feat(examples): open the carousel with the social card, and correct its licence

The carousel now leads with SocialCardExample's artwork rather than restating
it, so the post opens on the picture that already explains the premise.

That drove the page size. The card is a 1280pt canvas with absolute
coordinates, and the DSL has no node-level scale outside images, so scaling it
would have meant rebuilding it against a width. Widening the carousel to
1280x1600 keeps the frame at 4:5 and carries the card at native size instead.
Everything else was drawn against a 1080-wide page, so the three type helpers
multiply by the ratio and the slides keep their proportions.

Its own page takes a zero margin so the artwork reaches the edges, and a spacer
centres it in the taller frame; both share the night background, so the space
above and below reads as letterboxing rather than a gap.

The closing slide said APACHE-2.0. The repository is MIT - LICENSE, the README
badge and the card's own footer all agree - so the carousel was contradicting
the slide it now opens with. The Maven coordinate also broke mid-artifact at
that width and is set as groupId over artifactId.

Author: DemchaAV

examples/src/main/java/com/demcha/examples/flagships/LinkedInCarouselExample.java

@@ -2,6 +2,7 @@
 
 import com.demcha.compose.GraphCompose;
 import com.demcha.compose.document.api.DocumentSession;
+import com.demcha.compose.document.api.PageMarginRule;
 import com.demcha.compose.document.chart.AxisSpec;
 import com.demcha.compose.document.chart.ChartData;
 import com.demcha.compose.document.chart.ChartSize;
@@ -25,6 +26,7 @@
 import com.demcha.examples.support.ExampleVersion;
 
 import java.nio.file.Path;
+import java.util.List;
 import java.util.Locale;
 
 /**
@@ -46,12 +48,23 @@
  */
 public final class LinkedInCarouselExample {
 
-    /** LinkedIn renders document posts in a 4:5 frame; this is that frame. */
-    public static final double PAGE_WIDTH = 1080;
-    /** LinkedIn renders document posts in a 4:5 frame; this is that frame. */
-    public static final double PAGE_HEIGHT = 1350;
+    /**
+     * LinkedIn renders document posts in a 4:5 frame; this is that frame, sized
+     * so the opening slide can carry {@link SocialCardExample}'s card at its
+     * native {@value SocialCardExample#CARD_WIDTH}pt width without scaling.
+     */
+    public static final double PAGE_WIDTH = SocialCardExample.CARD_WIDTH;
+    /** Four-by-five against {@link #PAGE_WIDTH}. */
+    public static final double PAGE_HEIGHT = PAGE_WIDTH * 5 / 4;
+
+    /**
+     * Everything below was drawn against a 1080-wide page. Rather than restate
+     * every size, the type helpers scale by this ratio, so the slides keep their
+     * proportions on the wider frame.
+     */
+    private static final double SCALE = PAGE_WIDTH / 1080.0;
 
-    private static final double MARGIN = 80;
+    private static final double MARGIN = 80 * SCALE;
     private static final double CONTENT_WIDTH = PAGE_WIDTH - 2 * MARGIN;
 
     private static final DocumentColor NIGHT = DocumentColor.rgb(9, 12, 27);
@@ -66,7 +79,7 @@ public final class LinkedInCarouselExample {
     private static final DocumentColor AMBER = DocumentColor.rgb(230, 160, 68);
 
     /** Uniform padding inside every card, as passed to {@code softPanel}. */
-    private static final double CARD_PAD = 30;
+    private static final double CARD_PAD = 30 * SCALE;
 
     /**
      * Width available inside a card.
@@ -173,9 +186,17 @@ static void compose(DocumentSession document) {
                 .producer("GraphCompose")
                 .build());
 
+        // The opening slide is the social card at native size. Its own page gets
+        // no margin so the artwork reaches the edges, and a spacer centres it in
+        // the taller frame - both share the same night background, so the space above
+        // and below reads as deliberate letterboxing rather than a gap.
+        document.pageMargins(List.of(PageMarginRule.page(1, DocumentInsets.zero())));
+
         document.pageFlow()
                 .name("Carousel")
                 .spacing(0)
+                .addSection("Card", LinkedInCarouselExample::cardSlide)
+                .addPageBreak(b -> b.name("ToCover"))
                 .addSection("Cover", LinkedInCarouselExample::cover)
                 .addPageBreak(b -> b.name("ToBackend"))
                 .addSection("Backend", LinkedInCarouselExample::backendSlide)
@@ -190,15 +211,22 @@ static void compose(DocumentSession document) {
 
     // ───────────────────────── slides ─────────────────────────
 
+    private static void cardSlide(SectionBuilder slide) {
+        slide.spacing(0);
+        slide.addSpacer(sp -> sp.width(PAGE_WIDTH)
+                .height((PAGE_HEIGHT - SocialCardExample.CARD_HEIGHT) / 2));
+        slide.add(SocialCardExample.scene());
+    }
+
     private static void cover(SectionBuilder slide) {
-        slide.spacing(56);
+        slide.spacing(56 * SCALE);
         eyebrow(slide, "GRAPHCOMPOSE " + ExampleVersion.currentLine(), VIOLET_LIGHT);
         slide.addParagraph(p -> p
                 .text("One composition.\nTwo formats.")
                 .textStyle(headline(132))
                 .lineSpacing(1.03)
                 .margin(DocumentInsets.zero()));
-        slide.addShape(shape -> shape.size(160, 7).fillColor(VIOLET)
+        slide.addShape(shape -> shape.size(160 * SCALE, 7 * SCALE).fillColor(VIOLET)
                 .margin(DocumentInsets.symmetric(14, 0)));
         slide.addParagraph(p -> p
                 .text("A Java DSL describes the document. The engine resolves layout "
@@ -219,7 +247,7 @@ private static void cover(SectionBuilder slide) {
     }
 
     private static void backendSlide(SectionBuilder slide) {
-        slide.spacing(30);
+        slide.spacing(30 * SCALE);
         eyebrow(slide, "WHAT " + ExampleVersion.currentLine() + " ADDS", MINT);
         slide.addParagraph(p -> p
                 .text("PowerPoint is a\nfirst-class backend.")
@@ -245,7 +273,7 @@ private static void backendSlide(SectionBuilder slide) {
     }
 
     private static void numbersSlide(SectionBuilder slide, EngineDeckData.BenchRun bench) {
-        slide.spacing(40);
+        slide.spacing(40 * SCALE);
         eyebrow(slide, "MEASURED, NOT CLAIMED", AMBER);
         slide.addParagraph(p -> p
                 .text("A " + TIER + "-row report")
@@ -279,7 +307,7 @@ private static void numbersSlide(SectionBuilder slide, EngineDeckData.BenchRun b
     }
 
     private static void guaranteesSlide(SectionBuilder slide) {
-        slide.spacing(30);
+        slide.spacing(30 * SCALE);
         eyebrow(slide, "HOW IT STAYS HONEST", VIOLET_LIGHT);
         slide.addParagraph(p -> p
                 .text("Guarantees you\ncan run.")
@@ -304,8 +332,8 @@ private static void guaranteesSlide(SectionBuilder slide) {
     }
 
     private static void closeSlide(SectionBuilder slide) {
-        slide.spacing(30);
-        eyebrow(slide, "OPEN SOURCE · APACHE-2.0", MINT);
+        slide.spacing(30 * SCALE);
+        eyebrow(slide, "OPEN SOURCE · MIT", MINT);
         slide.addParagraph(p -> p
                 .text("Try it.")
                 .textStyle(headline(132))
@@ -315,9 +343,15 @@ private static void closeSlide(SectionBuilder slide) {
                     .stroke(DocumentStroke.of(LINE, 1))
                     .spacing(4);
             card.addSpacer(sp -> sp.width(CARD_INNER).height(0));
+            // Split on the colon rather than set in one line: the coordinate is
+            // wider than the card at this size and broke mid-artifact.
+            card.addParagraph(p -> p
+                    .text("io.github.demchaav")
+                    .textStyle(mono(31, ON_DARK_MUTED))
+                    .margin(DocumentInsets.zero()));
             card.addParagraph(p -> p
-                    .text("io.github.demchaav:graph-compose-bundle")
-                    .textStyle(mono(37, ON_DARK))
+                    .text("graph-compose-bundle")
+                    .textStyle(mono(40, ON_DARK))
                     .margin(DocumentInsets.zero()));
             // Deliberately not the reactor version: this file renders from a
             // -SNAPSHOT tree, and printing that would advertise a coordinate that
@@ -372,7 +406,7 @@ private static void point(SectionBuilder slide, String title, DocumentColor acce
                     .text(title)
                     .textStyle(DocumentTextStyle.builder()
                             .fontName(FontName.HELVETICA_BOLD)
-                            .size(40)
+                            .size(40 * SCALE)
                             .color(ON_DARK)
                             .build())
                     .margin(DocumentInsets.zero()));
@@ -394,7 +428,7 @@ private static void formatChip(RowBuilder row, String name, String lane,
                     .text(name)
                     .textStyle(DocumentTextStyle.builder()
                             .fontName(FontName.HELVETICA_BOLD)
-                            .size(56)
+                            .size(56 * SCALE)
                             .color(accent)
                             .build())
                     .align(TextAlign.CENTER)
@@ -421,7 +455,7 @@ private static void ratio(RowBuilder row, String value, String label, DocumentCo
                     .text(value)
                     .textStyle(DocumentTextStyle.builder()
                             .fontName(FontName.HELVETICA_BOLD)
-                            .size(64)
+                            .size(64 * SCALE)
                             .color(accent)
                             .build())
                     .margin(DocumentInsets.zero()));
@@ -446,7 +480,7 @@ private static ChartSpec latencyChart(EngineDeckData.BenchRun bench) {
                 .showCategoryLabels(true)
                 .legend(LegendPosition.NONE)
                 .valueLabels(ValueLabelMode.OUTSIDE)
-                .size(ChartSize.fixedHeight(470))
+                .size(ChartSize.fixedHeight(470 * SCALE))
                 .build();
     }
 
@@ -479,19 +513,19 @@ private static String snapshotDate(EngineDeckData.BenchRun bench) {
     private static DocumentTextStyle headline(double size) {
         return DocumentTextStyle.builder()
                 .fontName(FontName.HELVETICA_BOLD)
-                .size(size)
+                .size(size * SCALE)
                 .color(ON_DARK)
                 .build();
     }
 
     private static DocumentTextStyle body(double size, DocumentColor color) {
-        return DocumentTextStyle.builder().size(size).color(color).build();
+        return DocumentTextStyle.builder().size(size * SCALE).color(color).build();
     }
 
     private static DocumentTextStyle mono(double size, DocumentColor color) {
         return DocumentTextStyle.builder()
                 .fontName(FontName.COURIER)
-                .size(size)
+                .size(size * SCALE)
                 .color(color)
                 .build();
     }

examples/src/main/java/com/demcha/examples/flagships/SocialCardExample.java

@@ -212,7 +212,16 @@ private static void compose(DocumentSession document) {
                 .build();
     }
 
-    private static DocumentNode scene() {
+    /**
+     * The card artwork as a single node.
+     *
+     * <p>Package-private so {@link LinkedInCarouselExample} can open with the
+     * same picture instead of redrawing it. It is a canvas of {@link #CARD_WIDTH}
+     * by {@link #CARD_HEIGHT}, so a host page has to be at least that wide.</p>
+     *
+     * @return the composed card
+     */
+    static DocumentNode scene() {
         List<CanvasChild> layers = new ArrayList<>();
         layers.addAll(grid());