Thomson , Case 1: precomputed Kronecker statistics, part 3 of 3
DefinitionThomsonN7_case_one_stats_3In H. Tran's proof of the Thomson problem for seven electrons, the polynomial identity of the Case 1 certificate is checked by a Kronecker substitution: each of the 13 pieces of the identity expression (the minorant part , the four kernel blocks and the eight sum-of-squares blocks ) is mapped to a tuple of statistics with , .
This file records, as plain data, the precomputed tuples for the pieces S3, S4, S5, S6, S7. They are not trusted: the solution of the Case 1 lemma proves, by kernel evaluation, that each piece's statistics equal these values before using them.
Formalization Note In the source file these tuples appear as the right-hand sides of the theorems c1_stat_*; they are moved into definitions (with the large integers written in hexadecimal) only because of the platform's limits on submitted files.
import Definitions.Def_ThomsonN7_core
namespace ThomsonN7.Case1Stats
/-- Precomputed Kronecker statistics of piece `S3` of the Case 1 identity (`w = 179`, `D = 11`). -/
def val_S3 : ThomsonN7.Case1.C1Stat :=
(0x3b89d55d5d36430124f25ac035c500182fb6f0cc9a, 8, 8, 9,
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: Int))
/-- Precomputed Kronecker statistics of piece `S4` of the Case 1 identity (`w = 179`, `D = 11`). -/
def val_S4 : ThomsonN7.Case1.C1Stat :=
(0x158fdb6496330fbf92076e88ff3b5a4dbe0d7b8c8c, 9, 8, 8,
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: Int))
/-- Precomputed Kronecker statistics of piece `S5` of the Case 1 identity (`w = 179`, `D = 11`). -/
def val_S5 : ThomsonN7.Case1.C1Stat :=
(0x158b9f1871d1ece9526285f2d792b771488011e4f8, 8, 9, 8,
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: Int))
/-- Precomputed Kronecker statistics of piece `S6` of the Case 1 identity (`w = 179`, `D = 11`). -/
def val_S6 : ThomsonN7.Case1.C1Stat :=
(0x158255ccd55129c7a86b7480d7ad91d191e1d62b70, 8, 8, 9,
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: Int))
/-- Precomputed Kronecker statistics of piece `S7` of the Case 1 identity (`w = 179`, `D = 11`). -/
def val_S7 : ThomsonN7.Case1.C1Stat :=
(0x3f3af8c24c1f3578dc02cdcfd8c506665493ce8d94, 8, 8, 8,
((-0xe5aaec362fd06d7b3f3188ee08c65ef045054d7ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc69544f2740be4a130339dc47dce6843eebeaca0000000964cca8fa719e9025f7ba895a584affbbfe7870000000000000000000000000000000000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end ThomsonN7.Case1Stats