Feat: Add directed asymptotic escape and analytic Schwarzschild exterior

Replace radius-only escape termination with a common asymptotic exterior protocol: declared ends, moving escape worldtubes, directed inside->outside crossings, and a PENDING_ENTRY lifecycle shared by single-frame and movie tracing.

Add an analytic Carlson-integral Schwarzschild monopole exterior (angle primitive, bracketed turning radius, ingoing Kerr-Schild coordinate-time transfer, conserved-energy frequency) so a camera outside the escape sphere is traced through an entry event.

Make the lifecycle tri-state (no ends / ready / protocol error), carry end_id through the endpoint and lens mesh, validate sources in constructors via spacetime_source_finalize(), and refresh the Schwarzschild reference images for the corrected finish.

src/frame.c

@@ -116,6 +116,7 @@ int frame_lens_mesh_trace(FrameLensMesh *mesh, const SpacetimeSource *spacetime,
     RayEndpoint endpoint = geodesic_trace_past(spacetime, observer,
                                                vertex->camera_direction, trace);
     vertex->status = endpoint.status;
+    vertex->end_id = endpoint.end_id;
     vertex->traced = 1;
     if (endpoint.status == RAY_ENDPOINT_ESCAPED) {
       for (int axis = 0; axis < 3; ++axis)
@@ -437,11 +438,20 @@ static int all_vertices_traced(const FrameLensMesh *mesh) {
 
 static int terminal_mismatch(const LensVertex *a, const LensVertex *b,
                              const LensVertex *c) {
-  int escaped = 0, captured = 0;
+  int escaped = 0, captured = 0, have_end = 0;
+  SpacetimeEndId end = SPACETIME_END_NONE;
   const LensVertex *vertices[] = {a, b, c};
   for (size_t i = 0; i < 3; ++i) {
     escaped |= vertices[i]->status == RAY_ENDPOINT_ESCAPED;
     captured |= vertices[i]->status == RAY_ENDPOINT_CAPTURED;
+    if (vertices[i]->status == RAY_ENDPOINT_ESCAPED) {
+      if (!have_end) {
+        end = vertices[i]->end_id;
+        have_end = 1;
+      } else if (vertices[i]->end_id != end) {
+        return 1; /* two different infinity ends must not be interpolated */
+      }
+    }
   }
   return escaped && captured;
 }
@@ -576,6 +586,7 @@ int frame_lens_mesh_install_sample(FrameLensMesh *mesh, size_t sample_id,
                            ? &mesh->vertices[sample->vertex_id]
                            : &sample->vertex;
   vertex->status = endpoint->status;
+  vertex->end_id = endpoint->end_id;
   vertex->traced = 1;
   if (endpoint->status == RAY_ENDPOINT_ESCAPED) {
     for (int axis = 0; axis < 3; ++axis)
@@ -610,6 +621,8 @@ static int discrete_jacobian(const FrameLensMesh *mesh,
   if (a->status != RAY_ENDPOINT_ESCAPED || b->status != RAY_ENDPOINT_ESCAPED ||
       c->status != RAY_ENDPOINT_ESCAPED)
     return 0;
+  if (a->end_id != b->end_id || a->end_id != c->end_id)
+    return 0;
   const double image_area = spherical_signed_area(
       a->camera_direction, b->camera_direction, c->camera_direction);
   if (!isfinite(image_area) || fabs(image_area) <= 1e-15)