Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
| A          | B             | C        |   D |          E | F     | G                                                                                                          |      H |     I |      J |      K |      L |      M |      N |          O |      P |       Q |      R |      S |       T |
|:-----------|:--------------|:---------|----:|-----------:|:------|:-----------------------------------------------------------------------------------------------------------|-------:|------:|-------:|-------:|-------:|-------:|-------:|-----------:|-------:|--------:|-------:|-------:|--------:|
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   1 |     155713 | STONE | STONE`SYNTHETIC`FIRST QUALITY`1 PT OR 1.25 MM`AMETHYST`ROUND`FULL`````````````                             |   5.5  |   4.4 |   3    |   4    |   8.51 |   6.81 |   3.01 |  0.547273  |   6.33 |   5.064 |   5.1  |   2.1  |   -1.71 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   1 |     158758 | STONE | STONE`PRECIOUS``1 PT OR 1.25 MM`CITRINE`ROUND`FACETED`````````````                                         |   5.5  |   4.4 |   3.79 |   5.05 |  10.74 |   8.59 |   5.24 |  0.952727  |   6.33 |   5.064 |   5.1  |   1.31 |   -3.49 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   1 |     162578 | STONE | STONE: PRECIOUS.AA.1 PT OR 1.25 MM.GARNET.ROUND.FACETED.FACETED. 7000G2800100000                           |   5.5  |   4.4 |   4.3  |   5.73 |  12.19 |   9.75 |   6.69 |  1.21636   |   6.33 |   5.064 |   5.1  |   0.8  |   -4.65 |
| RUBY       | PRECIOUS      | GENUINE3 |   1 |     162461 | STONE | STONE`PRECIOUS``1 PT OR 1.25 MM`RUBY`ROUND`FACETED`````````````                                            |   6    |   4.8 |   5.01 |   6.68 |  14.21 |  11.37 |   8.21 |  1.36833   |   6.9  |   5.52  |   5.55 |   0.54 |   -5.82 |
| BSR        | PRECIOUS      | GENUINE2 |   1 |    1220256 | STONE | STONE`PRECIOUS`AAA`1.25 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                        |   6    |   4.8 |   5.16 |   6.88 |  14.64 |  11.71 |   8.64 |  1.44      |   6.9  |   5.52  |   5.55 |   0.39 |   -6.16 |
| EMERALD    | PRECIOUS      | GENUINE3 |   1 |     162537 | STONE | STONE`PRECIOUS``1 PT OR 1.25 MM`EMERALD`ROUND``````````````                                                |   6    |   4.8 |   5.51 |   7.34 |  15.62 |  12.5  |   9.62 |  1.60333   |   6.9  |   5.52  |   5.55 |   0.04 |   -6.95 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   2 | 2000099057 | STONE | STONE`GENUINE``2 PT OR 1.75 MM`BLACK ONYX`ROUND`FACETED`````````````                                       |   5.75 |   4.6 |   2.84 |   3.79 |   8.06 |   6.45 |   2.31 |  0.401739  |   6.61 |   5.288 |   5.3  |   2.46 |   -1.15 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   2 |     162586 | STONE | STONE`GENUINE``2 PT OR 1.75 MM`GARNET`ROUND`FACETED`````````````                                           |   5.75 |   4.6 |   3.04 |   4.05 |   8.62 |   6.9  |   2.87 |  0.49913   |   6.61 |   5.288 |   5.3  |   2.26 |   -1.6  |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   2 |     636191 | STONE | STONE..PRECIOUS.FIRST QUALITY.2 PT OR 1.75 MM.CITRINE..FACETED.FACETED.................. 7000G0400200000   |   5.75 |   4.6 |   3.58 |   4.77 |  10.15 |   8.12 |   4.4  |  0.765217  |   6.61 |   5.288 |   5.3  |   1.72 |   -2.82 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   2 | 2000088738 | STONE | STONE`SEMI-PRECIOUS``2 PT OR 1.75 MM`AMETHYST`ROUND`FACETED`FACETED````````````                            |   5.75 |   4.6 |   3.74 |   4.99 |  10.62 |   8.5  |   4.87 |  0.846957  |   6.61 |   5.288 |   5.3  |   1.56 |   -3.2  |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   2 |     158832 | STONE | STONE`PRECIOUS``2 PT OR 1.75 MM`AQUAMARINE`ROUND``````````````                                             |   5.75 |   4.6 |   4.2  |   5.6  |  11.91 |   9.53 |   6.16 |  1.0713    |   6.61 |   5.288 |   5.3  |   1.1  |   -4.23 |
| EMERALD    | PRECIOUS      | GENUINE3 |   2 |     162545 | STONE | STONE`PRECIOUS``2 PT OR 1.75 MM`EMERALD`ROUND``````````````                                                |   6.5  |   5.2 |   4.68 |   6.24 |  13.28 |  10.62 |   6.78 |  1.04308   |   7.48 |   5.984 |   6    |   1.32 |   -4.62 |
| BSR        | PRECIOUS      | GENUINE2 |   2 |     162453 | STONE | STONE`PRECIOUS``2 PT OR 1.75 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                   |   6.5  |   5.2 |   6.12 |   8.16 |  17.36 |  13.89 |  10.86 |  1.67077   |   7.48 |   5.984 |   6    |  -0.12 |   -7.89 |
| RUBY       | PRECIOUS      | GENUINE3 |   2 |     162479 | STONE | STONE`PRECIOUS``2 PT OR 1.75 MM`RUBY`ROUND`FACETED`````````````                                            |   6.5  |   5.2 |   6.12 |   8.16 |  17.36 |  13.89 |  10.86 |  1.67077   |   7.48 |   5.984 |   6    |  -0.12 |   -7.89 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   3 |     157396 | STONE | STONE..GENUINE.MEDIUM QUALITY.3 PT OR 2.0 MM.BLACK ONYX.ROUND.REGULAR................... 700072500300000   |   6    |   4.8 |   2.85 |   3.8  |   8.09 |   6.47 |   2.09 |  0.348333  |   6.9  |   5.52  |   5.55 |   2.7  |   -0.92 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   3 |     162594 | STONE | STONE: PRECIOUS.3 PT OR 2.0 MM.GARNET.ROUND.FACETED. 7000G2800300000                                       |   6    |   4.8 |   3.04 |   4.05 |   8.62 |   6.9  |   2.62 |  0.436667  |   6.9  |   5.52  |   5.55 |   2.51 |   -1.35 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   3 |     158766 | STONE | STONE..PRECIOUS.AA.3 PT OR 2.0 MM.CITRINE.ROUND.FACETED................... 7000G0400300000                 |   6    |   4.8 |   3.58 |   4.77 |  10.15 |   8.12 |   4.15 |  0.691667  |   6.9  |   5.52  |   5.55 |   1.97 |   -2.57 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   3 | 2000150552 | STONE | STONE`GENUINE``2 MM`AMETHYST`ROUND`FACETED`FACETED````````````                                             |   6    |   4.8 |   4.3  |   5.73 |  12.19 |   9.75 |   6.19 |  1.03167   |   6.9  |   5.52  |   5.55 |   1.25 |   -4.2  |
| RUBY       | PRECIOUS      | GENUINE3 |   3 |     162487 | STONE | STONE`PRECIOUS``3 PT OR 2.0 MM`RUBY`ROUND`FACETED````````````` 7000G2500300000                             |   7    |   5.6 |   5.18 |   6.9  |  14.68 |  11.74 |   7.68 |  1.09714   |   8.05 |   6.44  |   6.45 |   1.27 |   -5.29 |
| EMERALD    | PRECIOUS      | GENUINE3 |   3 |     162552 | STONE | STONE`PRECIOUS``3 PT OR 2.0 MM`EMERALD`ROUND`FACETED`````````````                                          |   7    |   5.6 |   6.01 |   8.01 |  17.04 |  13.63 |  10.04 |  1.43429   |   8.05 |   6.44  |   6.45 |   0.44 |   -7.18 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   3 |     158840 | STONE | STONE`PRECIOUS``3 PT OR 2.0 MM`AQUAMARINE`ROUND``````````````                                              |   6    |   4.8 |   6.06 |   8.08 |  17.19 |  13.75 |  11.19 |  1.865     |   6.9  |   5.52  |   5.55 |  -0.51 |   -8.2  |
| BSR        | PRECIOUS      | GENUINE2 |   3 |     162511 | STONE | STONE`PRECIOUS``3 PT OR 2.0 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                    |   7    |   5.6 |   6.39 |   8.52 |  18.13 |  14.5  |  11.13 |  1.59      |   8.05 |   6.44  |   6.45 |   0.06 |   -8.05 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   4 |     157404 | STONE | STONE`GENUINE`MEDIUM QUALITY`4 PT OR 2.1 MM`BLACK ONYX`ROUND`REGULAR````````````` 700072500400000          |   6.25 |   5   |   2.84 |   3.79 |   8.06 |   6.45 |   1.81 |  0.2896    |   7.19 |   5.752 |   5.75 |   2.91 |   -0.7  |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   4 |     166462 | STONE | STONE`PRECIOUS``4 PT OR 2.1 MM`GARNET`ROUND`FACETED`````````````                                           |   6.25 |   5   |   3.58 |   4.77 |  10.15 |   8.12 |   3.9  |  0.624     |   7.19 |   5.752 |   5.75 |   2.17 |   -2.37 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   4 |     158774 | STONE | STONE`PRECIOUS``4 PT OR 2.1 MM`CITRINE`ROUND`FACETED`````````````                                          |   6.25 |   5   |   3.85 |   5.13 |  10.91 |   8.73 |   4.66 |  0.7456    |   7.19 |   5.752 |   5.75 |   1.9  |   -2.98 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   4 |     158907 | STONE | STONE`PRECIOUS``4 PT OR 2.1 MM`AMETHYST`ROUND`FACETED`````````````                                         |   6.25 |   5   |   4.36 |   5.81 |  12.36 |   9.89 |   6.11 |  0.9776    |   7.19 |   5.752 |   5.75 |   1.39 |   -4.14 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   4 |     158857 | STONE | STONE`GENUINE``4 PT OR 2.1 MM`AQUAMARINE`ROUND``````````````                                               |   6.25 |   5   |   5.79 |   7.72 |  16.43 |  13.14 |  10.18 |  1.6288    |   7.19 |   5.752 |   5.75 |  -0.04 |   -7.39 |
| EMERALD    | PRECIOUS      | GENUINE3 |   4 |     162560 | STONE | STONE..PRECIOUS..4 PT OR 2.1 MM.EMERALD.ROUND.FACETED................... 120610004                         |   7.5  |   6   |   6.01 |   8.01 |  17.04 |  13.63 |   9.54 |  1.272     |   8.63 |   6.904 |   6.9  |   0.89 |   -6.73 |
| RUBY       | PRECIOUS      | GENUINE3 |   4 |     162495 | STONE | STONE`PRECIOUS`C`4 PT OR 2.1 MM`RUBY`ROUND`FACETED`````````````                                            |   7.5  |   6   |   7.11 |   9.48 |  20.17 |  16.14 |  12.67 |  1.68933   |   8.63 |   6.904 |   6.9  |  -0.21 |   -9.24 |
| BSR        | PRECIOUS      | GENUINE2 |   4 |     158576 | STONE | STONE`PRECIOUS`AA`4 PT OR 2.1 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                  |   7.5  |   6   |   8.03 |  10.7  |  22.77 |  18.22 |  15.27 |  2.036     |   8.63 |   6.904 |   6.9  |  -1.13 |  -11.32 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   5 |     157412 | STONE | STONE`GENUINE`MEDIUM QUALITY`5 PT OR 2.25 MM`BLACK ONYX`ROUND`REGULAR`````````````                         |   6.5  |   5.2 |   2.87 |   3.83 |   8.15 |   6.52 |   1.65 |  0.253846  |   7.48 |   5.984 |   6    |   3.13 |   -0.52 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   5 |     162891 | STONE | STONE`PRECIOUS``5 PT OR 2.25 MM`GARNET`ROUND``````````````                                                 |   6.5  |   5.2 |   3.19 |   4.25 |   9.04 |   7.23 |   2.54 |  0.390769  |   7.48 |   5.984 |   6    |   2.81 |   -1.23 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   5 |     158782 | STONE | STONE`PRECIOUS`AA`5 PT OR 2.25 MM`CITRINE`ROUND`FACETED`````````````                                       |   6.5  |   5.2 |   3.85 |   5.13 |  10.91 |   8.73 |   4.41 |  0.678462  |   7.48 |   5.984 |   6    |   2.15 |   -2.73 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   5 |     158915 | STONE | STONE`PRECIOUS``5 PT OR 2.25 MM`AMETHYST`ROUND`FACETED`````````````                                        |   6.5  |   5.2 |   4.3  |   5.73 |  12.19 |   9.75 |   5.69 |  0.875385  |   7.48 |   5.984 |   6    |   1.7  |   -3.75 |
| BSR        | PRECIOUS      | GENUINE2 |   5 |     162925 | STONE | STONE`PRECIOUS``5 PT OR 2.25 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                   |   8    |   6.4 |   7.11 |   9.48 |  20.17 |  16.14 |  12.17 |  1.52125   |   9.2  |   7.36  |   7.4  |   0.29 |   -8.74 |
| EMERALD    | PRECIOUS      | GENUINE3 |   5 |     162958 | STONE | STONE`PRECIOUS``5 PT OR 2.25 MM`EMERALD`ROUND`FACETED`````````````                                         |   8    |   6.4 |   7.11 |   9.48 |  20.17 |  16.14 |  12.17 |  1.52125   |   9.2  |   7.36  |   7.4  |   0.29 |   -8.74 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   5 |     158865 | STONE | STONE.PRECIOUS..5 PT OR 2.25 MM.AQUAMARINE.ROUND.................... 7000G0500500000                       |   6.5  |   5.2 |   7.3  |   9.73 |  20.7  |  16.56 |  14.2  |  2.18462   |   7.48 |   5.984 |   6    |  -1.3  |  -10.56 |
| RUBY       | PRECIOUS      | GENUINE3 |   5 |     162941 | STONE | STONE`PRECIOUS`B`5 PT OR 2.25 MM`RUBY`ROUND`FACETED`````````````                                           |   8    |   6.4 |   7.72 |  10.29 |  21.89 |  17.51 |  13.89 |  1.73625   |   9.2  |   7.36  |   7.4  |  -0.32 |  -10.11 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   6 |     157420 | STONE | STONE`GENUINE`MEDIUM QUALITY`6 PT OR 2.5 MM`BLACK ONYX`ROUND`REGULAR````````````` 700072500600000          |   6.75 |   5.4 |   2.92 |   3.89 |   8.28 |   6.62 |   1.53 |  0.226667  |   7.76 |   6.208 |   6.25 |   3.33 |   -0.37 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   6 |     162909 | STONE | STONE.PRECIOUS..6 PT OR 2.5 MM.GARNET.ROUND.FACETED................... 7000G2800600000                     |   6.75 |   5.4 |   3.58 |   4.77 |  10.15 |   8.12 |   3.4  |  0.503704  |   7.76 |   6.208 |   6.25 |   2.67 |   -1.87 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   6 |     900549 | STONE | STONE..GENUINE..6 PT OR 2.5 MM.AMETHYST.ROUND.FACETED.FACETED...........G07006.......                      |   6.75 |   5.4 |   4.46 |   5.95 |  12.66 |  10.13 |   5.91 |  0.875556  |   7.76 |   6.208 |   6.25 |   1.79 |   -3.88 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   6 |    1082529 | STONE | STONE`GENUINE``6 PT OR 2.5 MM`CITRINE`ROUND`FACETED`FACETED```````YELLOW TONE`````                         |   6.75 |   5.4 |   4.9  |   6.53 |  13.89 |  11.11 |   7.14 |  1.05778   |   7.76 |   6.208 |   6.25 |   1.35 |   -4.86 |
| BSR        | PRECIOUS      | GENUINE2 |   6 |     163188 | STONE | STONE.PRECIOUS.C.6 PT OR 2.5 MM.BLUE SAPPHIRE.ROUND.FACETED................... 7000G2600600000             |  10.5  |   8.4 |   5.58 |   7.44 |  15.83 |  12.66 |   5.33 |  0.507619  |  12.08 |   9.664 |   9.7  |   4.12 |   -2.96 |
| RUBY       | PRECIOUS      | GENUINE3 |   6 |     163154 | STONE | STONE.PRECIOUS.B.6 PT OR 2.5 MM.RUBY.ROUND.FACETED................... 7000G2500600000                      |  10.5  |   8.4 |   6.87 |   9.16 |  19.49 |  15.59 |   8.99 |  0.85619   |  12.08 |   9.664 |   9.7  |   2.83 |   -5.89 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   6 |     158873 | STONE | STONE.PRECIOUS..6 PT OR 2.5 MM.AQUAMARINE.ROUND.REGULAR................... 7000G0500600000                 |   6.75 |   5.4 |   7.72 |  10.29 |  21.89 |  17.51 |  15.14 |  2.24296   |   7.76 |   6.208 |   6.25 |  -1.47 |  -11.26 |
| EMERALD    | PRECIOUS      | GENUINE3 |   6 |     163295 | STONE | STONE.PRECIOUS.C.6 PT OR 2.5 MM.EMERALD.ROUND.FACETED................... 7000G2700600000                   |  10.5  |   8.4 |   9.1  |  12.13 |  25.81 |  20.65 |  15.31 |  1.4581    |  12.08 |   9.664 |   9.7  |   0.6  |  -10.95 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |   8 |     157438 | STONE | STONE`GENUINE`MEDIUM QUALITY`8 PT OR 2.75 MM`BLACK ONYX`ROUND`REGULAR```````````````````` 700072500800000  |   7    |   5.6 |   2.99 |   3.99 |   8.49 |   6.79 |   1.49 |  0.212857  |   8.05 |   6.44  |   6.45 |   3.46 |   -0.34 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |   8 |     162917 | STONE | STONE: PRECIOUS.AA.8 PT OR 2.75 MM.GARNET.ROUND.FACETED.FACETED. 7000G2800800000                           |   7    |   5.6 |   3.15 |   4.2  |   8.94 |   7.15 |   1.94 |  0.277143  |   8.05 |   6.44  |   6.45 |   3.3  |   -0.7  |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |   8 |     158808 | STONE | STONE`PRECIOUS``8 PT OR 2.75 MM`CITRINE`ROUND`FACETED`````````````                                         |   7    |   5.6 |   3.72 |   4.96 |  10.55 |   8.44 |   3.55 |  0.507143  |   8.05 |   6.44  |   6.45 |   2.73 |   -1.99 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |   8 |     158923 | STONE | STONE`PRECIOUS``8 PT OR 2.75 MM`AMETHYST`ROUND`FACETED`````````````                                        |   7    |   5.6 |   4.53 |   6.04 |  12.85 |  10.28 |   5.85 |  0.835714  |   8.05 |   6.44  |   6.45 |   1.92 |   -3.83 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |   8 |     158881 | STONE | STONE`PRECIOUS``8 PT OR 2.75 MM`AQUAMARINE`ROUND`FACETED`````````````                                      |   7    |   5.6 |   8.2  |  10.93 |  23.26 |  18.61 |  16.26 |  2.32286   |   8.05 |   6.44  |  12.45 |   4.25 |   -6.16 |
| EMERALD    | PRECIOUS      | GENUINE3 |   8 |     163303 | STONE | STONE.PRECIOUS.A.8 PT OR 2.75 MM.EMERALD.ROUND.FACETED.FACETED.................. 7000G2700800000           |  13.5  |  10.8 |   8.93 |  11.9  |  25.32 |  20.26 |  11.82 |  0.875556  |  15.53 |  12.424 |  12.45 |   3.52 |   -7.81 |
| BSR        | PRECIOUS      | GENUINE2 |   8 |     163196 | STONE | STONE.PRECIOUS.C.8 PT OR 2.75 MM.BLUE SAPPHIRE.ROUND.FACETED................... 7000G2600800000            |  13.5  |  10.8 |  10.42 |  13.89 |  29.55 |  23.64 |  16.05 |  1.18889   |  15.53 |  12.424 |  12.45 |   2.03 |  -11.19 |
| RUBY       | PRECIOUS      | GENUINE3 |   8 |     163162 | STONE | STONE.PRECIOUS.C.8 PT OR 2.75 MM.RUBY.ROUND.FACETED................... 7000G2500800000                     |  13.5  |  10.8 |  10.51 |  14.01 |  29.81 |  23.85 |  16.31 |  1.20815   |  15.53 |  12.424 |  12.45 |   1.94 |  -11.4  |
| BKO        | SEMI-PRECIOUS | GENUINE1 |  10 |     157446 | STONE | STONE`GENUINE`MEDIUM QUALITY`10 PT OR 3.0 MM`BLACK ONYX`ROUND`REGULAR````````````` 700072501000000         |  13.5  |  10.8 |   3    |   4    |   8.51 |   6.81 |  -4.99 | -0.36963   |  15.53 |  12.424 |  12.45 |   9.45 |    5.64 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |  10 |     163329 | STONE | STONE: PRECIOUS.10 PT OR 3.0 MM.GARNET.ROUND.FACETED. 7000G2801000000                                      |  13.5  |  10.8 |   3.22 |   4.29 |   9.13 |   7.3  |  -4.37 | -0.323704  |  15.53 |  12.424 |  12.45 |   9.23 |    5.15 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |  10 |     158816 | STONE | STONE: PRECIOUS.10 PT OR 3.0 MM.CITRINE.ROUND.FACETED. 7000G0401000000                                     |  13.5  |  10.8 |   3.79 |   5.05 |  10.74 |   8.59 |  -2.76 | -0.204444  |  15.53 |  12.424 |  12.45 |   8.66 |    3.86 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |  10 |     158931 | STONE | STONE`PRECIOUS``10 PT OR 3.0 MM`AMETHYST`ROUND`FACETED`````````````                                        |  13.5  |  10.8 |   4.74 |   6.32 |  13.45 |  10.76 |  -0.05 | -0.0037037 |  15.53 |  12.424 |  12.45 |   7.71 |    1.69 |
| EMERALD    | PRECIOUS      | GENUINE3 |  10 |     163287 | STONE | STONE.PRECIOUS.C+.10 PT OR 3.0 MM.EMERALD.ROUND.................... 7000G2701000000                        |  18.5  |  14.8 |  10.75 |  14.33 |  30.49 |  24.39 |  11.99 |  0.648108  |  21.28 |  17.024 |  17.05 |   6.3  |   -7.34 |
| BSR        | PRECIOUS      | GENUINE2 |  10 |     163204 | STONE | STONE`PRECIOUS``10 PT OR 3.0 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                   |  18.5  |  14.8 |  11.31 |  15.08 |  32.09 |  25.67 |  13.59 |  0.734595  |  21.28 |  17.024 |  17.05 |   5.74 |   -8.62 |
| RUBY       | PRECIOUS      | GENUINE3 |  10 |     163170 | STONE | STONE.PRECIOUS..10 PT OR 3.0 MM.RUBY.ROUND.FACETED................... 7000G2501000000                      |  18.5  |  14.8 |  13.24 |  17.65 |  37.55 |  30.04 |  19.05 |  1.02973   |  21.28 |  17.024 |  17.05 |   3.81 |  -12.99 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |  12 |     157453 | STONE | STONE..GENUINE.MEDIUM QUALITY.12 PT OR 3.25 MM.BLACK ONYX.ROUND.REGULAR................... 700072501200000 |  16    |  12.8 |   3.32 |   4.43 |   9.43 |   7.54 |  -6.57 | -0.410625  |  18.4  |  14.72  |  14.75 |  11.43 |    7.21 |
| BSR        | PRECIOUS      | GENUINE2 |  12 |     611186 | STONE | STONE`PRECIOUS`FIRST QUALITY`12 PT`BLUE SAPPHIRE`ROUND`FACETED`FACETED````````````                         |  28.5  |  22.8 |  12.13 |  16.17 |  34.4  |  27.52 |   5.9  |  0.207018  |  32.78 |  26.224 |  22    |   9.87 |   -5.52 |
| RUBY       | PRECIOUS      | GENUINE3 |  12 |     168245 | STONE | STONE: PRECIOUS.AA.12 PT OR 3.25 MM.RUBY.ROUND. 7000G0201200000                                            |  28.5  |  22.8 |  19.11 |  25.47 |  54.19 |  43.35 |  25.69 |  0.901404  |  32.78 |  26.224 |  26.25 |   7.14 |  -17.1  |
| EMERALD    | PRECIOUS      | GENUINE3 |  12 |     160770 | STONE | STONE`GENUINE``12 PT OR 3.25 MM`EMERALD`ROUND`FACETED`````````````                                         |  28.5  |  22.8 |  19.97 |  26.62 |  56.64 |  45.31 |  28.14 |  0.987368  |  32.78 |  26.224 |  26.25 |   6.28 |  -19.06 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |  15 |     904322 | STONE | STONE..GENUINE..15 PT OR 3.5 MM.GARNET.ROUND.FACETED...................                                    |  21    |  16.8 |   4    |   5.33 |  11.34 |   9.07 |  -9.66 | -0.46      |  24.15 |  19.32  |  19.35 |  15.35 |   10.28 |
| AMETHYST   | SEMI-PRECIOUS | GENUINE1 |  15 |     904323 | STONE | STONE..GENUINE..15 PT OR 3.5 MM.AMETHYST.ROUND.FACETED...................                                  |  21    |  16.8 |   4.2  |   5.6  |  11.91 |   9.53 |  -9.09 | -0.432857  |  24.15 |  19.32  |  19.35 |  15.15 |    9.82 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |  15 |     900516 | STONE | STONE..GENUINE.FIRST QUALITY.15 PT OR 3.5 MM.AQUAMARINE.ROUND....................                          |  21    |  16.8 |   8.61 |  11.48 |  24.43 |  19.54 |   3.43 |  0.163333  |  24.15 |  19.32  |  32    |  23.39 |   12.46 |
| BSR        | PRECIOUS      | GENUINE2 |  15 |     164343 | STONE | STONE`GENUINE`AA`15 PT OR 3.5 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                  |  48    |  38.4 |   9.19 |  12.25 |  26.06 |  20.85 | -21.94 | -0.457083  |  55.2  |  44.16  |  32    |  22.81 |   11.15 |
| RUBY       | PRECIOUS      | GENUINE3 |  15 |     248088 | STONE | STONE`GENUINE`AA`15 PT OR 3.5 MM`RUBY`ROUND`FACETED`````````````                                           |  48    |  38.4 |  33.45 |  44.59 |  94.87 |  75.9  |  46.87 |  0.976458  |  55.2  |  44.16  |  44.2  |  10.75 |  -31.7  |
| EMERALD    | PRECIOUS      | GENUINE3 |  15 |     168252 | STONE | STONE.PRECIOUS..15 PT OR 3.5 MM.EMERALD.ROUND.FACETED................... 7000G0301500000                   |  48    |  38.4 |  35.32 |  47.08 | 100.17 |  80.14 |  52.17 |  1.08688   |  55.2  |  44.16  |  44.2  |   8.88 |  -35.94 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |  20 |     951530 | STONE | STONE.SEMI-PRECIOUS..3.75MM.CITRINE.ROUND.FACETED.FACETED..................                                |  32.5  |  26   |   4.57 |   6.09 |  12.96 |  10.37 | -19.54 | -0.601231  |  37.38 |  29.904 |  29.9  |  25.33 |   19.53 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |  20 |     157461 | STONE | STONE`GENUINE`MEDIUM QUALITY`20 PT OR 3.75 MM`BLACK ONYX`ROUND`REGULAR`````````````                        |  32.5  |  26   |   4.94 |   6.59 |  14.02 |  11.22 | -18.48 | -0.568615  |  37.38 |  29.904 |  29.9  |  24.96 |   18.68 |
| BSR        | PRECIOUS      | GENUINE2 |  20 |     162412 | STONE | STONE.PRECIOUS..20 PT OR 3.75 MM.BLUE SAPPHIRE.ROUND.FACETED................... 7000G0102000000            |  75    |  60   |  15.95 |  21.26 |  45.23 |  36.18 | -29.77 | -0.396933  |  86.25 |  69     |  57    |  41.05 |   20.82 |
| RUBY       | PRECIOUS      | GENUINE3 |  20 |     951531 | STONE | STONE.PRECIOUS..3.75MM.RUBY.ROUND.FACETED.FACETED..................                                        |  75    |  60   |  39.18 |  52.23 | 111.13 |  88.9  |  36.13 |  0.481733  |  86.25 |  69     |  69    |  29.82 |  -19.9  |
| EMERALD    | PRECIOUS      | GENUINE3 |  20 |    1492992 | STONE | STONE`GENUINE``20 PT OR 3.75 MM`EMERALD``ROUND`FACET```AAA QUALITY`````````                                |  75    |  60   |  63.47 |  84.61 | 180.02 | 144.02 | 105.02 |  1.40027   |  86.25 |  69     |  69    |   5.53 |  -75.02 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |  25 |     157479 | STONE | STONE`GENUINE`MEDIUM QUALITY`25 PT OR 4.0 MM`BLACK ONYX`ROUND`REGULAR`````````````                         |  45    |  36   |   3.16 |   4.21 |   8.96 |   7.17 | -36.04 | -0.800889  |  51.75 |  41.4   |  41.4  |  38.24 |   34.23 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |  25 |     920686 | STONE | STONE`GENUINE``25 PT OR 4.0 MM`GARNET`ROUND`FACETED`FACETED```````````G12-025`                             |  45    |  36   |   3.3  |   4.4  |   9.36 |   7.49 | -35.64 | -0.792     |  51.75 |  41.4   |  41.4  |  38.1  |   33.91 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |  25 |    1046709 | STONE | STONE`SEMI-PRECIOUS``4 MM`CITRINE`ROUND`FACETED`FACETED````````````                                        |  45    |  36   |   4.19 |   5.59 |  11.89 |   9.51 | -33.11 | -0.735778  |  51.75 |  41.4   |  41.4  |  37.21 |   31.89 |
| AQUAMARINE | SEMI-PRECIOUS | GENUINE2 |  25 |    1061894 | STONE | STONE`GENUINE`AA`25 PT OR 4.0 MM`AQUAMARINE`ROUND`FACETED`````````````                                     |  45    |  36   |  39.18 |  52.23 | 111.13 |  88.9  |  66.13 |  1.46956   |  51.75 |  41.4   |  95    |  55.82 |    6.1  |
| BSR        | PRECIOUS      | GENUINE2 |  25 |     266288 | STONE | STONE`PRECIOUS``25 PT OR 4.0 MM`BLUE SAPPHIRE`ROUND`FACETED`````````````                                   | 125    | 100   |  52.43 |  69.89 | 148.7  | 118.96 |  23.7  |  0.1896    | 143.75 | 115     |  95    |  42.57 |  -23.96 |
| RUBY       | PRECIOUS      | GENUINE3 |  25 |     194498 | STONE | STONE`GENUINE`A`25 PT OR 4.0 MM`RUBY`ROUND`FACETED`````````````                                            | 125    | 100   |  57.95 |  77.25 | 164.36 | 131.49 |  39.36 |  0.31488   | 143.75 | 115     | 135    |  77.05 |    3.51 |
| EMERALD    | PRECIOUS      | GENUINE3 |  25 |     488973 | STONE | STONE.PRECIOUS.AA.25 PT OR 4.0 MM.EMERALD.ROUND.FACETED................... 7000G0302500000                 | 125    | 100   |  74.51 |  99.32 | 211.32 | 169.06 |  86.32 |  0.69056   | 143.75 | 115     | 135    |  60.49 |  -34.06 |
| BKO        | SEMI-PRECIOUS | GENUINE1 |  50 | 2000155656 | STONE | STONE`GENUINE``5 MM`BLACK ONYX`ROUND``````````````                                                         |  75    |  60   |   3.4  |   4.53 |   9.64 |   7.71 | -65.36 | -0.871467  |  86.25 |  69     |  69    |  65.6  |   61.29 |
| GARNET     | SEMI-PRECIOUS | GENUINE1 |  50 |     166470 | STONE | STONE`GENUINE``50 PT`GARNET`ROUND`FACETED`````````````                                                     |  75    |  60   |   3.49 |   4.65 |   9.89 |   7.91 | -65.11 | -0.868133  |  86.25 |  69     |  69    |  65.51 |   61.09 |
| CITRINE    | SEMI-PRECIOUS | GENUINE1 |  50 |     794909 | STONE | STONE..GENUINE..50 PT OR 5.0 MM.CITRINE.ROUND.................... 7000G0405000000                          |  75    |  60   |   3.89 |   5.19 |  11.04 |   8.83 | -63.96 | -0.8528    |  86.25 |  69     |  69    |  65.11 |   60.17 |
| BSR        | PRECIOUS      | GENUINE2 |  50 |     166710 | STONE | STONE.PRECIOUS.AA.50 PT OR 5.0 MM.BLUE SAPPHIRE.ROUND.FACETED................... 7000G0105000000           | 425    | 340   | 117.6  | 156.76 | 333.53 | 266.82 | -91.47 | -0.215224  | 488.75 | 391     | 325    | 207.4  |   58.18 |
| EMERALD    | PRECIOUS      | GENUINE3 |  50 |     909478 | STONE | STONE.GENUINE.A.50 PT OR 5.0 MM.EMERALD.ROUND.FACETED.FACETED..................                            | 425    | 340   | 140.75 | 187.62 | 399.19 | 319.35 | -25.81 | -0.0607294 | 488.75 | 391     | 391    | 250.25 |   71.65 |
| RUBY       | PRECIOUS      | GENUINE3 |  50 |     166165 | STONE | STONE`GENUINE``50 PT OR 5.0 MM`RUBY`ROUND`FACETED`````````````                                             | 425    | 340   | 243.93 | 325.16 | 691.83 | 553.46 | 266.83 |  0.627835  | 488.75 | 391     | 391    | 147.07 | -162.46 |



label: N=L-H
O=N/H
S=R-J
T=R-M
labeled_formulas: N=L-H
O=N/H
S=R-J
T=R-M
output: {"Arithmetic-Relationship": ["N=L-H", "O=N/H", "S=R-J", "T=R-M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_688287___xlsx_216d58b302d32b0156af3d29b5c5d71688f1abae.xlsx___line_93