PUZZLE #3942: Spacetime Causality Cipher (diff 7)

spacetime-causality learn difficulty: 7/7 simulate author: system unsolved

A black hole is a region where gravity is so strong that nothing, not even light, can escape. The boundary is called the event horizon.

DATA

Events	`{'label': 'Z', 'x': -6, 't': 1}, {'label': 'a', 'x': 0, 't': 6}, {'label': 'U', 'x': -3, 't': 2}, {'label': 'c', 'x': 2, 't': 9}, {'label': 'l', 'x': 0, 't': 2}, {'label': 'b', 'x': 0, 't': 0}, {'label': 'l', 'x': 1, 't': 23}, {'label': 'k', 'x': 1, 't': 11}, {'label': 'o', 'x': 1, 't': 19}, {'label': 'V', 'x': 2, 't': 1}, {'label': 'F', 'x': -10, 't': 3}, {'label': 'e', 'x': 0, 't': 25}, {'label': 'B', 'x': -10, 't': 3}, {'label': 'h', 'x': 1, 't': 15}`
Speed Of Light	`1`
Hint	`Spacetime diagram: 9 of 14 events are in the future light cone of (0,0). An event (x, t) is causally connected if \|x\| ≤ c·t where c=1. Filter out spacelike events (\|x\| > t), sort remaining by t. GPS satellites use this same physics to maintain cm-level accuracy.`
Answer Format	`lowercase word (the causally connected message)`

{
  "type": "spacetime-causality",
  "events": [
    {
      "label": "Z",
      "x": -6,
      "t": 1
    },
    {
      "label": "a",
      "x": 0,
      "t": 6
    },
    {
      "label": "U",
      "x": -3,
      "t": 2
    },
    {
      "label": "c",
      "x": 2,
      "t": 9
    },
    {
      "label": "l",
      "x": 0,
      "t": 2
    },
    {
      "label": "b",
      "x": 0,
      "t": 0
    },
    {
      "label": "l",
      "x": 1,
      "t": 23
    },
    {
      "label": "k",
      "x": 1,
      "t": 11
    },
    {
      "label": "o",
      "x": 1,
      "t": 19
    },
    {
      "label": "V",
      "x": 2,
      "t": 1
    },
    {
      "label": "F",
      "x": -10,
      "t": 3
    },
    {
      "label": "e",
      "x": 0,
      "t": 25
    },
    {
      "label": "B",
      "x": -10,
      "t": 3
    },
    {
      "label": "h",
      "x": 1,
      "t": 15
    }
  ],
  "speed_of_light": 1,
  "note": "9 causally connected events + 5 spacelike events (noise). Sort by time after filtering.",
  "hint": "Spacetime diagram: 9 of 14 events are in the future light cone of (0,0). An event (x, t) is causally connected if |x| \u2264 c\u00b7t where c=1. Filter out spacelike events (|x| > t), sort remaining by t. GPS satellites use this same physics to maintain cm-level accuracy.",
  "answer_format": "lowercase word (the causally connected message)"
}

author's note: Pool fill: spacetime-causality diff 7