: Event markers or time ticks. PTC solution : Encode a low-frequency polynomial timing waveform (e.g., ( \sin(2\pi f_0 t) ) and ( \sin(2\pi f_0 t + \phi_i) )) into each trace’s baseline. The polygraph’s playback scanner digitizes all traces; PTC decoding recovers per-trace skew and realigns them with sub-millimeter accuracy.
Let ( p(t) ) be a polynomial of degree ( m-1 ) over ( GF(2) ) or over the reals (depending on modulation). Choose ( m \leq N ). Define ( m ) basis sequences ( b_j[t] ), e.g., ( b_j[t] = t^j \mod 2 ) (binary) or ( b_j[t] = \sin(2\pi f_j t) ) (analog). poly track track codes
The woman stared at the roll. The barcode seemed to pulse. "I just want him to be here. I can't let him go." : Event markers or time ticks
We consider ( N ) parallel tracks indexed ( i = 0, \dots, N-1 ). Time is discretized into bit cells ( t = 0, 1, \dots, L-1 ). Each track ( i ) transmits a binary sequence ( x_i[t] \in 0,1 ). The physical medium introduces: Let ( p(t) ) be a polynomial of
"You don't need the whole sequence," Elias said. "You don't need to freeze him. You need to stabilize the resonance. Use this code as a bridge, not a cage."
Poly track track codes provide a unified framework for synchronization and error correction in multi-track systems. By exploiting polynomial relationships across tracks, they eliminate the need for dedicated clock tracks and offer robust performance against skew and dropouts. Future work includes adaptive polynomial degree selection and application to shingled magnetic recording and DNA storage.
The customer, a man in a trench coat with anxious eyes, nodded quickly. He didn't look at the gravel. He looked at the scanner. "No issues with the... reading?" the man asked.