← Back to EHAX 2026

Quantum Message

Forensics 359 pts

Challenge Description

"my quantum physics professor was teaching us about 1-D harmonic oscillator, he gave me a problem in which the angular frequency was 57 1035 (weird number) and it asked to calculate the energy eigenvalues, then he called someone, who did he call?"

Solution

1. File Analysis

The challenge file is a 14MB WAV file: mono, 44100 Hz sample rate, IEEE 32-bit float, 81.6 seconds duration.

2. Frequency Analysis

Spectral analysis revealed the audio contains only 7 distinct frequencies, all concentrated below 4000 Hz:

Frequency (Hz)IndexHarmonic (2n+1)
30101
90213
150325
210437
270549
3306511
3907613

These are the odd harmonics of ~301 Hz: 301 * (2n+1) for n=0..6.

This directly relates to the quantum harmonic oscillator hint. The energy eigenvalues of a 1D harmonic oscillator are E_n = hbar * omega * (n + 1/2), which are equally spaced at odd half-integer multiples of the base energy.

3. Tone Structure

Each time segment contains exactly two simultaneously active frequencies. The audio always pairs one "low" frequency (indices 0-3) with one "high" frequency (indices 4-6), creating a 4x3 grid identical to a phone keypad (DTMF-like encoding):

            f4(2705)  f5(3306)  f6(3907)
f0(301):      1         2         3
f1(902):      4         5         6
f2(1503):     7         8         9
f3(2104):     *         0         #

4. Duration Encoding

Each tone has a duration of 1, 2, or 3 seconds. The duration indicates how many times the digit repeats. For example:

  • Tone (2,5) for 2 seconds = digit "8" repeated twice = "88"
  • Tone (2,6) for 3 seconds = digit "9" repeated thrice = "999"

5. Decoding

After expanding all 63 tone groups with their durations, the full digit string is:

69725288123113117521101161171099511210412111549995395495395534895539952114121125

This string represents variable-length ASCII decimal codes (2 or 3 digits per character):

69  72  52  88  123  113  117  52  110  116  117  109  95  112  104  121
E   H   4   X   {    q    u    4   n    t    u    m    _   p    h    y

115  49  99  53  95  49  53  95  53  48  95  53  99  52  114  121  125
s    1   c   5   _   1   5   _   5   0   _   5   c   4   r    y    }

The decoding is unambiguous - dynamic programming confirms there is exactly one valid ASCII interpretation of the digit string.

Tools Used

  • Python 3 with scipy, numpy for WAV parsing and FFT analysis
  • scipy.signal.find_peaks for frequency peak detection
  • Dynamic programming for unambiguous variable-length ASCII decoding