PUZZLE #5307: Elastic Path Cipher (diff 1)

elastic learn difficulty: 1/7 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	`1`
Char Count	`5`
Char X	`0.0, 20.0, 40.0, 60.0, 80.0`
Spacing	`20.0`
Height Scale	`3.5`
Samples Per Char	`8`
X Sample Start	`0.0`
X Sample End	`80.0`
X Offset	`0.0`
Baseline Start Y	`119.0`
Baseline End Y	`126.0`
Xorkey	`0x7f`
Weights	`f1ZDNzIyOUdacIKNlZmXkIZ4bmdlaXF8jqO3xcvMx7yp`
Weight Count	`33`
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 33 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": 1,
  "char_count": 5,
  "char_x": [
    0.0,
    20.0,
    40.0,
    60.0,
    80.0
  ],
  "spacing": 20.0,
  "height_scale": 3.5,
  "samples_per_char": 8,
  "x_sample_start": 0.0,
  "x_sample_end": 80.0,
  "x_offset": 0.0,
  "baseline_start_y": 119.0,
  "baseline_end_y": 126.0,
  "xorkey": "0x7f",
  "weights": "f1ZDNzIyOUdacIKNlZmXkIZ4bmdlaXF8jqO3xcvMx7yp",
  "weight_count": 33,
  "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 33 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 1