: exact; -webkit-print-color-adjust: exact; } }
@media print {
  /* on paper a figure starts on the page that holds its head row and first block; its blocks are not split */
  .cat2-head { break-after: avoid; break-inside: avoid; }
  .cat2-grid { padding-top: 0; margin-top: .8rem; break-before: avoid; }
  .cat2-grid > *, .cat2-grid > * > * { break-inside: avoid; }
}