residue_carry.tex
Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates
residue_carry.tex
This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.
1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,
2 every node/.style={font=\sffamily\small},line cap=round,line join=round]
3 \node[anchor=east] at (-0.4500,0.0000) {$j=0$};
4 \filldraw[fill=black!70,draw=white] (0.0,-0.26) rectangle ++(.48,.52);
5 \node[text=white,font=\scriptsize] at (0.2400,0.0000) {-6};
6 \draw[black!12] (0.56,-0.26) rectangle ++(.48,.52);
7 \draw[black!12] (1.12,-0.26) rectangle ++(.48,.52);
8 \filldraw[fill=black!70,draw=white] (1.6800000000000002,-0.26) rectangle ++(.48,.52);
9 \node[text=white,font=\scriptsize] at (1.9200,0.0000) {-3};
10 \draw[black!12] (2.24,-0.26) rectangle ++(.48,.52);
11 \draw[black!12] (2.8000000000000003,-0.26) rectangle ++(.48,.52);
12 \filldraw[fill=black!70,draw=white] (3.3600000000000003,-0.26) rectangle ++(.48,.52);
13 \node[text=white,font=\scriptsize] at (3.6000,0.0000) {0};
14 \draw[black!12] (3.9200000000000004,-0.26) rectangle ++(.48,.52);
15 \draw[black!12] (4.48,-0.26) rectangle ++(.48,.52);
16 \filldraw[fill=black!70,draw=white] (5.040000000000001,-0.26) rectangle ++(.48,.52);
17 \node[text=white,font=\scriptsize] at (5.2800,0.0000) {3};
18 \draw[black!12] (5.6000000000000005,-0.26) rectangle ++(.48,.52);
19 \draw[black!12] (6.16,-0.26) rectangle ++(.48,.52);
20 \filldraw[fill=black!70,draw=white] (6.720000000000001,-0.26) rectangle ++(.48,.52);
21 \node[text=white,font=\scriptsize] at (6.9600,0.0000) {6};
22 \node[anchor=east] at (-0.4500,-0.8500) {$j=1$};
23 \draw[black!12] (0.0,-1.1099999999999999) rectangle ++(.48,.52);
24 \filldraw[fill=black!70,draw=white] (0.56,-1.1099999999999999) rectangle ++(.48,.52);
25 \node[text=white,font=\scriptsize] at (0.8000,-0.8500) {-5};
26 \draw[black!12] (1.12,-1.1099999999999999) rectangle ++(.48,.52);
27 \draw[black!12] (1.6800000000000002,-1.1099999999999999) rectangle ++(.48,.52);
28 \filldraw[fill=black!70,draw=white] (2.24,-1.1099999999999999) rectangle ++(.48,.52);
29 \node[text=white,font=\scriptsize] at (2.4800,-0.8500) {-2};
30 \draw[black!12] (2.8000000000000003,-1.1099999999999999) rectangle ++(.48,.52);
31 \draw[black!12] (3.3600000000000003,-1.1099999999999999) rectangle ++(.48,.52);
32 \filldraw[fill=black!70,draw=white] (3.9200000000000004,-1.1099999999999999) rectangle ++(.48,.52);
33 \node[text=white,font=\scriptsize] at (4.1600,-0.8500) {1};
34 \draw[black!12] (4.48,-1.1099999999999999) rectangle ++(.48,.52);
35 \draw[black!12] (5.040000000000001,-1.1099999999999999) rectangle ++(.48,.52);
36 \filldraw[fill=black!70,draw=white] (5.6000000000000005,-1.1099999999999999) rectangle ++(.48,.52);
37 \node[text=white,font=\scriptsize] at (5.8400,-0.8500) {4};
38 \draw[black!12] (6.16,-1.1099999999999999) rectangle ++(.48,.52);
39 \draw[black!12] (6.720000000000001,-1.1099999999999999) rectangle ++(.48,.52);
40 \node[anchor=east] at (-0.4500,-1.7000) {$j=2$};
41 \draw[black!12] (0.0,-1.96) rectangle ++(.48,.52);
42 \draw[black!12] (0.56,-1.96) rectangle ++(.48,.52);
43 \filldraw[fill=black!70,draw=white] (1.12,-1.96) rectangle ++(.48,.52);
44 \node[text=white,font=\scriptsize] at (1.3600,-1.7000) {-4};
45 \draw[black!12] (1.6800000000000002,-1.96) rectangle ++(.48,.52);
46 \draw[black!12] (2.24,-1.96) rectangle ++(.48,.52);
47 \filldraw[fill=black!70,draw=white] (2.8000000000000003,-1.96) rectangle ++(.48,.52);
48 \node[text=white,font=\scriptsize] at (3.0400,-1.7000) {-1};
49 \draw[black!12] (3.3600000000000003,-1.96) rectangle ++(.48,.52);
50 \draw[black!12] (3.9200000000000004,-1.96) rectangle ++(.48,.52);
51 \filldraw[fill=black!70,draw=white] (4.48,-1.96) rectangle ++(.48,.52);
52 \node[text=white,font=\scriptsize] at (4.7200,-1.7000) {2};
53 \draw[black!12] (5.040000000000001,-1.96) rectangle ++(.48,.52);
54 \draw[black!12] (5.6000000000000005,-1.96) rectangle ++(.48,.52);
55 \filldraw[fill=black!70,draw=white] (6.16,-1.96) rectangle ++(.48,.52);
56 \node[text=white,font=\scriptsize] at (6.4000,-1.7000) {5};
57 \draw[black!12] (6.720000000000001,-1.96) rectangle ++(.48,.52);
58 \node[] at (3.5500,0.6600) {Every integer belongs to exactly one residue packet.};
59 \node[] at (3.5500,-2.5000) {$n=2=3\cdot0+2\quad\mapsto\quad n=3=3\cdot1+0$};
60 \end{tikzpicture}
Other PDFs for this work
Original file and source record
This copy matches the recorded source file. Its publication here does not change the work’s review status.
SHA-256: 7feb54375762a5ee2f8d49b2d6c4792d6e79deff0c37628ed50e143cc6997aaf
Back to Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates