- verification script and data (gzip) Note the compressed size of the archive is 13M.
*Description of the files in the archive:***lemma_2_13-verify.sage**– the verification Sage script**extremal-7**– the densities of 7-vertex 3-graphs in the extremal limit (the 3-graphs are ordered as in the list of all K_{4}^{−}-free graphs generated by flagmatic 1.5.1, see below)**flags.rat**– the pairing densities for the types σ_1, …, σ_8 (generated by flagmatic 1.5.1)**ineq1**and**ineq2**– the inequalities (2.10) and (2.11) expressed as a combination of 7-vertex 3-graphs**gamma1**and**gamma2**– coefficients for the inequalities (2.10) and (2.11)**vectors_sigma1**, …,**vectors_sigma8**– list of vectors v^j_i for matrices M_1, …, M_8**weights_sigma1**, …,**weights_sigma8**– weights w^j_i of vectors v^j_i for matrices M_1, …, M_8

USAGE: run

*sage lemma_2_13-verify.sage*- Note that the computation requires around 7GB of RAM memory and hence a 64bit version of Sage.
- Also note that it takes around 60 minutes to run the computation (tested on Intel Core i7-3770 with 16GB RAM and AMD FX-8150 with 16GB RAM).

- Final vector generated by the script (gzip) Note the compressed size is 46M. This is file is not needed for the verification itself.
- list of 7-vertex 3-graphs and flags rooted on σ_1, …, σ_8 (gzip) Lists were generated by flagmatic 1.5.1. This file is not needed for the verification itself.

- verification script and data (gzip)
*Description of the files in the archive:***theorem_2_22-verify.sage**– the verification Sage script**pair1**, …,**pair4**– the pairing densities for the types σ_1, …, σ_4**M1**, …,**M4**– the positive definite matrices M'_1, …, M'_4**T1**, …,**T4**– the matrices T_1, … T_4

USAGE: run

*sage theorem_2_22-verify.sage* - list of 6-vertex 3-graphs and flags rooted on σ_1, …, σ_4 (gzip) This file is not needed for the verification itself.

- verification script and data (gzip)
*Description of the files in the archive:***thm_3_4-verify.sage**– the verification Sage script**goal_vector**– the vector of coefficients for 7-vertex graphs denoting K_4 density**pair1**,**pair2**– the pairing densities for the types σ_1 and σ_2**N1**,**N2**– the positive definite matrices N_1 and N_2**D1**,**D2**– the matrices D_1 and D_2

USAGE: run

*sage thm_3_4-verify.sage* - list of 7-vertex permutation graphs and flags rooted on σ_1 and σ_2 (gzip) This file is not needed for the verification itself.

- verification script and data (gzip)
*Description of the files in the archive:***thm_3_19-verify.sage**– the verification Sage script**goal_vector**– the vector of coefficients for 7-vertex graphs denoting K_5 density**pair1**, …,**pair4**– the pairing densities for the types σ_1, …, σ_4**N1**,**N2**,**M3**,**M4**– the positive definite matrices N_1, N_2, M_3 and M_4**D1**,**D2**– the matrices D_1 and D_2

USAGE: run

*sage thm_3_19-verify.sage* - list of 7-vertex permutation graphs and flags rooted on σ_1, …, σ_4 (gzip) This file is not needed for the verification itself.

- verification script and data (gzip) Note the compressed size of the archive is 5M.
*Description of the files in the archive:***thm_3_22-verify.sage**– the verification Sage script**goal_vector**– the vector of coefficients for 8-vertex graphs denoting K_6 density**pair1**, …,**pair31**– the pairing densities for the types σ_1, …, σ_31**N1**,**N2**,**N3**,**M4**,**N5**,**N6**,**M7**,**N8**,**M9**, …,**N31**– the positive definite matrices**D1**,**D2**,**D3**,**D5**,**D6**,**D8**– the matrices D_1, D_2, D_3, D_5, D_6 and D_8

USAGE: run

*sage thm_3_22-verify.sage*- Note that the computation requires around 3.5GB of RAM memory and hence a 64bit version of Sage.
- Also note that it takes around 20 minutes to run the computation (tested on Intel Core i7-3770 with 16GB RAM).

- list of 8-vertex permutation graphs and flags rooted on σ_1, …, σ_31 (gzip) This file is not needed for the verification itself.