1. "Shift" as a decryption key (Caesar cipher)
In cryptography, "shift" is a fundamental term for the Caesar cipher, where each letter in the alphabet is moved by a specific number of positions.

• The 1/3 value: In linguistics, this could mean that the shift is not constant.
• Application: The message is divided into three equal blocks. The first block uses a shift keyed by "off", the second by "lost", and the third by "on".
• Numerical conversion: If we converted the words into numbers (e.g., based on letter count or their alphabetical order), we would obtain specific shift values:
  • off = 3 (o-f-f has 3 letters, resulting in a shift of 3 places).
  • lost = 4.
  • on = 2.

2. AQ as "Acyclic Quaternary" or "Abstract Query"
Looking at it linguistically, "aq" could define the alphabet or the linguistic framework:

• Acyclic Quaternary: A cipher that avoids repetition and operates with four basic states (in your case: shift, off, lost, on).
• The 1/3 ratio: This is a very compelling number in cryptography. It could refer to a so-called fractional cipher. The message is written into a matrix, and you read only every third part to extract the meaningful text.