Answer the review: direction settles distance, brightness is one-sided, and a lost id stops the scene

Three findings from the adversarial review of the merge, all reproduced.

The distance test was hiding 1 489 stars that sit under an arcsecond from
their Gaia entry with a Hipparcos parallax off by half — thirty of them at a
false few parsecs from the Sun (HIP 82724 at 3.7 pc, where Gaia has it at
62.8) — and the first audit did not see them because it counted residual
doubles through the same 50 % filter. Under three arcseconds the distances
are now not consulted: a coincidence of direction that close is never chance
at this depth (the quarter-degree shift finds none), and the parallax is the
thing to fix. Brightness keeps its say at any separation, and is now
one-sided: a folded entry may be five magnitudes fainter (a red dwarf in V
against G) but not one brighter, because an entry a magnitude brighter than
what is already at that spot is a primary Gaia does not carry — Almach,
Alfirk and Ashlesha had all been folded into their companions' entries,
93 in all. The sky grid wraps at 0h.

The Gaia query orders by source_id after G, so the row order — and the ids
assigned from it — is a function of the archive's content rather than of the
server's plan for 20 064 ties; the cache key is a hash of the query.

And a bookmark to a star id the catalogue no longer holds — 56 000 Gaia ids
change with this — sent the scene through reconcileSelection, enterSystem,
its decline, finishTransition and reconcileSelection again until the stack
overflowed. The selection is cleared instead, at the one place every path
goes through.

Regenerated: 423 641 stars, 57 512 HYG identities on Gaia positions, no HYG
id or name lost, no star within 20 pc left with an unclaimed Gaia entry under
an arcsecond. 403 HYG survivors still have an unclaimed Gaia entry within
60": 13 under an arcsecond, where the brightness guard does not trust HYG's
magnitude, and the rest components 3" to 60" from their counterpart.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01QL6F9Bgfh8SgAiAAcPB9Hw

src/app/shared/astro/star-merge.spec.ts

@@ -38,19 +38,45 @@ describe('isSameStar', () => {
   it('keeps a bright primary out of the entry of its faint companion', () => {
     // Gaia has no Sirius — it saturates — but has Sirius B, 6″ away at the same distance and ten
     // magnitudes fainter. Direction and distance say "same star"; the brightness says otherwise.
-    const sirius = at(32263, 101.2875, -16.7161, 2.637, { name: 'Sirius', magnitude: -1.44 });
-    const siriusB = at(1, 101.2875 + arcsecOfRa(6.1, -16.7161), -16.7161, 2.67, { name: 'Gaia DR3 2947050466531873024', magnitude: 8.5, source: 'gaia' });
-    expect(isSameStar(sirius, siriusB)).toBe(false);
-    expect(isSameStar(sirius, { ...siriusB, magnitude: -1.3 })).toBe(true);
+    const siriusB = at(1, 101.2875, -16.7161, 2.67, { name: 'Gaia DR3 2947050466531873024', magnitude: 8.5, source: 'gaia' });
+    const sirius = at(32263, 101.2875 + arcsecOfRa(6.1, -16.7161), -16.7161, 2.637, { name: 'Sirius', magnitude: -1.44 });
+    expect(isSameStar(siriusB, sirius)).toBe(false);
+    expect(isSameStar(siriusB, { ...sirius, magnitude: 8.6 })).toBe(true);
+  });
+
+  it('lets the folded entry be fainter, as a red star is in V, but not much brighter', () => {
+    // Wolf 359 is V 13.45 in HYG and G 11.0 in Gaia — the same star, 5″ apart on a Gliese
+    // position. Almach is V 2.1 and sits 10″ from γ² And, G 4.9: Gaia has no Almach, and its
+    // name must not land on the companion.
+    const wolf359 = at(1, 164.1, 7.0, 2.41, { name: 'Gaia DR3 3864972938605115520', magnitude: 11.0, source: 'gaia' });
+    expect(isSameStar(wolf359, at(118720, 164.1 + arcsecOfRa(5, 7), 7.0, 2.39, { name: 'Wolf 359', magnitude: 13.45 }))).toBe(true);
+    const gamma2And = at(2, 30.97, 42.33, 50, { name: 'Gaia DR3 346231302441905920', magnitude: 4.9, source: 'gaia' });
+    expect(isSameStar(gamma2And, at(9640, 30.97 + arcsecOfRa(9.9, 42.33), 42.33, 50, { name: 'Almach', magnitude: 2.1 }))).toBe(false);
   });
 
   it('does not match two different stars that happen to be at the same distance', () => {
     expect(isSameStar(at(1, 200, 10, 200), at(2, 200.5, 10, 200))).toBe(false);
   });
 
-  it('does not match along a line of sight when the distances genuinely conflict', () => {
-    // Same direction, one three times further away: a background star, not the same object.
-    expect(isSameStar(at(1, 200, 10, 100), at(2, 200, 10, 300))).toBe(false);
+  it('takes two entries within three arcseconds for one star, whatever their distances say', () => {
+    // HD 225021: 143.7 pc by its Hipparcos parallax, 239.4 by Gaia's, 0.01″ apart; HIP 82724:
+    // 3.7 pc by Hipparcos, 62.8 by Gaia, 2.3″ apart. A coincidence of direction that close is
+    // never chance at this depth; the parallax is what is wrong.
+    const gaia = at(1, 1.72, -8.9, 239.4, { name: 'Gaia DR3 395581679270412160', source: 'gaia' });
+    expect(isSameStar(gaia, at(213, 1.72 + arcsecOfRa(0.1, -8.9), -8.9, 143.7, { name: 'HD 225021' }))).toBe(true);
+    expect(isSameStar(at(2, 253.6, -38.1, 62.8, { source: 'gaia' }), at(82724, 253.6 + arcsecOfRa(2.3, -38.1), -38.1, 3.7))).toBe(true);
+  });
+
+  it('past those three arcseconds, does not match along a line of sight when the distances conflict', () => {
+    // Nearly the same direction, one three times further away: a background star, not the same object.
+    expect(isSameStar(at(1, 200, 10, 100), at(2, 200 + arcsecOfRa(5, 10), 10, 300))).toBe(false);
+  });
+
+  it('still hears the brightness inside those three arcseconds', () => {
+    // Ashlesha (ε Hya, V 3.38) has a companion 2.7″ away that Gaia does carry, three magnitudes
+    // fainter, while it does not carry Ashlesha. Direction alone would put the name on the companion.
+    const companion = at(1, 131.69, 6.42, 40, { name: 'Gaia DR3 1', magnitude: 6.7, source: 'gaia' });
+    expect(isSameStar(companion, at(43109, 131.69 + arcsecOfRa(2.7, 6.42), 6.42, 40, { name: 'Ashlesha', magnitude: 3.38 }))).toBe(false);
   });
 
   it('matches on direction rather than on 3D proximity', () => {
@@ -181,6 +207,13 @@ describe('mergeStarCatalogues', () => {
       ]);
       expect(stars).toHaveLength(1);
     }
+
+    // And the one edge the grid has to wrap: 3.6″ apart, either side of 0h.
+    const { stars } = mergeStarCatalogues([
+      { ...HIPPARCOS, stars: [at(1, 359.9995, 0, 100)] },
+      { ...GAIA, stars: [at(2, 0.0005, 0, 100)] }
+    ]);
+    expect(stars).toHaveLength(1);
   });
 
   it('handles a single catalogue as a plain pass-through', () => {