19_UBP Table of Elements Spatial Clusters

(this post is a copy of the PDF which includes images and is formatted correctly)

19_UBP_Table_of_Elements_Spatial_Clusters

UBP Table of Elements Spatial Clusters

Euan Craig, New Zealand August 9, 2025

Abstract

This document contains a detailed qualitative and quantitative presentation of element clusters derived from the Universal Binary Principle (UBP) spatial model- ing of the periodic table. For each cluster (0–14) the document lists: (1) Traditional periodic-table properties; (2) Encoded OffBit layer values (per the encoding scheme: Reality = Z/2, Information = Mass/5, Activation = Group, Unactivated = Period); (3) Summary statistics for encoded layers; and (4) qualitative observations prompts for interpretation.

1 Introduction

The Universal Binary Principle (UBP) maps elemental properties into a high-dimensional binary-spatial representation (OffBits placed in a 6D Bitfield). The following sections pro- vide a cluster-by-cluster presentation of the findings from K-Means clustering performed in the UBP 6D coordinate space. Each cluster block below is self-contained for easy re- view or extraction into a larger report. This is a first run attempt of mapping the Table of Elements within a fully functional UBP BitField, refinement of how the elements are encoded can be refined.

2 Cluster 0 (11 elements) Elements

Hf, Os, Hg, Bi, At, Rf, Hs, Mt, Cn, Lv, Ts

Traditional Periodic Table Properties

Symbol Name Z Group Period Block Electronegativity Mass

Hf Hafnium 72 Os Osmium 76 Hg Mercury 80 Bi Bismuth 83 At Astatine 85 Rf Rutherfordium 104 Hs Hassium 108 Mt Meitnerium 109 Cn Copernicium 112 Lv Livermorium 116 Ts Tennessine 117

Encoded OffBit Layer Values (Based on Encoding Scheme)

4 6d 1.30

8 6d 2.20 12 6d 2.00 15 6p 2.02 17 6p 2.20

4 7d 1.30 8 7d 2.20

178.49 190.23 200.59 208.98 210.00 267.00 277.00 276.00 285.00 293.00 294.00

9 7
12 7
16 7
17 7p 2.20

d 2.30 d 2.30 p 2.10

Reality (Z/2)

Information (Mass/5)

Activation (Group)

Unactivated (Period)

6 6 6 6 6 7 7 7 7 7 7

36 35 38 38 40 40 41 41 42 42 52 53 54 55 54 55 56 57 58 58 58 58

Summary Statistics for Encoded Layers within Cluster

Reality (Z/2)

count 11.000 000 mean 48.090 909 std 8.630 812 min 36.000 000 25% 40.500 000 50% 52.000 000 75% 55.000 000 max 58.000 000

Information (Mass/5)

11.000 000 48.363 636 9.058 396 35.000 000 40.500 000 53.000 000 56.000 000 58.000 000

Activation (Group)

11.000 000 11.090 909 4.846 742 4.000 000 8.000 000 12.000 000 15.500 000 17.000 000

Unactivated (Period)

11.000 000 6.545 455 0.522 233 6.000 000 6.000 000 7.000 000 7.000 000 7.000 000

Qualitative Observations

• Do elements in this cluster tend to be from similar Groups or Periods?
• Are they all metals, nonmetals, or metalloids?
• Do their encoded layer values show a tight range (indicating similar original properties)? • Are there any ’outliers’ in terms of traditional classification or encoded values?

3 Cluster 1 (7 elements) Elements

Sc, Ge, As, Zr, Ru, Te, Nd

Traditional Periodic Table Properties

Symbol Name

Sc Scandium Ge Germanium As Arsenic
Zr Zirconium Ru Ruthenium Te Tellurium Nd Neodymium

Z Group Period

Block Electronegativity Mass

21 3 4 d 32 14 4 p 33 15 4p

1.36 44.956 2.01 72.640 2.18 74.922

40 4 5 44 8 5 52 16 5 60 3 6

d 1.33 d 2.20 p 2.10 f 1.14

91.224 101.070 127.600 144.242

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2) Information (Mass/5) Activation (Group)

10 9 3 16 14 14 16 15 15 20 18 4 22 20 8 26 25 16 30 28 3

Summary Statistics for Encoded Layers within Cluster

Unactivated (Period)

Reality (Z/2)

count 7.000 000 mean 20.000 000 std 6.733 003 min 10.000 000 25% 16.000 000 50% 20.000 000 75% 24.000 000 max 30.000 000

Information (Mass/5)

7.000 000 18.428 571 6.553 807 9.000 000 14.500 000 18.000 000 22.500 000 28.000 000

Activation (Group)

7.000 000 9.000 000 5.887 841 3.000 000 3.500 000 8.000 000

14.500 000 16.000 000

4 4 4 5 5 5 6

Unactivated (Period)

7.000 000 4.714 286 0.755 929 4.000 000 4.000 000 5.000 000 5.000 000 6.000 000

Qualitative Observations

4 Cluster 2 (13 elements) Elements

Xe, Ce, W, Ir, Pt, Au, Pb, Po, Rn, Fr, Ac, Th, Pu

Traditional Periodic Table Properties

Symbol Name

Xe Xenon
Ce Cerium
W Tungsten Ir Iridium
Pt Platinum Au Gold
Pb Lead
Po Polonium Rn Radon
Fr Francium Ac Actinium Th Thorium Pu Plutonium

Z Group

Period Block Electronegativity Mass

Encoded OffBit Layer Values

(Based on Encoding Scheme)

18 5p 3 6 f 6 6 d 9 6 d

10 6 d 11 6d 14 6p 16 6p 18 6p

1 7 s 3 7 f 3 7 f 3 7 f

2.60 131.293 1.12 140.116 2.36 183.840 2.20 192.217 2.28 195.084 2.54 196.967 2.33 207.200 2.00 209.000 2.20 222.000 0.70 223.000 1.10 227.000 1.30 232.038 1.28 244.000

Reality (Z/2)

Information (Mass/5)

Activation (Group)

Unactivated (Period)

27 26 29 28 37 36 38 38 39 39 39 39 41 41 42 41 43 44 43 44 44 45 45 46 47 48

Summary Statistics for Encoded Layers within Cluster

Reality (Z/2)

count 13.000 000 mean 39.538 462 std 5.882 394 min 27.000 000 25% 38.000 000 50% 41.000 000 75% 43.000 000 max 47.000 000

Information (Mass/5)

13.000 000 39.615 385 6.576 961 26.000 000 38.000 000 41.000 000 44.000 000 48.000 000

Activation (Group)

13.000 000 8.846 154 6.175 842 1.000 000 3.000 000 9.000 000

14.000 000 18.000 000

Unactivated (Period)

13.000 000 6.230 769 0.599 145 5.000 000 6.000 000 6.000 000 7.000 000 7.000 000

Qualitative Observations

5 Cluster 3 (5 elements) Elements

Tc, Ag, Sn, Cs, Re

Traditional Periodic Table Properties

Symbol Name

Tc Technetium Ag Silver
Sn Tin
Cs Cesium

Re Rhenium

Z Group

Period Block Electronegativity Mass

43 47 50 55 75

7 5d 11 5d 14 5p

1 6s 7 6d

1.90 98.000 1.93 107.868 1.96 118.710 0.79 132.905 1.90 186.207

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

21 23 25 27 37

Information (Mass/5)

19 21 23 26 37

Activation (Group)

7 11 14 1 7

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

5 5 5 6 6

Unactivated (Period)

5.000 000 5.400 000 0.547 723 5.000 000 5.000 000 5.000 000 6.000 000 6.000 000

Reality (Z/2)

count 5.000 000 mean 26.600 000 std 6.228 965 min 21.000 000 25% 23.000 000 50% 25.000 000 75% 27.000 000 max 37.000 000

Information (Mass/5)

5.000 000 25.200 000 7.085 196 19.000 000 21.000 000 23.000 000 26.000 000 37.000 000

Activation (Group)

5.000 000 8.000 000 4.898 979 1.000 000 7.000 000 7.000 000

11.000 000 14.000 000

Qualitative Observations

6 Cluster 4 (3 elements) Elements

H, Ca, Kr

Traditional Periodic Table Properties

Symbol Name Z Group Period Block Electronegativity Mass

H Hydrogen 1 1 Ca Calcium 20 2 Kr Krypton 36 18

1 s 4 s 4 p

2.2 1.008 1.0 40.078 3.0 83.798

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2) Information (Mass/5) Activation (Group) Unactivated (Period)

0011 10 8 2 4 18 16 18 4

Summary Statistics for Encoded Layers within Cluster

count mean std min 25% 50% 75% max

Reality (Z/2)

3.000 000 9.333 333 9.018 500 0.000 000 5.000 000

10.000 000 14.000 000 18.000 000

Information (Mass/5)

3.0 8.0 8.0 0.0 4.0 8.0

12.0 16.0

Activation (Group)

3.000 000 7.000 000 9.539 392 1.000 000 1.500 000 2.000 000

10.000 000 18.000 000

Unactivated (Period)

3.000 000 3.000 000 1.732 051 1.000 000 2.500 000 4.000 000 4.000 000 4.000 000

Qualitative Observations

7 Cluster 5 (6 elements) Elements

Cr, Mn, Ni, Cu, Rb, Sr

Traditional Periodic Table Properties

Symbol Name Z Group

Period Block Electronegativity Mass

Cr Chromium 24 Mn Manganese 25 Ni Nickel 28 Cu Copper 29 Rb Rubidium 37 Sr Strontium 38

6 4d 1.66

7 4d 1.55 10 4d 1.91 11 4d 1.90

1 5s 0.82 2 5s 0.95

51.996 54.938 58.693 63.546 85.468 87.620

Encoded OffBit Layer Values

(Based on Encoding Scheme)

Reality (Z/2)

Information (Mass/5)

Activation (Group)

7 10 11 1 2

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

4 4 4 4 5 5

Unactivated (Period)

6.000 000 4.333 333 0.516 398 4.000 000 4.000 000 4.000 000 4.750 000 5.000 000

Reality (Z/2)

count 6.000 000 mean 14.833 333 std 2.994 439 min 12.000 000 25% 12.500 000 50% 14.000 000 75% 17.000 000 max 19.000 000

Information (Mass/5)

6.000 000 13.000 000 3.162 278 10.000 000 11.000 000 11.500 000 15.750 000 17.000 000

Activation (Group)

6.000 000 6.166 667 4.070 217 1.000 000 3.000 000 6.500 000 9.250 000

11.000 000

Qualitative Observations

• Are there any ’outliers’ in terms of traditional classification or encoded values? 8 Cluster 6 (9 elements)

Elements

K, Ti, V, Fe, Co, Zn, Ga, Se, Br

Traditional Periodic Table Properties

Symbol Name

Z Group

Period Block Electronegativity Mass

K Potassium 19 Ti Titanium 22 V Vanadium 23 Fe Iron 26 Co Cobalt 27 Zn Zinc 30 Ga Gallium 31 Se Selenium 34 Br Bromine 35

1 4s 4 4d 5 4d 8 4d 9 4d

12 4d 13 4 p 16 4 p 17 4 p

0.82 39.098 1.54 47.867 1.63 50.942 1.83 55.845 1.88 58.933 1.65 65.409 1.81 69.723 2.55 78.960 2.96 79.904

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2) Information (Mass/5) Activation (Group) Unactivated (Period)

9714 11 9 4 4 11 10 5 4 13 11 8 4 13 11 9 4 15 13 12 4 15 14 13 4 17 15 16 4 17 16 17 4

Summary Statistics for Encoded Layers within Cluster

count mean std min 25% 50% 75% max

Reality (Z/2)

9.000 000 13.444 444 2.788 867 9.000 000 11.000 000 13.000 000 15.000 000 17.000 000

Information (Mass/5)

9.000 000 11.777 778 2.948 634 7.000 000 10.000 000 11.000 000 14.000 000 16.000 000

Activation (Group)

9.000 000 9.444 444 5.502 525 1.000 000 5.000 000 9.000 000

13.000 000 17.000 000

Unactivated (Period)

9.0 4.0 0.0 4.0 4.0 4.0 4.0 4.0

Qualitative Observations

9 Cluster 7 (11 elements) Elements

Pa, U, Np, Ubn95, Bh, Ds, Rg, Fl, Mc, Og, Ubn119

Traditional Periodic Table Properties

Symbol Name Z Group Period

Block Electronegativity

Mass

231.036 000 238.029 000 237.000 000 227.038 419 270.000 000 281.000 000 280.000 000 289.000 000 288.000 000 294.000 000 302.847 887

Pa Protactinium 91 3 U Uranium 92 3 Np Neptunium 93 3 Ubn95 Element-95 95 11 Bh Bohrium 107 7 Ds Darmstadtium 110 10 Rg Roentgenium 111 11 Fl Flerovium 114 14 Mc Moscovium 115 15 Og Oganesson 118 18 Ubn119 Element-119 119 9

7 f 7 f 7 f 8 d 7 d 7 d 7 d 7 p 7 p 7 p 8 f

1.500 000 1.380 000 1.360 000 1.360 000 2.200 000 2.300 000 2.300 000 2.000 000 2.100 000 2.200 000 2.106 814

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

Information (Mass/5)

Activation (Group)

3 3 3

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

7 7 7 8 7 7 7 7 7 7 8

Unactivated (Period)

11.000 000 7.181 818 0.404 520 7.000 000 7.000 000 7.000 000 7.000 000 8.000 000

Reality (Z/2)

count 11.000 000 mean 52.636 364 std 5.554 687 min 45.000 000 25% 46.500 000 50% 55.000 000 75% 57.000 000 max 59.000 000

Information (Mass/5)

11.000 000 53.000 000 5.567 764 45.000 000 47.000 000 56.000 000 57.000 000 60.000 000

Activation (Group)

11.000 000 9.454 545 5.106 146 3.000 000 5.000 000

10.000 000 12.500 000 18.000 000

Qualitative Observations

10 Cluster 8 (5 elements)

Elements

He, N, Ne, P, Ar

Traditional Periodic Table Properties

Symbol Name Z Group

Period Block Electronegativity Mass

He Helium 2 N Nitrogen 7 Ne Neon 10 P Phosphorus 15 Ar Argon 18

18 1s 0.00 15 2p 3.04 18 2p 0.00 15 3p 2.19 18 3p 0.00

4.003 14.007 20.180 30.974 39.948

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

1 3 5 7 9

Information (Mass/5)

0 2 4 6 8

Activation (Group)

18 15 18 15 18

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

1 2 2 3 3

Unactivated (Period)

5.000 00 2.200 00 0.836 66 1.000 00 2.000 00 2.000 00 3.000 00 3.000 00

Reality (Z/2)

count 5.000 000 mean 5.000 000 std 3.162 278 min 1.000 000 25% 3.000 000 50% 5.000 000 75% 7.000 000 max 9.000 000

Information (Mass/5)

5.000 000 4.000 000 3.162 278 0.000 000 2.000 000 4.000 000 6.000 000 8.000 000

Activation (Group)

5.000 000 16.800 000 1.643 168 15.000 000 15.000 000 18.000 000 18.000 000 18.000 000

Qualitative Observations

11 Cluster 9 (6 elements)

Elements

Nb, Rh, Cd, In, I, Ba

Traditional Periodic Table Properties

Symbol Name

Nb Niobium Rh Rhodium Cd Cadmium In Indium

I Iodine Ba Barium

Z Group

Period Block Electronegativity Mass

415 5 d 459 5 d

48 12 5 d
49 13 5 p

53 17 5p 562 6s

1.60 92.906 2.28 102.906 1.69 112.411 1.78 114.818 2.66 126.904 0.89 137.327

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

Information (Mass/5)

Activation (Group)

9 12 13 17 2

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

5 5 5 5 5 6

Unactivated (Period)

6.000 000 5.166 667 0.408 248 5.000 000 5.000 000 5.000 000 5.000 000 6.000 000

Reality (Z/2)

count 6.000 000 mean 24.000 000 std 2.828 427 min 20.000 000 25% 22.500 000 50% 24.000 000 75% 25.500 000 max 28.000 000

Information (Mass/5)

6.000 000 22.500 000 3.271 085 18.000 000 20.500 000 22.500 000 24.500 000 27.000 000

Activation (Group)

6.000 000 9.666 667 5.501 515 2.000 000 6.000 000

10.500 000 12.750 000 17.000 000

Qualitative Observations

12 Cluster 10 (5 elements) Elements

Ta, Tl, Ra, Db, Nh

Traditional Periodic Table Properties

Symbol Name Z Group Period

Block Electronegativity Mass

Ta Tantalum 73 Tl Thallium 81 Ra Radium 88 Db Dubnium 105 Nh Nihonium 113

5 6 d 13 6 p 2 7 s 5 7 d 13 7 p

1.50 180.948 1.62 204.383 0.90 226.000 1.50 270.000 1.80 284.000

Encoded OffBit Layer Values

(Based on Encoding Scheme)

Reality (Z/2)

36 40 44 52 56

Information (Mass/5)

36 40 45 54 56

Activation (Group)

5 13 2 5 13

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

6 6 7 7 7

Unactivated (Period)

5.000 000 6.600 000 0.547 723 6.000 000 6.000 000 7.000 000 7.000 000 7.000 000

Reality (Z/2)

count 5.000 000 mean 45.600 000 std 8.294 577 min 36.000 000 25% 40.000 000 50% 44.000 000 75% 52.000 000 max 56.000 000

Information (Mass/5)

5.000 000 46.200 000 8.671 793 36.000 000 40.000 000 45.000 000 54.000 000 56.000 000

Activation (Group)

5.000 00 7.600 00 5.079 37 2.000 00 5.000 00 5.000 00

13.000 00 13.000 00

Qualitative Observations

13 Cluster 11 (8 elements) Elements

Be, B, O, F, Mg, Al, S, Cl

Traditional Periodic Table Properties

Symbol Name Z Group

Period Block Electronegativity Mass

Be Beryllium 4 B Boron 5 O Oxygen 8 F Fluorine 9 Mg Magnesium 12 Al Aluminum 13 S Sulfur 16 Cl Chlorine 17

2 2s 1.57 13 2p 2.04 16 2p 3.44 17 2p 3.98

2 3s 1.31 13 3p 1.61 16 3p 2.58 17 3p 3.16

9.012 10.811 15.999 18.998 24.305 26.982 32.065 35.453

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2) Information (Mass/5) Activation (Group) Unactivated (Period)

2122 2 2 13 2 4 3 16 2 4 3 17 2 6423 6 5 13 3 8 6 16 3 8 7 17 3

Summary Statistics for Encoded Layers within Cluster

Reality (Z/2)

count 8.000 000 mean 5.000 000 std 2.390 457 min 2.000 000 25% 3.500 000 50% 5.000 000 75% 6.500 000 max 8.000 000

Information (Mass/5)

8.000 00 3.875 00 2.031 01 1.000 00 2.750 00 3.500 00 5.250 00 7.000 00

Activation (Group)

8.000 000 12.000 000 6.369 571 2.000 000 10.250 000 14.500 000 16.250 000 17.000 000

Unactivated (Period)

8.000 000 2.500 000 0.534 522 2.000 000 2.000 000 2.500 000 3.000 000 3.000 000

Qualitative Observations

14 Cluster 12 (6 elements) Elements

Y, Mo, Pd, Sb, La, Pr

Traditional Periodic Table Properties

Symbol Name

Y Yttrium
Mo Molybdenum Pd Palladium
Sb Antimony
La Lanthanum
Pr Praseodymium

Z Group Period Block Electronegativity Mass

39 3 5d 1.22 42 6 5d 2.16 46 10 5d 2.20 51 15 5p 2.05 57 3 6f 1.10 59 3 6f 1.13

88.906

95.940 106.420 121.760 138.905 140.908

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

Information (Mass/5)

Activation (Group)

6 10 15 3 3

Unactivated (Period)

5 5 5 5 6 6

19 17 21 19 23 21 25 24 28 27 29 28

Summary Statistics for Encoded Layers within Cluster

Reality (Z/2)

count 6.000 000 mean 24.166 667 std 3.920 034 min 19.000 000 25% 21.500 000 50% 24.000 000 75% 27.250 000 max 29.000 000

Information (Mass/5)

6.000 000 22.666 667 4.412 105 17.000 000 19.500 000 22.500 000 26.250 000 28.000 000

Activation (Group)

6.000 000 6.666 667 4.926 121 3.000 000 3.000 000 4.500 000 9.000 000

15.000 000

Unactivated (Period)

6.000 000 5.333 333 0.516 398 5.000 000 5.000 000 5.000 000 5.750 000 6.000 000

Qualitative Observations

15 Cluster 13 (5 elements) Elements

Ubn103, Ubn103, Ubn103, Ubn103, Sg
(Note: the provided table contains multiple repeated Ubn103 entries followed by Sg; the encoded rows below reflect the provided list.) I left this in here for transparency.

Traditional Periodic Table Properties

Symbol Name

Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Ubn103 Element-103 Sg Seaborgium

Z Group Period

Block Electronegativity

Mass

245.130 268 249.933 375 245.130 268 249.933 375 245.130 268 249.933 375 245.130 268 249.933 375 271.000 000

103 8 103 8 103 8 103 8 103 8 103 8 103 8 103 8 106 6

8 g 8 f 8 g 8 f 8 g 8 f 8 g 8 f 7 d

1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9 1.9

Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2)

Information (Mass/5)

Activation (Group)

8 8 8 8 8 8 8 8 6

Unactivated (Period)

Summary Statistics for Encoded Layers within Cluster

8 8 8 8 8 8 8 8 7

Unactivated (Period)

9.000 000 7.888 889 0.333 333 7.000 000 8.000 000 8.000 000 8.000 000 8.000 000

Reality (Z/2)

count 9.000 000 mean 51.222 222 std 0.666 667 min 51.000 000 25% 51.000 000 50% 51.000 000 75% 51.000 000 max 53.000 000

Information (Mass/5)

9.000 000 50.000 000 1.581 139 49.000 000 49.000 000 50.000 000 50.000 000 54.000 000

Activation (Group)

9.000 000 7.777 778 0.666 667 6.000 000 8.000 000 8.000 000 8.000 000 8.000 000

Qualitative Observations

16 Cluster 14 (4 elements)

Elements

Li, C, Na, Si

Traditional Periodic Table Properties

Symbol Name Z Group Period

Block Electronegativity Mass

Li Lithium 3 1 2 CCarbon6142
Na Sodium 11 1 3 s 0.93 22.990

p 1.90 28.086 Encoded OffBit Layer Values (Based on Encoding Scheme)

Reality (Z/2) Information (Mass/5) Activation (Group) Unactivated (Period)

1112 3 2 14 2 5413 7 5 14 3

Si Silicon 14 14 3

s 0.98 6.941 p 2.55 12.011

Summary Statistics for Encoded Layers within Cluster

Reality (Z/2)

count 4.000 000 mean 4.000 000 std 2.581 989 min 1.000 000 25% 2.500 000 50% 4.000 000 75% 5.500 000 max 7.000 000

Information (Mass/5)

4.000 000 3.000 000 1.825 742 1.000 000 1.750 000 3.000 000 4.250 000 5.000 000

Activation (Group)

4.000 000 7.500 000 7.505 553 1.000 000 1.000 000 7.500 000

14.000 000 14.000 000

Unactivated (Period)

4.000 00 2.500 00 0.577 35 2.000 00 2.000 00 2.500 00 3.000 00 3.000 00

Qualitative Observations

Appendix: Cluster-by-Cluster UBP Interpretation and Recom- mendations

Preface

The interpretation below treats each cluster as a compact set of UBP OffBit encodings (Reality = Z/2, Information = Mass/5, Activation = Group, Unactivated = Period) and attempts to read those numbers as coordinates in the UBP semantic space. For each cluster I provide:

A concise UBP interpretation (what the cluster represents in the encoded space).
True fits — elements that are consistent with that interpretation.
Anomalies / points of interest — elements that break expectation and merit follow- up.
Suggested follow-up tests that can confirm whether the observed grouping is chemi- cally meaningful or an artifact of encoding choices.

Cluster 0 (Hf, Os, Hg, Bi, At, Rf, Hs, Mt, Cn, Lv, Ts)

UBP interpretation: A heavy-element cluster dominated by late d-block and heavy p-block species. In OffBit terms this cluster sits at high Reality and Information values with moderately high Activation numbers (groups 4–17). It appears to capture high atomic number + high mass neighbourhoods (heavy, often relativistic elements).

True fits:

• Hf, Os, Hg, Bi, Cn, Lv: heavy elements with similar mass-scaled Information and high Reality.

Anomalies / points of interest:

At, Ts (halogen-like p-block) appear alongside heavy transition elements — suggests mass/period dominance in clustering overcame group chemical identity.
Mt, Rf, Hs — synthetic superheavies grouped by numerical proximity rather than estab- lished chemistry (expected for synthetic isotopes).

Suggested follow-ups:
- Test whether using electronegativity or block (s/p/d/f) as either additional encoded layers or as weights reduces the mixing of halogens with transition elements.
- Calculatepairwisechemicalsimilarity(e.g.,Paulingdifference+commonoxidationstates) and correlate with UBP distances to quantify chemical vs numeric grouping.

Cluster 1 (Sc, Ge, As, Zr, Ru, Te, Nd)

UBP interpretation: A mixed cluster with medium Reality/Information values and wide Activation variability. It groups early transition metals, metalloids and a lanthanoid, implying the OffBit encoding gives similar numeric signatures to chemically distinct elements when mass and period align.

True fits:

• Sc, Zr, Ru: transition metals with moderate Reality values.

Anomalies:

• Ge and As (metalloids/p-block) and Nd (f-block) clustered together — likely because mass/period quantization collapsed distinctions.

Suggested follow-ups:

Re-encode group such that group differences in the p-block and d-block produce larger separations (e.g., non-linear scaling of Activation).
Visualize cluster topology in 2D via UMAP with color by block to see if metalloids bridge transition/metalloid regions or are misplaced.

Cluster 2 (Xe, Ce, W, Ir, Pt, Au, Pb, Po, Rn, Fr, Ac, Th, Pu)

UBP interpretation: Another heavy cluster, but including noble gases (Xe, Rn), noble metals (Pt, Au), and early actinides — it captures inert/heavy behaviour and f-block proximity when encoded mass is large.

True fits:

• Pt, Au, W, Ir: late transition metals with clustered high Information and Reality.

• Ce, Ac, Th, Pu: f-block elements with comparable mass scaled values.

Anomalies:
- Xenon and Radon: noble gases mixing with heavy metals suggests encoded mass and period overshadow chemical inertness.
- Francium (Fr): alkali but placed here — again a mass/period dominated effect.
  
  Suggested follow-ups:
  - Introduce a binary flag layer for “noble gas / inert” (based on electronic closed shells) to preserve their distinctness in UBP coordinates.
  - Check whether replacing raw mass by mass density relative to block (mass minus block median) reduces noble gas drift.

Cluster 3 (Tc, Ag, Sn, Cs, Re)

UBP interpretation: An intermediate cluster with medium Reality and Information; a mix- ture of late 4th–6th period metals and a single alkali (Cs) — indicates local numeric similarity (Z/2 and mass/5) with divergent Activation values.

True fits:

• Ag, Sn, Re, Tc: metals whose mass/half-Z fall in a similar band.

Anomalies:

• Cs: alkali metal included despite low Activation value — implies period/mass alignment created proximity.

Suggested follow-ups:

•

Reassess distance metric: use a composite metric that penalizes Activation (group) dis- agreement more strongly than Reality/Information agreement.

Perform silhouette analysis per cluster to quantify how tightly elements are bound in chemical vs numeric sense.

Cluster 4 (H, Ca, Kr)

UBP interpretation: Small, widely spread cluster: hydrogen, an alkaline earth, and a noble gas. This suggests the encoding placed these three at low-to-moderate Reality/Information with distinct Activation/Period coordinates that nonetheless produce geometric proximity in the 6D embedding.

True fits:

• No clear homogeneous chemical interpretation — cluster likely an artefact of coarse quan- tization (small integer values).

Anomalies:

• H very special chemically; its placement with Ca and Kr likely exposes limits of dividing Z by 2 as a single Reality scale for elements at extremes.

Suggested follow-ups:

Apply non-linear scaling to Z for light elements (e.g., log or piecewise mapping) to avoid compressing H into low numeric bins that overlap with heavier elements.
Consider introducing a hydrogen special case or an electron configuration derived layer (1s occupancy) to preserve its uniqueness.

18 Cluster 5 (Cr, Mn, Ni, Cu, Rb, Sr)

UBP interpretation: A cluster dominated by 3d transition metals (Cr, Mn, Ni, Cu) plus two s-block metals (Rb, Sr) — indicates the 3d metals form a tight band in OffBit space but that neighbouring s-block elements can be pulled into proximity by mass encoding.

True fits:

• Cr, Mn, Ni, Cu: classic 3d series tightly grouped.

Anomalies:

• Rb and Sr: appearance suggests mass/period similarity to the 3d metals under current scaling.

Suggested follow-ups:

•

Weight the Activation (group) higher for s-block vs d-block separation so s-block elements do not collapse into d-block clusters purely by mass.

Compare clustering result with one obtained using electron configuration vectors (e.g., shell occupancy) as input.

Cluster 6 (K, Ti, V, Fe, Co, Zn, Ga, Se, Br)

UBP interpretation: A broad mid-period cluster spanning s, d and p block. Activation values in this cluster span 1 to 17 while Reality/Information remain midrange — the cluster seems to capture mid-Z elements that are numerically close.

True fits:

• Ti, V, Fe, Co, Zn: mid-Z transition metals that belong together.

Anomalies:

• Br, Se, Ga, K: p- and s-block elements appearing in the same cluster — again a conse- quence of coarse mass scaling.

Suggested follow-ups:

Introduce a small penalty term to the distance metric for block mismatch (s/p/d/f) to tighten block coherence where chemically necessary.
Run clustering constrained to the d-block only to validate intrinsic d-block structure.

20 Cluster 7 (Pa, U, Np, Ubn95, Bh, Ds, Rg, Fl, Mc, Og, Ubn119)

UBP interpretation: A high-Reality, high-Information cluster composed of heavy actinides and transactinides. The encoding reliably groups f-block and the heaviest synthetic elements together — a successful grouping by high mass and atomic number.

True fits:

• Pa, U, Np, Ac/Th family and superheavies: coherent in the high numeric band.

Anomalies:

• Some transactinides show Activation values scattered (groups 7–15) but remain close by Reality/Information — suggests numeric dominance over Activation.

Suggested follow-ups:

• Use this cluster as a benchmark: if chemically coherent (f-block and superheavy proxim- ity), your encoding captures heavy-element neighborhoods well. Validate using nuclear property correlations (half-life, common isotopic patterns).

Cluster 8 (He, N, Ne, P, Ar)

UBP interpretation: Light, nonmetal cluster — noble gases and small p-block elements. High Activation values (15–18) and low Reality/Information identify this as a light, highly electronegative / inert neighbourhood.

True fits:

N, P: p-block nonmetals with high electronegativity and mid Information relative to He/Ne/Ar.
He, Ne, Ar: noble gases correctly near each other in Activation though mass scaling moves them numerically.

Anomalies:

• Helium’s encoded electronegativity set to 0 and its small mass may still place it close to N/P in the current numeric scheme — consider special rules for noble gases.

Suggested follow-ups:
- Encode closed-shellness as an orthogonal bit (binary) to maintain noble gas separation where required.
- Correlate UBP distances in this cluster with ionization energy differences to confirm physical meaning.

22 Cluster 9 (Nb, Rh, Cd, In, I, Ba)

UBP interpretation: Mid-mass cluster mixing transition metals, a p-block halogen and an alkaline earth. Suggests the cluster is a numeric band of mid-Reality/Information where Acti- vation differences were insufficient to separate chemistries.

True fits:
• Nb, Rh, Cd, In: mid-Z elements whose mass and Z/2 values are numerically similar. Anomalies:
• Iodine and Barium co-located with transition metals — likely encoding artifact. Suggested follow-ups:

•

Increase resolution of Information layer (mass/5 may be too coarse for mid-Z discrimina- tions) — perhaps mass/2.5 or mass quantized into more levels.

Evaluate whether substituting isotopic stability (neutron:proton ratio) for raw mass im- proves grouping.

Cluster 10 (Ta, Tl, Ra, Db, Nh)

UBP interpretation: Heavy mid-to-late cluster mixing heavy transition metals with heavy p-block / s-block. Again, high Reality/Information values dominate.

True fits:

• Ta, Db: transition metals clustered by high Z/2 and high mass.

Anomalies:

• Tl, Ra, Nh: p- or s-block heavy elements grouped with d-block; suggests Activation was under-weighted.

Suggested follow-ups:

Reweight Activation (group) upward for heavy elements to distinguish d-block vs p-block in superheavy region.
Testhierarchicalclusteringtorevealwhethersubclusters(dvspheavyelements)naturally separate when using a stricter Activation weight.

24 Cluster 11 (Be, B, O, F, Mg, Al, S, Cl)

UBP interpretation: A chemically coherent light-element cluster: second and third period light metals and nonmetals. Low Reality/Information with moderate Activation spread; this cluster is one of the clearer chemical successes.

True fits:

• B, C-neighbours, O, F, Cl: p-block nonmetals show reasonable proximity. Mg, Al, Be also sit nearby as light metals.

Anomalies:

• The cluster actually reads well; it is an example where the encoding aligns with chemical intuition.

Suggested follow-ups:

• Use this cluster as a validation set — compute correlation between UBP distance and experimentally measured chemical properties (electronegativity, atomic radius).

Cluster 12 (Y, Mo, Pd, Sb, La, Pr)

UBP interpretation: Mid-heavy elements with a mixture of d and f block — suggests the encoding groups elements that share intermediate Reality/Information but differ in Activation. This cluster is suggestive of transitional behaviour between d and f blocks.

True fits:
• Mo, Pd, Y: d-block elements with similar numeric signatures.
• La, Pr: f-block elements with adjacent Reality/Information values.
Anomalies:
• Sb (p-block) sits here probably because its mass scaled value is near the d/f band. Suggested follow-ups:

Explore block-aware clustering (cluster within block partitions and compare results).
Consider adding an electron shell occupancy vector as encoded bits instead of raw group for better chemical separation.

26 Cluster 13 (Ubn103 repeated entries, Sg)

UBP interpretation: Highly consistent band mostly composed from repeated Ubn103 entries with a single Seaborgium outlier. The repetition in the dataset amplifies a highly tight numeric signature (Reality ≈ 51, Information ≈ 49–50) Included for transparency of this document.

True fits:

• The repeated Ubn103 records form a near-degenerate subspace — consistent numerically by construction.

Anomalies:

• Sg (Seaborgium) differs slightly but remains close numerically; presence of many identical records reduces interpretability.

Suggested follow-ups:

•

Remove duplicated entries (or consolidate them with average metadata) to avoid artifi- cially tightening clusters.

If duplicates represent different measured/estimated masses or blocks, make that explicit as separate metadata fields rather than identical symbol repeats.

Cluster 14 (Li, C, Na, Si)

UBP interpretation: A light, divergent cluster mixing alkali and p-block elements. Low Reality/Information and mixed Activation; it is another example where coarse scaling produces mixed chemical identity.

True fits:
• Li and Na: alkali pairing is chemically coherent.
• C and Si: p-block semiconductor / nonmetal pairing is also coherent. Anomalies:

• The cluster contains two chemically coherent pairs but grouped together by numeric proximity — suggests the cluster is actually two subclusters joined by small numeric gaps.

Suggested follow-ups:

Apply a finer clustering resolution (larger k or hierarchical cut) to split the alkali and p-block subclusters.
Consider dynamic quantization for Activation (group) to preserve semiconductor vs alkali separations when Reality/Information coincide.

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19_UBP Table of Elements Spatial Clusters

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