Say which band each star was measured in, whose catalogue it is, and how sure its distance is

The readout named Hipparcos, Yale and Gliese while 378 775 of the 455 608 stars are described by
Gaia DR3, printed one "Magnitude" for G and V alike, and gave every distance to the parsec. The
band cannot be read off the star's source, which records whose position it has: 62 002 stars Gaia
places keep HYG's V and B-V, and the 575 hosts renamed after their planets are Gaia's, in G.

stars-meta.bin gains two byte columns, 14 to 16 bytes a star (6 378 512 to 7 289 728 bytes; gzip
-9 2 804 049 to 3 110 991). One holds the magnitude's band (V 76 555 stars, G 378 744, none 309,
whose magnitude is a stand-in), which colour the colour index is (B-V 75 203, BP-RP 376 703), and
whether the distance is Gaia's parallax. The other holds the distance's relative error as its
square root in 255ths: a step is 0.08 % of distance at 1 %, 0.35 % at 20 %, and 100 % is the top.
encode, decode, BYTES_PER_STAR_META and the build.ts round trip cover both; no workflow reads the
format.

Where the errors come from:
- Gaia rows keep the parallax_error their query already fetched: median 0.3 %, 90th percentile
  1.2 %, at most 20 %, the query's own cut.
- A HYG star at Gaia's distance takes the cross-match's parallax_over_error, and a star merged
  into a Gaia entry keeps that entry's error with its position.
- The 3 067 Hipparcos stars that keep their Hipparcos distance, Rigel, Deneb and Alnilam among
  them, take e_plx from van Leeuwen's 2007 reduction: a new cached query of
  public.hipparcos_newreduction on the ESA archive, whose 117 955 rows HYG's distances invert.
- The archive's stars take sy_disterr1/2 from pscomppars, in a query and cache file of their own
  so the composite rows already cached were not refetched.
- 439 distances have no published error: 357 Gliese rows and 82 archive hosts.

Of the errors, 392 786 are 1 % or less and are not printed; 61 156 print as "117 ± 12 pc" to the
distance's own digits; 1 196 between 20 and 100 %, and 30 past it, print as the range the
parallax gives, since a symmetric error in parallax is a lopsided one in distance.

The star card (measured on the dev server) now reads, for example:
- Rigel: 265 ± 23 pc, V 0.18, B-V -0.03, source HYG.
- Deneb: 433 ± 60 pc.
- Alnilam: "476 pc to 833 pc" (Hipparcos 1.65 ± 0.45 mas).
- Gaia DR3 5612323414549657984: 111 ± 2 pc, G 4.63, BP-RP -0.15, source Gaia DR3.
- Proxima Centauri: 1.30 pc, V 11.01, source "HYG, Gaia DR3 distance".
- TRAPPIST-1: G 15.62, BP-RP 4.90, source Gaia DR3.
- Kepler-186: V 15.14, source NASA Exoplanet Archive.
The neighbourhood's subtitle reads "Gaia DR3 378,775 · HYG 73,556 · NASA Exoplanet Archive
3,277", counted by the catalogue describing each star.

build.ts validateStars now fails a catalogue with more than 1 000 stars without a band (309
today) or without a distance error (439). Dropping G from the Gaia rows gave 379 040 without a
band, and dropping their parallax_error gave 441 216 without an error; both runs failed.

Decoding the catalogue in Node took a median 29 ms before and 24 ms after (nine runs each, within
noise). In the app, five cold boots gave a 654-786 ms long task after the data landed and the
HUD at 1.83-2.07 s.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

src/app/shared/format/quantity.spec.ts

@@ -1,6 +1,6 @@
 import { describe, expect, it } from 'vitest';
 
-import { formatAu, formatDensity, formatLuminosity, formatMassEarth, formatParsecs, formatPeriod, formatRadiusKm, formatTemperature } from './quantity';
+import { formatAu, formatDensity, formatDistance, formatLuminosity, formatMassEarth, formatParsecs, formatPeriod, formatRadiusKm, formatTemperature } from './quantity';
 
 describe('formatParsecs', () => {
   it('switches to kiloparsecs past a thousand parsecs', () => {
@@ -13,6 +13,26 @@ describe('formatParsecs', () => {
   });
 });
 
+describe('formatDistance', () => {
+  it('gives the error to the digits the distance is shown to', () => {
+    expect(formatDistance(117.3, 0.1)).toBe('117 ± 12 pc');
+    expect(formatDistance(4.2, 0.05)).toBe('4.20 ± 0.21 pc');
+    expect(formatDistance(1830, 0.15)).toBe('1.8 ± 0.3 kpc');
+  });
+
+  it('leaves off an error of a per cent or less, or one too small to show', () => {
+    expect(formatDistance(117.3, 0.01)).toBe('117 pc');
+    expect(formatDistance(12, 0.03)).toBe('12 pc');
+    expect(formatDistance(117.3, undefined)).toBe('117 pc');
+  });
+
+  it("gives a range once the error is a fifth of the parallax, and no upper end past all of it", () => {
+    // Alnilam: 1.65 ± 0.45 mas in Hipparcos.
+    expect(formatDistance(606.06, 0.45 / 1.65)).toBe('476 pc to 833 pc');
+    expect(formatDistance(250, 1)).toBe('125 pc or more');
+  });
+});
+
 describe('formatAu', () => {
   it('holds four decimals for close-in orbits', () => {
     // 0.0026 AU is a real published semi-major axis; two decimals would render it — and every

src/app/shared/format/quantity.ts

@@ -9,7 +9,35 @@
 
 /** Distance in parsecs, switching to kiloparsecs where the number would otherwise run long. */
 export function formatParsecs(distancePc: number): string {
-  return distancePc >= 1000 ? `${(distancePc / 1000).toFixed(1)} kpc` : `${distancePc.toFixed(distancePc < 10 ? 2 : 0)} pc`;
+  const { divisor, digits, unit } = parsecScale(distancePc);
+  return `${(distancePc / divisor).toFixed(digits)} ${unit}`;
+}
+
+function parsecScale(distancePc: number): { divisor: number; digits: number; unit: string } {
+  return distancePc >= 1000 ? { divisor: 1000, digits: 1, unit: 'kpc' } : { divisor: 1, digits: distancePc < 10 ? 2 : 0, unit: 'pc' };
+}
+
+/**
+ * A star's distance with its uncertainty, given as a fraction of it: `117 ± 12 pc`, to the
+ * digits the distance itself is shown to. Left off where it is 1 % or less, or would round to
+ * nothing at those digits, since the figure is then already as good as it reads.
+ *
+ * Past a fifth, a range: the distance is the inverse of a parallax, so the parallax's symmetric
+ * error bar is a lopsided one in distance — Alnilam's 1.65 ± 0.45 mas is 476 to 833 pc, not
+ * 606 ± 165. Only a Hipparcos or archive distance gets there; Gaia's query stops at a fifth. An
+ * error as large as the parallax leaves no upper bound at all.
+ */
+export function formatDistance(distancePc: number, relativeError: number | undefined): string {
+  if (relativeError === undefined || relativeError <= 0.01) {
+    return formatParsecs(distancePc);
+  }
+  if (relativeError < 0.2) {
+    const { divisor, digits, unit } = parsecScale(distancePc);
+    const error = ((distancePc * relativeError) / divisor).toFixed(digits);
+    return Number(error) === 0 ? formatParsecs(distancePc) : `${(distancePc / divisor).toFixed(digits)} ± ${error} ${unit}`;
+  }
+  const nearest = formatParsecs(distancePc / (1 + relativeError));
+  return relativeError >= 1 ? `${nearest} or more` : `${nearest} to ${formatParsecs(distancePc / (1 - relativeError))}`;
 }
 
 /** Distance in astronomical units, for anything inside a system. */