5 August 2019 AD; Dedication of Basilica of St Mary Major in Rome (Our Lady of the Snows); St Emygdius

The sum of the pairs of elements will form either **a triangle** (sum of the internal angles equal to 180 deg) - this is a **pair of Quark and Graviton**.

Or another sum of the angles of the pair will form a quadrangle -** probably a rectangle**, with the sum of internal angles 360 deg this is the sum of **Neutrino and Boson**. If you add all four elements the sum of internal angles will be 540 deg forming **a pentagon (the sum of Quark angles, Graviton angles, Neutrino angles, and Boson angles)**. Other sums will have values of the angles between 180 deg and 360 deg.

To get the spherical angles correctly, I have to introduce an idea of a unit angle, which is about 90 deg.

For quark and graviton pair the calculation is as follows:

The sum of the quark angles equals to **90.4706 deg** + sum of the graviton angles equals to **90.5494 deg = 181.0200 deg. **

The arithmetic mean of this sum equals to** 181.0200 deg / 2 = 90.5100 deg.**

This is the unit angle for quark and graviton pair.

In a similar way unit angle of neutrino and boson, the sum equals to **257.8801 deg + 102.8371 deg = 360.7172 deg**

Dividing this value by 4 we get

**360.7172 deg / 4 = 90.1793 deg**

This is the unit angle for neutrino and boson pair.

Unit angles are necessary to calculate exactly value s of pairs, triplets, and singles as well as quadruplet of the sum of the angles.

**The first pair** of the angles - **quark and neutrino**:

Both neutrino/quark and neutrino/graviton pairs follow this rule:

**CP VilationPhase Angle δ = ( θ - 90 deg ) * ( 4 / 15 )**

where θ is the sum of the angles of a given pair of angles.

**90.4706 deg (quark) + 257.8801 deg (neutrino) = 348.3507 deg**

**δ CP quark/neutrino = 348.3507 deg - [( 90.5100 deg (quark unit angle) + 90. 1793 deg (neutrino unit angle) / 2 ] 348.3507 deg - 90. 3446 deg = 258.0060 deg 8 ( 4 / 15 ) = 68.8016 deg (spherical angle)**

**The second pair** of angles from the same family is **neutrino/graviton pair**:

257.8801 deg + 90.5494 deg = 348. 4295 deg

348.4295 deg - [ (90.5100 deg + 90.1793 deg ) / 2 ] = 258.0849 deg 8 ( 4 / 15 ) = **68.8226 deg (spherical CP angle)**

**The third pair** is **quark/boson pair** of angles.

They follow the rule:

**CP VilationPhase Angle δ = ( θ - 90 deg ) * ( 2 / 3 )**

where θ is the sum of the angles of a given pair of angles.

**90.4706 deg (quark) + 102.8371 deg (boson) = 193.3077 deg - 90.3446 deg = 102.9630 deg * ( 2 / 3 ) = 68.6420 deg (spherical CP Angle)**

**The fourth pair** is **boson/graviton pair**:

**δ CP Angle = 193.3865 deg - 90. 3446 deg = 103.0419 deg * ( 2 / 3 ) = 68.6946 deg (spherical CP Angle)**

**The fifth pair** is **quark/graviton pair:**

The rule is:

**δ CP Angle = ( θ + 180 deg ) * ( 4 / 21 )**

where θ is the sum of the angles of a given pair of angles.

**δ CP Angle = 90.4706 deg + 90.5494 deg + ( 181.0200 deg ) = 363.0399 deg * ( 4 / 21 ) = 68.9600 deg (spherical CP Angle)**

**The sixth pair** is **boson/neutrino pair.**

It follows the rule:

**δ CP Angle = ( θ ) * ( 4 / 21 )**

where θ is the sum of the angles of a given pair of angles.

**δ CP Angle = 102.8371 deg + 257.8801 deg = 360.7172 deg * ( 4 / 21 ) = 68.7080 deg (spherical CP Angle)**

**The arithmetic mean of all the six pairs is:**

**δ CP Mean Angle (pairs) = 412.6288 deg / 6 = 68.77147 deg**

To the same family belongs the **sum of all four elements** (quark/neutrino/boson/graviton), i.e. **pentagon**.

It follows the rule:

**δ CP Angle = ( θ - 180 deg ) * ( 4 / 21 )**

**δ CP Angle = 541.7372 deg (sum of all) - 2 * 90.3446 deg = 361.0479 deg * ( 4 / 21 ) = 68.7710 deg (spherical CP Angle for pentagon).**

The arithmetic mean of 6 pairs and a pentagon is equal to

**68.77147 deg * 6 + 68.7710 deg = 481.39987 deg / 7 = 68.77141 deg**

Next article - sums of the singles and triplets.

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