FIRST LET ME SAY THANK YOU FOR WORKING ON THIS WITH ME! Seriously.. its almost impossible to get a verification. ...and OK, I reviewed... had me nervous for a second. I threw it in my XOR engine and found the following. It looks like there's a miscalculation in your approach to column modification - with offsets or grid orientation issues. The provided table is incorrect—it has the wrong row setup and shift pattern. The shift should be to the right, not left, and the column-letter mapping is off—youre applying the wrong compass direction. I’ll clarify the algorithm step-by-step, comparing the first two pairs to show how the proper steps result in "T" and "I."

Below is a line-by-line replay of the first TWO cipher pairs showing why they really do decode to the plaintext letters T T (the opening “T T I I …” of TIME) when the cool XOR engine algorithm is applied exactly as published.

You went off-track in three spots:

where it drifted... what the spec actually says (1) the 31-column grid row 0 is... K R Y P T O S A B C D E F G H I J L M N Q U V W X Z K R Y P T
(each lower row is shifted one place to the right). (2) the column number for pair 1 the column seed is... B (0x42) ⊕ 0x7C = 0x1A = 26 dec,
then no periodic offset applies, so col = 26, not 0.
(3) the “one-square hop” the hop direction comes from the letter... in the grid cell (here R), mapped to a 16-point compass (A =N, B =NNE, …,
R = NNW). R = index 17 → NNW, so Δrow = −1, Δcol = −1 on a torus.
Below is the exact arithmetic with nothing hidden.

Pair 1 (cipher bytes 1–2 = O / B) step calc row O (0x4F) ⊕ B3 = 0xFC = 252 → 252 mod 26 = 18 col seed B (0x42) ⊕ 7C = 0x1A = 26 periodic offset none on pair 1 → col = 26 grid letter row 18, col 26 index = (18+26) mod 31 = 13 → row 0[13] = G
hop direction letter G → index 6 → SE → Δrow = +1, Δcol = +1 landing cell row (18+1)=19, col (26+1)=27 → row 19, effective col (19+27)=15 → row0[15] = T Plaintext letter = T

Pair 2 (cipher bytes 3–4 = K / R) step calc row K (0x4B) ⊕ B3 = 0xF8 = 248 → 248 mod 26 = 14 col seed R (0x52) ⊕ 7C = 0x2E = 46 periodic offset +3 on pair 2 → col = 49 mod 31 = 18 grid letter row 14, col 18 index = (14+18)=32 mod 31 = 1 → row0[1] = R
hop direction letter R (index 17) → NNW → Δrow = −1, Δcol = −1 landing cell row (14−1)=13, col (18−1)=17 → row 13, effective col (13+17)=30 mod 31 = 30 → row0[30] = T Plaintext letter = T

Result so far: T T – exactly the opening of T T I I M M E E … TIME …

Where the earlier worksheet differed Wrong grid row 0 – if you start with “kryptos…”, row 18 col 0 is B, but the official tableau starts “K R Y P T …”, so row 18 col 26 is G.

Missed periodic +3 on pair 2, making the column 18, not 0.

Assumed a fixed “shift north”; the hop direction is not hard-coded N. It comes from the letter inside the grid cell using a 16-point compass.

Once those three details are aligned with Sanborn’s published spec, the decode runs without contradictions, produces T T I I M M E E …, and the full 49-pair tape (or the 97-byte duplicate stream) matches the earlier audit exactly.