Fibonacci M747P168

Alpha

168 native Fibonacci residues on the period circle.

Clock position 168 is north. Remainder zero is displayed as 747.

Fibonacci recurrence modulo 747. The initial state (0, 1) first returns after 168 steps.

747 · 1 · 1 · 2 · 3 · 5 · 8 · 13 · 21 · 34 · 55 · 89 · 144 · 233 · 377 · 610 · 240 · 103 · 343 · 446 · 42 · 488 · 530 · 271 · 54 · 325 · 379 · 704 · 336 · 293 · 629 · 175 · 57 · 232 · 289 · 521 · 63 · 584 · 647 · 484 · 384 · 121 · 505 · 626 · 384 · 263 · 647 · 163 · 63 · 226 · 289 · 515 · 57 · 572 · 629 · 454 · 336 · 43 · 379 · 422 · 54 · 476 · 530 · 259 · 42 · 301 · 343 · 644 · 240 · 137 · 377 · 514 · 144 · 658 · 55 · 713 · 21 · 734 · 8 · 742 · 3 · 745 · 1 · 746 · 747 · 746 · 746 · 745 · 744 · 742 · 739 · 734 · 726 · 713 · 692 · 658 · 603 · 514 · 370 · 137 · 507 · 644 · 404 · 301 · 705 · 259 · 217 · 476 · 693 · 422 · 368 · 43 · 411 · 454 · 118 · 572 · 690 · 515 · 458 · 226 · 684 · 163 · 100 · 263 · 363 · 626 · 242 · 121 · 363 · 484 · 100 · 584 · 684 · 521 · 458 · 232 · 690 · 175 · 118 · 293 · 411 · 704 · 368 · 325 · 693 · 271 · 217 · 488 · 705 · 446 · 404 · 103 · 507 · 610 · 370 · 233 · 603 · 89 · 692 · 34 · 726 · 13 · 739 · 5 · 744 · 2 · 746 · 1

Beta

Interior interval sums on the native 747-position circle.

Original start: 4. No nonconstant doubling cycle in these interval sums.

Interior sums: 4, 26, 178, 1220, 892, 1289, 1408, 1097, 1042, 1715, 1252, 1073, 1030, 1655, 844, 1265, 1288, 1028, 1426, 1484, 1492, 2237, 2215, 2063, 1021, 1349, 952, 833, 1144, 1199, 526, 989, 1168, 1211, 586, 1397, 976, 953, 1213, 815, 757, 749. Modulo 747: 4, 26, 178, 473, 145, 542, 661, 350, 295, 221, 505, 326, 283, 161, 97, 518, 541, 281, 679, 737, 745, 743, 721, 569, 274, 602, 205, 86, 397, 452, 526, 242, 421, 464, 586, 650, 229, 206, 466, 68, 10, 2. First interval: clock positions 168 to 4. Endpoints excluded; wraparound included. Original phase is preserved.

4 → 26 → 178 → 473 → 145 → 542 → 661 → 350 → 295 → 221 → 505 → 326 → 283 → 161 → 97 → 518 → 541 → 281 → 679 → 737 → 745 → 743 → 721 → 569 → 274 → 602 → 205 → 86 → 397 → 452 → 526 → 242 → 421 → 464 → 586 → 650 → 229 → 206 → 466 → 68 → 10 → 2

Gamma

Primary nodal geometry.

Clockwise node order, starting from north.

Clock positions: 168, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164. The primary selection uses native residues divisible by three, including zero. Regular triangles are drawn only when their vertices lie in this node set. Additional formations are available in Geometry summary.

747 · 3 · 21 · 144 · 240 · 42 · 54 · 336 · 57 · 63 · 384 · 384 · 63 · 57 · 336 · 54 · 42 · 240 · 144 · 21 · 3 · 747 · 744 · 726 · 603 · 507 · 705 · 693 · 411 · 690 · 684 · 363 · 363 · 684 · 690 · 411 · 693 · 705 · 507 · 603 · 726 · 744

Epsilon

M747 shares M9’s unicursal geometry. Its native values become the repeating 9–3–6 sequence when reduced to modulus 9.

Native M747 · the path is present; its native values do not meet the 3–6–9 rule.

Clock position route: 168 → 56 → 140 → 84 → 28 → 112 → 168. Python checked: exact rational circle positions and reduced traversal. Physical interpretation not assessed.

747 → 336 → 411 → 747 → 336 → 411 → 747

Fibonacci M747P168

Native sequences and detected primary geometry in one frame.

Alpha uses 168 positions; Beta uses 747. White Epsilon path: exact M9 geometry and reduced traversal; native labels retained.

Only detected primary triangles and hexagons are drawn. Shared placement is a drawing convention and does not establish biological significance.

Alpha · Beta · Gamma · Epsilon

Modulus 747 · Pisano period 168 · M9 family

This page presents the recorded explanations, sequence values and evidence status. Long coordinate tables and formation enumerations are preserved in the complete linked data. Sequence arrays longer than 240 values are abbreviated in this HTML view.

Complete record JSON · Complete record CSV · Interactive geometry

Record SHA-256: ae4356b9c9cc5a3c1875a460e9556e4c131c0779543ac7d90ea2bb65805bc6ce
Dataset: m1-m1001-v1

conventions

index origin: 0
clock labels: 168 · 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11 · 12 · 13 · 14 · 15 · 16 · 17 · 18 · 19 · 20 · 21 · 22 · 23 · 24 · 25 · 26 · 27 · 28 · 29 · 30 · 31 · 32 · 33 · 34 · 35 · 36 · 37 · 38 · 39 · 40 · 41 · 42 · 43 · 44 · 45 · 46 · 47 · 48 · 49 · 50 · 51 · 52 · 53 · 54 · 55 · 56 · 57 · 58 · 59 · 60 · 61 · 62 · 63 · 64 · 65 · 66 · 67 · 68 · 69 · 70 · 71 · 72 · 73 · 74 · 75 · 76 · 77 · 78 · 79 · 80 · 81 · 82 · 83 · 84 · 85 · 86 · 87 · 88 · 89 · 90 · 91 · 92 · 93 · 94 · 95 · 96 · 97 · 98 · 99 · 100 · 101 · 102 · 103 · 104 · 105 · 106 · 107 · 108 · 109 · 110 · 111 · 112 · 113 · 114 · 115 · 116 · 117 · 118 · 119 · 120 · 121 · 122 · 123 · 124 · 125 · 126 · 127 · 128 · 129 · 130 · 131 · 132 · 133 · 134 · 135 · 136 · 137 · 138 · 139 · 140 · 141 · 142 · 143 · 144 · 145 · 146 · 147 · 148 · 149 · 150 · 151 · 152 · 153 · 154 · 155 · 156 · 157 · 158 · 159 · 160 · 161 · 162 · 163 · 164 · 165 · 166 · 167
orientation: clockwise from north
zero display: 747
alpha circle positions: 168
beta circle positions: 747
node rule: Native residues divisible by 3, including zero; preserves the approved M6/M9/M12 reference selection. Additional regular formations of all native values are catalogued separately.
m1 convention: Modulo 1 has period 1 and residue 0.

research

focus

OXTR gene expression

biological significance status

Not yet assessed

statistical significance status

Not yet assessed

quantum annealing status

Not yet performed

tiers

name
Creates cellular life
range
8 · 10
wss score
Not recorded
evidence
None recorded
name
Supports cellular life
range
5 · 7
wss score
Not recorded
evidence
None recorded
name
Creates elemental life
range
1 · 4
wss score
Not recorded
evidence
None recorded

background literature

register id: oxtr-phase1-literature
register version: 2026-10-18.1
register file: research-register.json
relationship: background_context
scope: Shared background literature for the initial OXTR research programme across M1–M1001. Studies of related mechanisms in other systems provide context for investigation.
publication ids: E01 · E02 · E03 · E04 · E05 · E06 · E07 · E08 · E09 · E10 · E11 · E12 · E13 · E14
hero publication ids: E03 · E06 · E08 · E11
modulus relevance status: Not yet assessed

verification

python: Passed
wolfram: Passed
scope: Native period, sequences, regular polygon index spacing and reference Epsilon routes; no physical or biological validation.
wolfram scope: Native Pisano period; complete Alpha, primary Gamma indices, Beta interval sums and residues, primary equilateral-triangle and hexagon indices. Independent integer Fibonacci evaluation and SHA-256 comparisons. Extended catalogue, Chevron and native/cycle-based Epsilon are Python-checked.
evidence: m1001-verification.json

geometry summary

rule version

native-pilot-v1

scope

Shapes in the primary Gamma node set (native residues divisible by 3, including zero). All regular polygons on the period circle are catalogued separately with their native values; their existence alone is a property of the plotting grid.

circle role

Pisano-period plotting framework

shapes

name
Equilateral triangle
status
Present
count
14
orientation
0° / 8.57143° / 17.1429° / 25.7143° / 34.2857° / 42.8571° / 51.4286° / 60° / 68.5714° / 77.1429° / 85.7143° / 94.2857° / 102.857° / 111.429°
rotation degrees
Not recorded
rotations degrees
0 · 8.571428571428571 · 17.142857142857142 · 25.714285714285715 · 34.285714285714285 · 42.857142857142854 · 51.42857142857143 · 60 · 68.57142857142857 · 77.14285714285714 · 85.71428571428571 · 94.28571428571429 · 102.85714285714286 · 111.42857142857143
alpha paths
1. 0 · 56 · 112 · 0
2. 4 · 60 · 116 · 4
3. 8 · 64 · 120 · 8
4. 12 · 68 · 124 · 12
5. 16 · 72 · 128 · 16
6. 20 · 76 · 132 · 20
7. 24 · 80 · 136 · 24
8. 28 · 84 · 140 · 28
9. 32 · 88 · 144 · 32
10. 36 · 92 · 148 · 36
11. 40 · 96 · 152 · 40
12. 44 · 100 · 156 · 44
13. 48 · 104 · 160 · 48
14. 52 · 108 · 164 · 52
name
Hexagon
status
Present
count
7
orientation
0° / 8.57143° / 17.1429° / 25.7143° / 34.2857° / 42.8571° / 51.4286°
rotation degrees
Not recorded
rotations degrees
0 · 8.571428571428571 · 17.142857142857142 · 25.714285714285715 · 34.285714285714285 · 42.857142857142854 · 51.42857142857143
alpha paths
1. 0 · 28 · 56 · 84 · 112 · 140 · 0
2. 4 · 32 · 60 · 88 · 116 · 144 · 4
3. 8 · 36 · 64 · 92 · 120 · 148 · 8
4. 12 · 40 · 68 · 96 · 124 · 152 · 12
5. 16 · 44 · 72 · 100 · 128 · 156 · 16
6. 20 · 48 · 76 · 104 · 132 · 160 · 20
7. 24 · 52 · 80 · 108 · 136 · 164 · 24
name
2D stellated octahedron
status
Present
count
7
orientation
0° / 8.57143° / 17.1429° / 25.7143° / 34.2857° / 42.8571° / 51.4286°
rotation degrees
Not recorded
rotations degrees
0 · 8.571428571428571 · 17.142857142857142 · 25.714285714285715 · 34.285714285714285 · 42.857142857142854 · 51.42857142857143
alpha paths
1. 0 · 56 · 112 · 0
2. 28 · 84 · 140 · 28
3. 4 · 60 · 116 · 4
4. 32 · 88 · 144 · 32
5. 8 · 64 · 120 · 8
6. 36 · 92 · 148 · 36
7. 12 · 68 · 124 · 12
8. 40 · 96 · 152 · 40
9. 16 · 72 · 128 · 16
10. 44 · 100 · 156 · 44
11. 20 · 76 · 132 · 20
12. 48 · 104 · 160 · 48
13. 24 · 80 · 136 · 24
14. 52 · 108 · 164 · 52
name
Chevron
status
Absent
count
0
orientation
Not recorded
rotation degrees
Not recorded
rotations degrees
None recorded
alpha paths
None recorded
name
Unicursal hexagram
status
Absent
count
0
orientation
Not recorded
rotation degrees
Not recorded
rotations degrees
None recorded
alpha paths
None recorded

other orientations status

Present

epsilon rule

A regular six-node formation must support the reference unicursal route through only 3, 6 and 9, containing all three. Rotations and reflections of the route are tested; reversed or cyclically shifted traversals are deduplicated.

alpha

residues: 0 · 1 · 1 · 2 · 3 · 5 · 8 · 13 · 21 · 34 · 55 · 89 · 144 · 233 · 377 · 610 · 240 · 103 · 343 · 446 · 42 · 488 · 530 · 271 · 54 · 325 · 379 · 704 · 336 · 293 · 629 · 175 · 57 · 232 · 289 · 521 · 63 · 584 · 647 · 484 · 384 · 121 · 505 · 626 · 384 · 263 · 647 · 163 · 63 · 226 · 289 · 515 · 57 · 572 · 629 · 454 · 336 · 43 · 379 · 422 · 54 · 476 · 530 · 259 · 42 · 301 · 343 · 644 · 240 · 137 · 377 · 514 · 144 · 658 · 55 · 713 · 21 · 734 · 8 · 742 · 3 · 745 · 1 · 746 · 0 · 746 · 746 · 745 · 744 · 742 · 739 · 734 · 726 · 713 · 692 · 658 · 603 · 514 · 370 · 137 · 507 · 644 · 404 · 301 · 705 · 259 · 217 · 476 · 693 · 422 · 368 · 43 · 411 · 454 · 118 · 572 · 690 · 515 · 458 · 226 · 684 · 163 · 100 · 263 · 363 · 626 · 242 · 121 · 363 · 484 · 100 · 584 · 684 · 521 · 458 · 232 · 690 · 175 · 118 · 293 · 411 · 704 · 368 · 325 · 693 · 271 · 217 · 488 · 705 · 446 · 404 · 103 · 507 · 610 · 370 · 233 · 603 · 89 · 692 · 34 · 726 · 13 · 739 · 5 · 744 · 2 · 746 · 1
display values: 747 · 1 · 1 · 2 · 3 · 5 · 8 · 13 · 21 · 34 · 55 · 89 · 144 · 233 · 377 · 610 · 240 · 103 · 343 · 446 · 42 · 488 · 530 · 271 · 54 · 325 · 379 · 704 · 336 · 293 · 629 · 175 · 57 · 232 · 289 · 521 · 63 · 584 · 647 · 484 · 384 · 121 · 505 · 626 · 384 · 263 · 647 · 163 · 63 · 226 · 289 · 515 · 57 · 572 · 629 · 454 · 336 · 43 · 379 · 422 · 54 · 476 · 530 · 259 · 42 · 301 · 343 · 644 · 240 · 137 · 377 · 514 · 144 · 658 · 55 · 713 · 21 · 734 · 8 · 742 · 3 · 745 · 1 · 746 · 747 · 746 · 746 · 745 · 744 · 742 · 739 · 734 · 726 · 713 · 692 · 658 · 603 · 514 · 370 · 137 · 507 · 644 · 404 · 301 · 705 · 259 · 217 · 476 · 693 · 422 · 368 · 43 · 411 · 454 · 118 · 572 · 690 · 515 · 458 · 226 · 684 · 163 · 100 · 263 · 363 · 626 · 242 · 121 · 363 · 484 · 100 · 584 · 684 · 521 · 458 · 232 · 690 · 175 · 118 · 293 · 411 · 704 · 368 · 325 · 693 · 271 · 217 · 488 · 705 · 446 · 404 · 103 · 507 · 610 · 370 · 233 · 603 · 89 · 692 · 34 · 726 · 13 · 739 · 5 · 744 · 2 · 746 · 1

beta

interval sums: 4 · 26 · 178 · 1220 · 892 · 1289 · 1408 · 1097 · 1042 · 1715 · 1252 · 1073 · 1030 · 1655 · 844 · 1265 · 1288 · 1028 · 1426 · 1484 · 1492 · 2237 · 2215 · 2063 · 1021 · 1349 · 952 · 833 · 1144 · 1199 · 526 · 989 · 1168 · 1211 · 586 · 1397 · 976 · 953 · 1213 · 815 · 757 · 749
interval residues: 4 · 26 · 178 · 473 · 145 · 542 · 661 · 350 · 295 · 221 · 505 · 326 · 283 · 161 · 97 · 518 · 541 · 281 · 679 · 737 · 745 · 743 · 721 · 569 · 274 · 602 · 205 · 86 · 397 · 452 · 526 · 242 · 421 · 464 · 586 · 650 · 229 · 206 · 466 · 68 · 10 · 2
display cycle: 4 · 26 · 178 · 473 · 145 · 542 · 661 · 350 · 295 · 221 · 505 · 326 · 283 · 161 · 97 · 518 · 541 · 281 · 679 · 737 · 745 · 743 · 721 · 569 · 274 · 602 · 205 · 86 · 397 · 452 · 526 · 242 · 421 · 464 · 586 · 650 · 229 · 206 · 466 · 68 · 10 · 2
minimal cycle: 4 · 26 · 178 · 473 · 145 · 542 · 661 · 350 · 295 · 221 · 505 · 326 · 283 · 161 · 97 · 518 · 541 · 281 · 679 · 737 · 745 · 743 · 721 · 569 · 274 · 602 · 205 · 86 · 397 · 452 · 526 · 242 · 421 · 464 · 586 · 650 · 229 · 206 · 466 · 68 · 10 · 2
native doubling: false
recognised doubling cycle: Not recorded
rotation to recognised: Not recorded
m9 doubling cycle present: false
start value: 4
start interval clock positions: 168 · 4
start interval values: 1 · 1 · 2
circle positions: 747
cycle length: 42
endpoint rule: Exclude endpoints, include wraparound; raw residues used for sums. Empty interiors sum to zero.

gamma

alpha indices

0 · 4 · 8 · 12 · 16 · 20 · 24 · 28 · 32 · 36 · 40 · 44 · 48 · 52 · 56 · 60 · 64 · 68 · 72 · 76 · 80 · 84 · 88 · 92 · 96 · 100 · 104 · 108 · 112 · 116 · 120 · 124 · 128 · 132 · 136 · 140 · 144 · 148 · 152 · 156 · 160 · 164

clock positions

168 · 4 · 8 · 12 · 16 · 20 · 24 · 28 · 32 · 36 · 40 · 44 · 48 · 52 · 56 · 60 · 64 · 68 · 72 · 76 · 80 · 84 · 88 · 92 · 96 · 100 · 104 · 108 · 112 · 116 · 120 · 124 · 128 · 132 · 136 · 140 · 144 · 148 · 152 · 156 · 160 · 164

clockwise values

triangle paths

0 · 56 · 112 · 0
4 · 60 · 116 · 4
8 · 64 · 120 · 8
12 · 68 · 124 · 12
16 · 72 · 128 · 16
20 · 76 · 132 · 20
24 · 80 · 136 · 24
28 · 84 · 140 · 28
32 · 88 · 144 · 32
36 · 92 · 148 · 36
40 · 96 · 152 · 40
44 · 100 · 156 · 44
48 · 104 · 160 · 48
52 · 108 · 164 · 52

epsilon status

Null: no tested regular six-node reference traversal contains only 3, 6 and 9 with all three present.

epsilon assessment

rule version: native-epsilon-diagnostics-v1
native 369 present: false
candidate count: 28
absence reason: No tested six-node formation contains only 3, 6 and 9 with all three present.
reference path available: true

reduction to m9

version

m9-reduction-v1

target modulus

status

Exact match

applicable

true

research question

Does the shared M9 pattern have shared biological relevance, or does native-modulus complexity change it? Unassessed: requires peer-reviewed evidence, in silico modelling (including proposed CUDA/CUDA-Q work), and appropriate experimental validation. No spatial-dimension claim or WSS score follows from this arithmetic match.

biological significance

Not yet assessed

native data preserved

true

repeat count

checks

alpha: true
gamma: true
beta: true
gamma indices: true

alpha residues

0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 0 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 0 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1

alpha display

9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1 · 9 · 1 · 1 · 2 · 3 · 5 · 8 · 4 · 3 · 7 · 1 · 8 · 9 · 8 · 8 · 7 · 6 · 4 · 1 · 5 · 6 · 2 · 8 · 1

gamma residues

0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6 · 0 · 3 · 3 · 0 · 6 · 6

gamma display

9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6 · 9 · 3 · 3 · 9 · 6 · 6

beta residues

4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2 · 4 · 8 · 7 · 5 · 1 · 2

beta display

recognised beta cycle

1 · 2 · 4 · 8 · 7 · 5

phase preserved

true

projected chevron

true

projected beta circle positions

gamma same single circle positions

false

geometry note

M18 and M9 share the same 24-position Gamma geometry. Reduced Beta is plotted on a nine-position circle. Longer periods require folding into 24-position cycles; their full circles are not identical.

identity

(F_n mod (9k)) mod 9 = F_n mod 9

interpretation

Exact reduction is a mathematical consequence of divisibility, not independent evidence of statistical or biological significance. Native Epsilon remains unchanged.

verification

Python full-period comparison

research register

schema version

1.0.0

id

oxtr-phase1-literature

version

2026-10-18.1

title

First Principles Genomics — research register

initial biological focus

OXTR

scope

Shared background literature for the initial OXTR research programme across M1–M1001. Studies of related mechanisms in other systems provide context for investigation.

relationship to atlas

background_context

modulus relevance status

Not yet assessed

hypothesis reference record id

fibonacci-m9-p24

hypothesis

The Alpha, Beta, Gamma and Epsilon sequences of M9P24 may offer useful descriptions of biological timing, cellular division and molecular organisation in the context of OXTR. Bioinformatics and in silico modelling provide the planned means of investigation.

interpretation

Publication findings describe their original experimental systems. Links from Atlas records identify shared reading; a sequence-to-biology correspondence remains open for assessment.

publication count

hero publication ids

E03 · E06 · E08 · E11

hero selection

Four lead references within the fourteen unique publications, one for each theme.

wss

status: Awaiting assessment
score: Not recorded
meaning: Future assessment of relevance to individual Atlas records. Publication trust scores remain separate from WSS.

appraisal method

id

provisional-editorial-v1

label

Provisional editorial trust

range

0 · 10

purpose

Prioritise closer reading of reported findings. This is an editorial assessment, without calibration or independent peer review.

components

design

range

0 · 3

criteria

0: Insufficient information
1: Descriptive observation
2: Structured measurement or comparative design
3: Controlled mechanistic test or quantitative prediction tested by manipulation

validation

range

0 · 3

criteria

0: Unassessed
1: Limited or abstract-level corroboration
2: Complementary evidence within the paper
3: Independent replication appraised

review

range

0 · 3

criteria

0: Unreviewed
1: Abstract, metadata or figure descriptions
2: Selected full-text sections
3: Main text, relevant methods/results and captions reviewed

provenance

range

0 · 1

criteria

0: Unverified
1: Verified primary peer-reviewed publication

independent replication appraisal

Not yet completed for this collection

citation policy

Crossref cited-by counts are a dated contextual snapshot and contribute no points. Coverage depends on deposited references. Unavailable counts remain null.

journal policy

Journal reputation and impact factor contribute no points.

jadad policy

Jadad concerns reporting of randomised clinical trials. It is not applicable to these fourteen study designs; no numeric Jadad score is assigned.

publications

id
E01
title
Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro
author
Nakajima et al.
year
2005
journal
Science
doi
10.1126/science.1108451
theme
Alpha · circadian timing
hero
Not recorded
methods
Purified cyanobacterial clock proteins; biochemical reconstitution
finding
KaiA, KaiB, KaiC and ATP supported self-sustaining phosphorylation oscillation. Temperature compensation and agreement between mutant periods in vitro and in vivo strengthened the biological interpretation.
relevance
direct evidence for a molecular timing mechanism; a broad Alpha reference independent of OXTR.
limit
biochemical reconstruction is more informative about mechanism than visual analogy. It is a cyanobacterial system, not a mammalian receptor study, and does not support a universal exact 24-hour period or M9 correspondence.
access
primary abstract and publication metadata. Replication and detailed methods require full-text appraisal before a formal quality rating.
score Parts
design
3
validation
1
review
1
provenance
1
score
6
score Reason
Molecular reconstitution tests a timing mechanism; appraisal currently covers the abstract and metadata.
jadad
Not applicable
citation Count
1020
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Reconstitution of Circadian Oscillation of Cyanobacterial KaiC Phosphorylation in Vitro
id
E02
title
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle
author
Feillet et al.
year
2014
journal
PNAS
doi
10.1073/pnas.1320474111
theme
Alpha / Beta · cycle coupling
hero
Not recorded
methods
Mouse fibroblasts; live-cell imaging and modelling
finding
live imaging of proliferating mouse fibroblasts, combined with modelling, identified phase locking and additional clock states under different conditions.
relevance
direct support for studying relationships between biological cycles; connects the Alpha and Beta research themes without making them equivalent.
limit
single-cell observations support the dynamical interpretation. Culture conditions and synchronisation matter, and related cells are not automatically independent replicates. No modular doubling or Atlas geometry was tested.
access
primary abstract and selected results, including period distributions. A phase-space representation is not evidence of a physical toroidal cell structure.
score Parts
design
2
validation
2
review
2
provenance
1
score
7
score Reason
Live-cell observations and modelling provide complementary evidence for phase locking; selected results appraised.
jadad
Not applicable
citation Count
216
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Phase locking and multiple oscillating attractors for the coupled mammalian clock and cell cycle
id
E03
title
Interaction between time-of-day and oxytocin efficacy in mice and humans with and without gestational diabetes
author
Duong et al.
year
2026 (online 2025)
journal
Molecular Metabolism
doi
10.1016/j.molmet.2025.102269
theme
Alpha · circadian regulation
hero
alpha
methods
Mouse genetics; human cells; retrospective human records
finding
mouse experiments support BMAL1 regulation of Oxtr and time-dependent oxytocin responsiveness. Human myometrial-cell experiments and records from 2,367 patients add distinct translational observations.
relevance
a direct OXTR connection to the Alpha theme.
limit
genetic perturbation and promoter experiments strengthen mechanism. Animal, cell and retrospective components need separate appraisal; the human observations can be confounded. Uterine findings do not establish effects in brain tissue.
access
final publication abstract and selected full-text results. The 2024 preprint is superseded for this register and is not counted as another study.
score Parts
design
3
validation
2
review
2
provenance
1
score
8
score Reason
Genetic and promoter experiments support mechanism; the human observational component has separate confounding limits.
jadad
Not applicable
citation Count
3
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Interaction between time-of-day and oxytocin efficacy in mice and humans with and without gestational diabetes
id
E04
title
Cryptochromes mediate rhythmic repression of the glucocorticoid receptor
author
Lamia et al.
year
2011
journal
Nature
doi
10.1038/nature10700
theme
Alpha · receptor regulation
hero
Not recorded
methods
Mouse cells and mice; genetic and biochemical experiments
finding
Cry1/Cry2 interacted with the glucocorticoid receptor and altered glucocorticoid-responsive transcription in mouse cells, with related metabolic phenotypes in mice.
relevance
direct circadian–receptor evidence provides a natural NR3C1 example beyond oxytocin.
limit
molecular interactions, genetic perturbations and physiological observations complement one another. Multiple pathways change in knockout animals; the results do not isolate a universal geometric explanation or establish human clinical effects.
access
primary abstract and selected experimental/results text. NR3C1 identifies the receptor target; the principal genetic perturbations here involved cryptochromes.
score Parts
design
3
validation
2
review
2
provenance
1
score
8
score Reason
Genetic perturbations, molecular interactions and physiological measurements support the reported mechanism.
jadad
Not applicable
citation Count
550
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Cryptochromes mediate rhythmic repression of the glucocorticoid receptor
id
E05
title
Experimental and theoretical study of mitotic spindle orientation
author
Théry et al.
year
2007
journal
Nature
doi
10.1038/nature05786
theme
Beta · mitotic geometry
hero
Not recorded
methods
Human HeLa cells; controlled adhesion geometry and modelling
finding
controlled adhesion patterns in human HeLa cells, combined with a physical model, accounted for spindle-orientation distributions across different microenvironment geometries.
relevance
direct evidence that geometry is a meaningful biological variable; supports interest in the Beta/division theme and related shape families.
limit
manipulation of the cell environment offers more than an observational resemblance. The model uses specific force assumptions and a transformed cell line. Division orientation is distinct from division rate, population doubling or a Fibonacci sequence.
access
publisher abstract and figure descriptions. Full methods and sample accounting remain to be appraised.
score Parts
design
3
validation
1
review
1
provenance
1
score
6
score Reason
Controlled adhesion geometry tests a quantitative model; full methods and sample accounting remain open for appraisal.
jadad
Not applicable
citation Count
424
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Experimental and theoretical study of mitotic spindle orientation
id
E06
title
Oxytocin promotes epicardial cell activation and heart regeneration after cardiac injury
author
Wasserman et al.
year
2022
journal
Frontiers in Cell and Developmental Biology
doi
10.3389/fcell.2022.985298
theme
Beta · proliferation
hero
beta
methods
Human stem-cell-derived epicardial cells and zebrafish
finding
OXT promoted activation and proliferation-related outcomes in human stem-cell-derived epicardial cells; OXTR knockdown removed the response. Zebrafish experiments supplied a separate regeneration context.
relevance
a direct OXTR-related example for the Beta research theme.
limit
receptor knockdown strengthens causal interpretation within the model. Check independent cell lines and differentiation batches; images are subsamples, not donors. Cultured epicardial cells and fish regeneration do not establish regeneration of adult human hearts.
access
primary full-text methods/results and relevant figure captions, including OXTR knockdown and proliferation measurements.
score Parts
design
3
validation
2
review
3
provenance
1
score
9
score Reason
Receptor knockdown provides a mechanistic test alongside cell and zebrafish experiments; methods and results appraised.
jadad
Not applicable
citation Count
25
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Oxytocin promotes epicardial cell activation and heart regeneration after cardiac injury
id
E07
title
Oxytocin stimulates hippocampal neurogenesis via oxytocin receptor expressed in CA3 pyramidal neurons
author
Lin et al.
year
2017
journal
Nature Communications
doi
10.1038/s41467-017-00675-5
theme
Beta · survival / proliferation
hero
Not recorded
methods
Mice; conditional Oxtr deletion
finding
conditional Oxtr deletion in mouse hippocampal excitatory neurons affected survival and maturation of newly generated neurons, while measured progenitor proliferation and early differentiation were unchanged.
relevance
direct evidence that the biological outcome must be named precisely. It bounds generalisations from E06 without contradicting a different tissue-specific finding.
limit
conditional genetics help localise the process. Appraise cell-type specificity, blinding and precision; an unchanged measured outcome does not prove absence of every possible effect.
access
primary results/discussion. Retained deliberately to avoid presenting all OXTR growth-related findings as evidence of duplication.
score Parts
design
3
validation
2
review
2
provenance
1
score
8
score Reason
Conditional genetics and cell-outcome measurements distinguish survival from proliferation in this mouse system.
jadad
Not applicable
citation Count
149
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Oxytocin stimulates hippocampal neurogenesis via oxytocin receptor expressed in CA3 pyramidal neurons
id
E08
title
Structural basis for the activation and ligand recognition of the human oxytocin receptor
author
Waltenspühl et al.
year
2022
journal
Nature Communications
doi
10.1038/s41467-022-31325-0
theme
Gamma · molecular recognition
hero
gamma
methods
Engineered human receptor complex; cryo-EM and functional assays
finding
cryo-EM at 3.2 Å and functional experiments characterised OXT recognition and receptor activation. All nine peptide residues participate in binding.
relevance
a direct structural foundation for Gamma's molecular-recognition theme; useful context, but not confirmation, for the OXT-specific Epsilon proposal.
limit
structure–function comparisons strengthen interpretation. Receptor stabilisation and an engineered G protein affect generalisation. The six-residue disulfide loop is not itself an aromatic hexagon; the reported contacts do not establish an Epsilon trajectory.
access
full primary article main text, receptor-engineering description and functional-assay captions. No new molecular analysis performed.
score Parts
design
3
validation
2
review
3
provenance
1
score
9
score Reason
Structural observations and functional residue tests provide complementary evidence; main text and assay descriptions appraised.
jadad
Not applicable
citation Count
46
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Structural basis for the activation and ligand recognition of the human oxytocin receptor
id
E09
title
X-ray structures and mechanism of the human serotonin transporter
author
Coleman, Green & Gouaux
year
2016
journal
Nature
doi
10.1038/nature17629
theme
Gamma · molecular recognition
hero
Not recorded
methods
Engineered human serotonin transporter; crystallography and assays
finding
structures of human SERT bound to antidepressants identified central and allosteric binding sites and explained aspects of inhibitor recognition.
relevance
direct structural evidence broadens Gamma beyond OXTR to SLC6A4.
limit
structural and binding/transport measurements are complementary. Thermostabilised constructs were used; the ts3 construct had no detectable transport activity. Results describe particular inhibitor-bound conformations rather than every physiological state.
access
publisher abstract and selected primary methods/results. These data concern the protein product and ligand recognition, not regulation of SLC6A4 gene expression.
score Parts
design
2
validation
2
review
2
provenance
1
score
7
score Reason
Structures and functional measurements complement one another; engineered constructs constrain interpretation.
jadad
Not applicable
citation Count
674
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
X-ray structures and mechanism of the human serotonin transporter
id
E10
title
Structure of a D2 dopamine receptor–G-protein complex in a lipid membrane
author
Yin et al.
year
2020
journal
Nature
doi
10.1038/s41586-020-2379-5
theme
Gamma · molecular recognition
hero
Not recorded
methods
Engineered human DRD2 complex in a lipid membrane; cryo-EM
finding
cryo-EM characterised an agonist-bound DRD2–Gi complex within a reconstituted phospholipid membrane, identifying receptor, G-protein and lipid interactions.
relevance
direct evidence for the structural context of molecular recognition; another Gamma hero example.
limit
including a lipid environment improves contextual relevance relative to isolated detergent structures. The receptor complex is engineered and ligand-bound; it does not represent every receptor state or establish clinical outcomes.
access
primary abstract and selected full-text structural results, with deposited structural metadata checked. No geometric correspondence to the Atlas was analysed.
score Parts
design
2
validation
1
review
2
provenance
1
score
6
score Reason
A membrane-reconstituted structural observation provides a defined molecular state; independent functional validation needs fuller appraisal.
jadad
Not applicable
citation Count
199
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Structure of a D2 dopamine receptor–G-protein complex in a lipid membrane
id
E11
title
Assembly of a π–π stack of ligands in the binding site of an acetylcholine-binding protein
author
Stornaiuolo et al.
year
2013
journal
Nature Communications
doi
10.1038/ncomms2900
theme
Epsilon · aromatic stacking
hero
epsilon
methods
Molluscan binding protein; crystallography and solution assays
finding
an Aplysia acetylcholine-binding protein accommodated a stack of three aromatic ligands. Solution binding measurements supported the structural observation.
relevance
direct experimental support for π-stacking as a molecular-recognition phenomenon; an Epsilon reference that does not depend on OXTR.
limit
crystallography, mutagenesis and solution assays help address crystallographic-artifact concerns. This soluble molluscan protein is a model for receptor ligand-binding domains, not a complete human receptor. Neither the three-ligand count nor the stacked geometry establishes the Atlas traversal.
access
full primary main text, including solution validation and scope of the receptor model.
score Parts
design
3
validation
2
review
3
provenance
1
score
9
score Reason
Structures, mutagenesis and solution assays support the binding interpretation; full main text appraised.
jadad
Not applicable
citation Count
66
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Assembly of a π–π stack of ligands in the binding site of an acetylcholine-binding protein
id
E12
title
Targeted disruption of pi–pi stacking in Malaysian banana lectin reduces mitogenicity while preserving antiviral activity
author
Covés-Datson et al.
year
2021
journal
Scientific Reports
doi
10.1038/s41598-020-80577-7
theme
Epsilon · aromatic stacking
hero
Not recorded
methods
Engineered plant lectin; structures and cellular assays
finding
an F84T mutation disrupted aromatic stacking in Malay BanLec, reduced mitogenic activity and retained antiviral activity in the studied assays.
relevance
a direct structure–function example for Epsilon; also connects molecular interactions with proliferation as a biological outcome.
limit
structural checks and functional comparisons strengthen the rationale. Mutation can change several properties simultaneously, so this is not a pure isolation of one energetic contribution. Plant-lectin effects do not establish OXTR behaviour or clinical benefit.
access
primary abstract and main structural/results sections. Published in 2021 despite “2020” appearing within the DOI.
score Parts
design
3
validation
2
review
2
provenance
1
score
8
score Reason
Targeted mutation and structural / cellular comparisons connect aromatic organisation with biological outcomes.
jadad
Not applicable
citation Count
24
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Targeted disruption of pi–pi stacking in Malaysian banana lectin reduces mitogenicity while preserving antiviral activity
id
E13
title
Reconstruction of molecular orbital densities from photoemission data
author
Puschnig et al.
year
2009
journal
Science
doi
10.1126/science.1176105
theme
Valence electron orbitals
hero
Not recorded
methods
Organic molecular films; photoemission and calculations
finding
photoemission measurements and Fourier reconstruction yielded orbital-density distributions for pentacene films and p-sexiphenyl monolayers, compared with density-functional calculations.
relevance
direct physics evidence for studying spatial electronic structure; contextual to the valence-electron theme and more distant from biological significance.
limit
comparison of measurement and theory is valuable. Reconstruction is model-dependent and the samples are non-living materials. Orbital densities are not classical electron orbits or evidence of unicursal electron motion.
access
primary abstract and metadata. No biological role, creation-of-life claim or numeric WSS assignment follows from this paper.
score Parts
design
2
validation
1
review
1
provenance
1
score
5
score Reason
Measurement and reconstruction are compared with calculations; current appraisal is abstract-level.
jadad
Not applicable
citation Count
334
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
Reconstruction of Molecular Orbital Densities from Photoemission Data
id
E14
title
CD38 is critical for social behaviour by regulating oxytocin secretion
author
Jin et al.
year
2007
journal
Nature
doi
10.1038/nature05526
theme
Supporting OXT context
hero
Not recorded
methods
Mice; Cd38 knockout and rescue experiments
finding
Cd38-knockout mice showed altered oxytocin secretion and behavioural phenotypes. Oxytocin replacement or hypothalamic delivery of human CD38 rescued selected outcomes.
relevance
direct support for CD38 involvement in the oxytocin system. Retained as supporting hero context without forcing it into a particular sequence family.
limit
knockout plus rescue strengthens causal interpretation in mice. Global deletion, behavioural measurement and human translation require careful appraisal. This concerns secretion, not proof of OXTR-expression regulation or geometric correspondence.
access
primary abstract and figure descriptions. Full methods are needed before formal risk-of-bias grading.
score Parts
design
3
validation
1
review
1
provenance
1
score
6
score Reason
Knockout and rescue experiments test the secretion mechanism; full methods remain open for appraisal.
jadad
Not applicable
citation Count
585
citation Source
Crossref cited-by count
citation Checked
17 October 2026
crossref Title
CD38 is critical for social behaviour by regulating oxytocin secretion

formation interval encoding

version: alpha-endpoints-v1
rule: For each formation interval, walk clockwise from from_index + 1 to to_index, excluding both endpoints and wrapping modulo P. Read values from alpha.residues. Endpoints, sum and residue are retained.