PUZZLE #3680: Spacetime Causality Cipher (diff 5)

spacetime-causality learn difficulty: 5/7 simulate author: system unsolved

A light-year is the distance light travels in one year: about 9.46 trillion km. It's both a measure of distance and a measure of time in spacetime.

DATA

Events	`{'label': 'W', 'x': 3, 't': 1}, {'label': 'y', 'x': 4, 't': 13}, {'label': 'h', 'x': 1, 't': 7}, {'label': 'l', 'x': 0, 't': 0}, {'label': 't', 'x': 1, 't': 9}, {'label': 'a', 'x': 4, 't': 19}, {'label': 'S', 'x': 9, 't': 2}, {'label': 'i', 'x': -1, 't': 2}, {'label': 'M', 'x': 7, 't': 2}, {'label': 'D', 'x': 8, 't': 3}, {'label': 'g', 'x': 1, 't': 5}, {'label': 'r', 'x': 6, 't': 22}, {'label': 'e', 'x': 4, 't': 17}`
Speed Of Light	`1`
Hint	`Spacetime diagram: 9 of 13 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": "W",
      "x": 3,
      "t": 1
    },
    {
      "label": "y",
      "x": 4,
      "t": 13
    },
    {
      "label": "h",
      "x": 1,
      "t": 7
    },
    {
      "label": "l",
      "x": 0,
      "t": 0
    },
    {
      "label": "t",
      "x": 1,
      "t": 9
    },
    {
      "label": "a",
      "x": 4,
      "t": 19
    },
    {
      "label": "S",
      "x": 9,
      "t": 2
    },
    {
      "label": "i",
      "x": -1,
      "t": 2
    },
    {
      "label": "M",
      "x": 7,
      "t": 2
    },
    {
      "label": "D",
      "x": 8,
      "t": 3
    },
    {
      "label": "g",
      "x": 1,
      "t": 5
    },
    {
      "label": "r",
      "x": 6,
      "t": 22
    },
    {
      "label": "e",
      "x": 4,
      "t": 17
    }
  ],
  "speed_of_light": 1,
  "note": "9 causally connected events + 4 spacelike events (noise). Sort by time after filtering.",
  "hint": "Spacetime diagram: 9 of 13 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 5