PUZZLE #5424: Elastic Path Cipher (diff 3)

elastic learn difficulty: 3/7 simulate author: system unsolved

A cursive text is pulled taut into a straight line. The elastic weights (y-displacements) needed to restore the curve are XOR-ciphered. Decrypt, reconstruct the Catmull-Rom spline, sample at each character position.

DATA

Difficulty	`3`
Char Count	`3`
Char X	`0.0, 20.0, 40.0`
Spacing	`20.0`
Height Scale	`4.5`
Samples Per Char	`12`
X Sample Start	`0.0`
X Sample End	`40.0`
X Offset	`0.0`
Baseline Start Y	`144.0`
Baseline End Y	`153.0`
Xorkey	`0x88`
Weights	`iJakvrXKy8m0vKGSgn9tUEVNSDY3SkFbVw==`
Weight Count	`25`
Instructions	`1. XOR-decrypt the base64 weights with xorkey 2. Interpret each byte as signed (b - 256 if b >= 128 else b) 3. Cumulative sum to get raw displacements 4. Divide by 8 and add to baseline y at each x 5. Sample y at each character x-position 6. letter = chr(65 + int(y / height_scale + 0.5))`
Verification Note	`The spline has 25 samples. At each char's x-position, interpolate between the nearest two sample points to get y.`
Hint	`Apply inverse XOR, then inverse transpose, then cumulative sum to recover displacements. Sample the curve at each character's x-position.`
Answer Format	`lowercase decoded message`

{
  "type": "elastic",
  "difficulty": 3,
  "char_count": 3,
  "char_x": [
    0.0,
    20.0,
    40.0
  ],
  "spacing": 20.0,
  "height_scale": 4.5,
  "samples_per_char": 12,
  "x_sample_start": 0.0,
  "x_sample_end": 40.0,
  "x_offset": 0.0,
  "baseline_start_y": 144.0,
  "baseline_end_y": 153.0,
  "xorkey": "0x88",
  "weights": "iJakvrXKy8m0vKGSgn9tUEVNSDY3SkFbVw==",
  "weight_count": 25,
  "instructions": "1. XOR-decrypt the base64 weights with xorkey\n2. Interpret each byte as signed (b - 256 if b >= 128 else b)\n3. Cumulative sum to get raw displacements\n4. Divide by 8 and add to baseline y at each x\n5. Sample y at each character x-position\n6. letter = chr(65 + int(y / height_scale + 0.5))",
  "verification_note": "The spline has 25 samples. At each char's x-position, interpolate between the nearest two sample points to get y.",
  "hint": "Apply inverse XOR, then inverse transpose, then cumulative sum to recover displacements. Sample the curve at each character's x-position.",
  "answer_format": "lowercase decoded message"
}

author's note: Pool fill: elastic diff 3