LINKED TABLE OF CONTENTS

FORWARD---1.1

INTRODUCTION---1.3

GLIMPSES---2.1

MUSIC OF WORLDS, HUMANITIES, INSTRUMENTS. (RE: ILLUSTRATION # P-1).---2.1

ORBIT OF PLUTO. (RE: ILLUSTRATION # P-2).---2.1

DOUBLING UNDERTONE, DIVIDING OVERTONE, (RE: ILLUSTRATION # P-3).---2.3

THE MAYAN KATON WHEEL 8 (RE: ILLUSTRATION # P-4).---2.3

VIBRATIONS OF A STRETCHED STRING. (RE: ILLUSTRATION # P-5).---2.4

MACROCOSMOS MULTIPLY - MICROCOSMOS DIVIDE. (RE: ILLUSTRATION # P-6).---2.5

SPIRAL GALAXIES TO QUASI STELLAR SOURCES. 12 (RE: ILLUSTRATION # P-7).---2.5

COLOR SPECTRUM MUSICAL INTERVALS PLANETS. (RE: ILLUSTRATION # P-8).---2.6

CHINESE COLOR MUSIC SCALE 15 VS. PYTHAGORAS COLOR MUSIC SCALE. 16 (RE: ILLUSTRATION # P-9).---2.6

COLOR NOTE VIBRATION SCALE. (RE: ILLUSTRATION # P-10).---2.6

COLOR NOTE VIBRATION SCALE. (RE: ILLUSTRATION # P-11).---2.7

FIELD OF OCTAVES OVERTONES-UNDERTONE. (RE: ILLUSTRATION # P-12).---2.7

FIELD OF OCTAVES OVERTONES UNDERTONE. (RE: ILLUSTRATION # P-13).---2.8

SPACE FOLDS ON A FIELD OF 64 DOTS. (RE: ILLUSTRATION # P-14).---2.8

EXPANDS. (RE: ILLUSTRATION # P-15).---2.9

PASCAL'S TRIANGLE. (RE: ILLUSTRATION # P-16).---2.9

SPACE FOLD CHART. (RE: ILLUSTRATION # P-17).---2.9

INVOLUTION EVOLUTION AXIS -ORBIT OF MUSICAL DIVISIONS. (RE: ILLUSTRATION # P-18).---2.10

BIRTH OF A MUSIC GALAXY. (RE: ILLUSTRATION # P-19).---2.11

ORBITS OF MUSICAL DIVISIONS (PULLED APART ON A FIELD OF NINE). (RE: ILLUSTRATION # P-20).---2.11

CORES OVERLAPPING. (RE: ILLUSTRATION # P-21).---2.11 ---2.11

IMPLOSION BECOMES EXPLOSION. (RE: ILLUSTRATION # P-22).---2.12

LOOPŠ. (RE: ILLUSTRATION # P-23).---2.12

CONTRACTING SPIRAL. (RE: ILLUSTRATION # P-24).---2.12

CHANGING DIRECTIONS. (RE: ILLUSTRATION # P-25).---2.13

PATTERNS OF MULTIPLES OF 2, 3, 5, 7. (RE: ILLUSTRATION # P-26).---2.13

BIBLIOGRAPHY---2.14

GLIMPSES OF BRIDGES OF ART---2.15

THOUGHTS WHILE WORKING---2.16

DIVISION OF STRING ON RIGHT ANGLES. (RE. ILLUSTRATION P-33). ---2.16

EYEŠ (CIRCLE) EXPANSION. EARŠ(SPIRAL) CONTRACTION. (RE. ILLUSTRATION P-34). ---2.16

AREA OF HEARING - DISTANCECOVERED BY A FALLING OBJECT. (RE. ILLUSTRATION P-35). ---2.17

MOBIUS STRIP. 4 (RE. ILLUSTRATION P-36). ---2.18

SECTIONING OF CIRCLES. (RE. ILLUSTRATIONS P-38 & P-39). ---2.19

I CHING PRIMAL ARRANGEMENT 10. (RE. ILLUSTRATION P-40). ---2.20

PRIMAL AXIS - INNER WORLD AXIS 11. (RE. ILLUSTRATION P-41). ---2.20

I CHING - PRIMAL AXIS, INNER WORLD AXIS. (RE. ILLUSTRATION P-42). ---2.21

I CHING CHART. (RE. ILLUSTRATION P-43). ---2.22

FIELD OF NOTES - INVOLUTION EVOLUTION AXIS. (RE. ILLUSTRATION P-44). ---2.22

I CHING SECOND ORDER. (RE. ILLUSTRATION P-45). ---2.22

PROGRESSION BY SQUARES. (RE. ILLUSTRATION P-46). ---2.23

CORES CONTRACTING EXPANDING. (RE. ILLUSTRATION P-48). ---2.26

COMPLETION OF CYCLE. (RE. ILLUSTRATION P-49). ---2.26

PROGRESSION BY SQUARES OVERLAPPING IN AN (S) CURVE. (RE. ILLUSTRATION P-50). ---2.27

FIVE STEPS. (RE. ILLUSTRATION P-51). ---2.27

DIAMETER OF EACH CIRCLE SECTIONED BY ITS RADIUS. (RE. ILLUSTRATION P-52). ---2.27

EXPANDS - CONTRACTS. (RE. ILLUSTRATION P-53). ---2.28

CONCAVE - CONVEX. (RE. ILLUSTRATION P-54). ---2.28

TIME - SPACE. (RE. ILLUSTRATION P-55). ---2.28

KEY. 15 (RE. ILLUSTRATION P-56). ---2.29

BIBLIOGRAPHY---2.30

SUGGESTED READING---2.30

GLIMPSES OF THE BRIDGES OF ART---3.1

MUSIC OF WORLDS HUMANITIES INSTRUMENTS---3.2

ILLUSTRATION: P-1---3.2

ILLUSTRATION: P-2---3.3

ORBIT OF PLUTO---3.3

DOUBLING - UNDERTONE / DIVIDING - OVERTONE---3.4

ILLUSTRATION: P-3---3.4

MAYAN KATON WHEEL---3.5

ILLUSTRATION: P-4---3.5

VIBRATIONS OF A STRETCHED STRING---3.6

ILLUSTRATION: P-5---3.6

ILLUSTRATION: P-6---3.7

MACROCOSMOS MULTIPLYŠ MICROCOSMOS DIVIDE---3.7

SPIRAL GALAXIES---3.8

ILLUSTRATION: P-7---3.8

ILLUSTRATION: P-8---3.9

COLOR SPECTRUMŠ MUSICAL INTERVALŠ PLANETS---3.9

CHINESE COLOR SCALE---3.10

ILLUSTRATION: P-9---3.10

ILLUSTRATION: P-10---3.11

COLOR NOTE VIBRATION SCALE---3.11

VIBRATING STRING---3.12

ILLUSTRATION: P-11---3.12

ILLUSTRATION: P-12---3.13

FIELD OF OCTAVES---3.13

FIELD OF OCTAVES---3.14

ILLUSTRATION: P-13---3.14

ILLUSTRATION: P-14---3.15

SPACE FOLDS ON A FIELD OF EIGHT---3.15

RE EXPANDS---3.16

ILLUSTRATION: P-15---3.16

ILLUSTRATION: P-16---3.17

PASCALS TRIANGLE---3.17

SPACE FOLD CHART---3.18

ILLUSTRATION: P-17---3.18

ILLUSTRATION: P-18---3.19

INVOLUTION AXIS EVOLUTION AXIS---3.19

BIRTH OF A MUSIC GALAXY---3.20

ILLUSTRATION: P-19---3.20

ILLUSTRATION: P-20---3.21

ORBITS OF MUSICAL DIVISIONS---3.21

CORES OVERLAPPING---3.22

ILLUSTRATION: P-21---3.22

ILLUSTRATION: P-22---3.23

IMPLOSION BECOMES EXPLOSION---3.23

LOOPŠ---3.24

ILLUSTRATION: P-23---3.24

ILLUSTRATION: P-24---3.25

CONTRACTING SPIRAL---3.25

CHANGING DIRECTIONS---3.26

ILLUSTRATION: P-25---3.26

PATTERNS OF MULTIPLES OF 2 3 5 7---3.27

ILLUSTRATION: P-26---3.27

CIRCLE OF FIFTHS---3.28

ILLUSTRATION: P-27---3.28

ILLUSTRATION: P-28---3.29

TIME CHART---3.29

MAN SPACE CHART---3.30

ILLUSTRATION: P-29---3.30

ILLUSTRATION: P-30---3.31

PERFECTION TRANSFORMATION CHART---3.31

SPACE IMMORTALITY CHART---3.32

ILLUSTRATION: P-31---3.32

ILLUSTRATION: P-32---3.33

TIME MOON CHART---3.33

DIVISION OF STRING ON RIGHT ANGLE---3.34

ILLUSTRATION: P-33---3.34

ILLUSTRATION: P-34---3.35

EYE CIRCLE EXPANSION---3.35

AREA OF HEARING---3.36

ILLUSTRATION: P-35---3.36

MOBIUS STRIP---3.37

ILLUSTRATION: P-36---3.37

I CHING HEXAGRAMS---3.38

MUSICAL RATIO AXIS---3.38

ILLUSTRATION: P-37---3.38

ILLUSTRATIONS: P-38 & P-39---3.39

SECTIONING OF CIRCLES---3.39

I CHING PRIMAL ARRANGEMENT---3.40

ILLUSTRATION: P-40---3.40

ILLUSTRATION: P-41---3.41

PRIMAL AXIS INNER WORLD AXIS---3.41

I CHING PRIMAL AXIS---3.42

INNER WORLD AXIS---3.42

ILLUSTRATION: P-42---3.42

ILLUSTRATION: P-43---3.43

I CHING CHART---3.43

FIELD OF NOTES---3.44

INVOLUTION-EVOLUTION AXIS---3.44

ILLUSTRATION: P-44---3.44

ILLUSTRATION: P-45---3.45

I CHING SECOND ORDER---3.45

PROGRESSION BY SQUARES---3.46

ILLUSTRATION: P-46---3.46

THE END BECOMES THE BEGINNING---3.47

ILLUSTRATION: P-47---3.47

CORES---3.48 CONTRACTING EXPANDING---3.48

ILLUSTRATION: P-48---3.48

ILLUSTRATION: P-49---3.49

COMPLETION OF CYCLE---3.49

PROGRESSION BY SQUARES OVERLAPPING IN AN (S) CURVE---3.50

ILLUSTRATION: P-50---3.50

ILLUSTRATION: P-51---3.51

FIVE STEPS---3.51

DIAMETER OF EACH CIRCLE SECTIONED BY ITS RADIUS---3.52

ILLUSTRATION: P-52---3.52

EXPANDS-CONTRACTS---3.53

ILLUSTRATION: P-53---3.53

CONCAVE-CONVEX---3.54

ILLUSTRATION: P-54---3.54

ILLUSTRATION: P-55---3.55

TIME-SPACE---3.55

KEY---3.56

ILLUSTRATION: P-56---3.56



STOP AND THINK---4.1



THE PAST CONTRACTS THE FUTURE EXPANDS 3" X 9"---4.2

ILLUSTRATION: S-1---4.2

PROJECTION OF A POLYGON 4" X 7"---4.3

ILLUSTRATION: S-2---4.3

PI EQUALS SIX 6" X 7"---4.4

ILLUSTRATION: S-3---4.4

ILLUSTRATION: S-4---4.5

RE ORBITŠ TI ORBITŠ LA ORBIT---4.5

THESE ARE SHAPES FOUND IN NATURE---4.6

ILLUSTRATION: S-5---4.6

ILLUSTRATION: S-6---4.7

WAVE LENGTHS OF SOUND WITH RINGS IN ORDER OF PROGRESSION 9" X 9"---4.7

INSIDE Š OUTSIDE---4.8

ILLUSTRATION: S-7---4.8

BLUES GREENS SEPARATE OUTWARDSŠ REDS YELLOWS SEPARATE INWARDS---4.9

ILLUSTRATION: S-8---4.9

BLACKS AND WHITES ARE BOUNDARY COLORS---4.10

ILLUSTRATION: S-9---4.10

ILLUSTRATION: S-10---4.11

COLORS BREATHE IN Š COLORS BREATHE OUTŠ VIBRATIONS OF EACH NOTE---4.11

TRAPEZOIDŠ (MULTIPLES OF TWOs AND THREEs)---4.12

ILLUSTRATION: S-11---4.12

TWO UNIVERSES BACK TO BACK---4.13

(THE DIRECTION OF A CURRENT IS COUNTERCLOCK-WISE FROM NEGATIVE TO POSITIVE)---4.13

ILLUSTRATION: S-12---4.13

TWO UNIVERSES BACK TO BACK THE FUTURE EXPANDSŠ THE PAST CONTRACTS---4.14

(MORE PARTICLES AT THE SOUTH POLE)---4.14

KLEIN: "THE FIFTH DIMENSION CURVES BACK UPON ITSELF).---4.14

ILLUSTRATION: S-13---4.14

VIBRATIONS ON FOUR DECREASING SOLIDS---4.15

(THE FIFTH CONTRACTS TO A LIGHT FORCE)---4.15

ILLUSTRATION: S-14---4.15

UNIVERSAL LADDER OF SOUNDS---4.16

ILLUSTRATION: S-15---4.16

NORTH OR NEGATIVE POLEŠ SOUTH OR POSITIVE POLE---4.17

ILLUSTRATION: S-16---4.17

PATTERN OF NOTES ON A GRID---4.18

ILLUSTRATION: S-17(1-5)---4.18

A NEW RULER FOR MEASUREMENT---4.19

ILLUSTRATION: S-18---4.19

PROJECTION OF ZIG ZAG ACCORDING TO PROGRESSION BY SQUARES.---4.20

ILLUSTRATION: S-19---4.20

PERIODIC TABLE OF ELEMENTS---4.21

(APPLIED TO RATIOS OF INTERVALS IN MUSIC)---4.21

ILLUSTRATION: S-20---4.21

PERIODIC TABLE OF ELEMENTSŠ SEVEN OCTAVES---4.22

ILLUSTRATION: S-21 (1-2)---4.22

ILLUSTRATION: S-22---4.23

FOLDING BACK INTO A SEED---4.23

ANGLES OF EACH NOTE PUT ON AN ANGLED AXIS---4.24

ILLUSTRATION: S-23---4.24

CLUSTER OF NOTES IN FIRST OCTAVE.---4.25

(16:15 ON A FIELD OF CŠ (DO) 54Š)---4.25

ILLUSTRATION: S-24---4.25

DOES THE SOUND WAVE TWIST?---4.26

ILLUSTRATION: S-25---4.26

ILLUSTRATION: S-26---4.27

OVERTONE SERIESŠ ONE VERSION---4.27

THINGS BEAR THEIR OWN MEASURE IN THEMSELVESŠ (OUSPENSKY)---4.28

ILLUSTRATION: S-27---4.28

ILLUSTRATION: S-28---4.29

LENGTH OF STRING---4.29

MACROCOSMOSŠ MICROCOSMOS---4.30

(THE ORBITS RESEMBLE ELECTRON ORBITS.)---4.30

ILLUSTRATION: S-29---4.30

ILLUSTRATION: S-30---4.31

(A) EXPANSION CONTRACTION ---4.31

(B) SPACE FOLD---4.32

ILLUSTRATION: S-31---4.32

ILLUSTRATION: S-32---4.33

(C) ANGLES---4.33

(D) MUSICAL INTERVALS---4.34

ILLUSTRATION: S-33---4.34

ILLUSTRATION: S-34---4.35

(E) ECHO---4.35

I CHING---4.36

ILLUSTRATION: S-35---4.36

ILLUSTRATION: S-36---4.37

STOP AND THINK---4.37

STOP AND THINK ---4.38

ILLUSTRATION: S-37---4.38

ILLUSTRATION: S-38---4.39

STOP AND THINK ---4.39



OTHER SIDE OF ART---5.1



EXPANSION-CONTRACTION---5.2

ILLUSTRATION: A-3---5.2

ILLUSTRATION: B-1---5.3

SHOWING HOW "256/243" EQUALS THE LIMIT OF A CYCLE---5.3

ANOTHER TYPE OF NUMBERED GRID---5.4

ILLUSTRATION: B-2---5.4

UNIVERSAL LADDER OF SOUNDS ON A WAVE FORM---5.5

ILLUSTRATION: B-3---5.5

TONES ADAPTED TO A DOUBLE HELIX---5.6

ILLUSTRATION: B-04---5.6

THE MULTIPLICATION TABLE AS A FRAMEWORK FOR THE RATIOS OF RELATIVE PITCH---5.7

ILLUSTRATION: B-5, B-6, B-7 & B-8---5.7

CLUSTER OF RINGS AT CENTER EQUALS EXPANSION---5.8

ILLUSTRATION: B-9---5.8

IS ... AN EXPANSION CONCAVE... OR CONVEX?---5.9

ILLUSTRATION: B-10---5.9

THE MISSING HARMONIC OF NATURE THE PENTAGON---5.10

ILLUSTRATION: B-11---5.10

A NEW KEYBOARD INSTRUMENT---5.11

ILLUSTRATION: B-12---5.11

ILLUSTRATION: B-13---5.12

MULTIPLES ON CURVED AXIS---5.12

ILLUSTRATION: B-14---5.13

MULTIPLES OF TWO, THREE, FIVE, SIXTEEN, EIGHTEEN FORM SOLID CUBES.---5.13

UNITS OF MEASUREMENT FOR EACH RELATIVE PITCH BASED ON THE HYPOTENUSE AND THE SIDES OF DIMINISHING TRIANGLES.---5.14

ILLUSTRATION: B-015---5.14

A SYNTHESIS OF SERIES IN THE FIRST OCTAVE COMBINING THE GRID AND WAVE DIVISIONSŠ---5.15

ILLUSTRATION: B-16---5.15

THE FIRST CYCLE MIGHT END IN A DISINTEGRATION.---5.16

ILLUSTRATION: B-17---5.16

ILLUSTRATION: B-18---5.17

MULTIPLES OF TWO AND FIVE AND THREE AND FIVEŠ---5.17

BŠ CONTRACTS---5.18

ILLUSTRATION: B-19---5.18

ILLUSTRATION: B-20---5.19

THE INVISIBLE VIBRATION WORLDŠ---5.19

DEPICTING A RANGE OF FREQUENCIES FROMŠ 256 TO 4000---5.20

ILLUSTRATION: B-21---5.20

ILLUSTRATION: B-22---5.21

EXPANDINGŠ CONTRACTING---5.21

UNIVERSAL LADDER OF SOUND---5.22

ILLUSTRATION: B-23---5.22

ILLUSTRATION: B-24---5.23

I CHING PRIMAL ARRANGEMENT---5.23

EXPANDING DIMINISHED ASCENDING SCALE---5.24

CONTRACTING INCREASING DESCENDING SCALEŠ---5.24

ILLUSTRATION: B-25---5.24

THE FINITE WITHINŠ THE INFINITE WITHOUT---5.25

ILLUSTRATION: B-26---5.25

INVISIBLE WORLDŠ MATERIAL WORLD---5.26

ILLUSTRATION: B-27---5.26

ILLUSTRATION: B-28---5.27

TRIANGLES IN ORBIT---5.27

THE REASON FOR THE REVERSE AXIS---5.28

ILLUSTRATION: B-29---5.28

ILLUSTRATION: B-30---5.29

THE FINITE NUMBERED GRID---5.29

MULTIPLES OF 2, 3, 5 AND 16 Š---5.30

ILLUSTRATION: B-31---5.30

ASCENDING ŠDESCENDING---5.31

ILLUSTRATION: B-32---5.31

THE CHINESE MAGIC SQUARE---5.32

ILLUSTRATION: B-33---5.32

MAYAN KATON WHEEL AS APPLIED TO EARTH'S MAGNETIC FIELD AND MUSIC TONES.---5.33

ILLUSTRATION: B-34---5.33

THE MEASUREMENT OF MANKIND---5.34

ILLUSTRATION: B-35---5.34

ILLUSTRATION: B-36---5.35

LIMITS OF THE CYCLESŠ HIGHER MULTIPLES.---5.35

LIMITS OF THE CYCLES---5.36

ILLUSTRATION: B-37---5.36

ILLUSTRATION: B-38---5.37

GROWTH VIBRATIONS OF A BUTTERFLY---5.37

THE PUZZLE OF 125---5.38

ILLUSTRATION: B-39---5.38

REPRINT OF LEONARDO ARTICLE --- 6.1



THEORIES AND QUERIES---6.6



SPHERES OF SOUND---6.7

ILLUSTRATION: C-1---6.7

LIMITS OF THE CYCLES---6.8

LIMITS OF EXPANSION---6.8

ILLUSTRATION: C-2---6.8

ILLUSTRATION: C-3---6.9

THE BEGINNING OF THE PENTAGON---6.9

A SQUARING OF THE CIRCLE---6.9

A VISUAL COMPARISON OF RELATIVE PITCH AND PLANETS IN THE SOLAR SYSTEM BOTH MEASURED ON A SCALE OF 360.---6.10

ILLUSTRATION: C-4---6.10

RELATIVE PITCH ARRANGED ON A HELICAL STRUCTURE.---6.11

ILLUSTRATION: C-5---6.11

PLANETARY ORBITS OF THE SOLAR SYSTEM.---6.12

ILLUSTRATION: C-6---6.12

ILLUSTRATION: C-7---6.13

MATTERŠ---6.13

ZONE OF MATTERŠ ZONE OF NON-MATTER---6.14

ILLUSTRATION: C-8---6.14

THE HANDSŠ WITH RINGS---6.15

ILLUSTRATION: C-9---6.15

THE SHELLŠ AND RELATIVE PITCH---6.16

ILLUSTRATION: C-10---6.16

ILLUSTRATION: C-11---6.17

THE SENSESŠ AND RELATIVE PITCH---6.17

HOW TO DETERMINE PROPORTIONS WITHIN A SPECIFIC RANGE ON MULTIPLES OF 5 X 2 AND 2 X 2---6.18

ILLUSTRATION: C-12---6.18

A HOROSCOPE BASED ON THE CIRCLE OF FIFTHS IN MUSIC.---6.19

ILLUSTRATION: C-13---6.19

DESCENDING CONTRACTING SCALE---6.20

ILLUSTRATION: C-14---6.20

ILLUSTRATION: C-15---6.21

A REVERES PROGRESSION BY SQUARES.---6.21

MODULES ILLUSTRATING RATIOS.---6.22

ILLUSTRATION: C-16---6.22

ILLUSTRATION: C-17---6.23

BARS REPRESENTING EACH TONE PERIODICITY ON A LAMBDOMA GRID.---6.23

SPACE FOLDS---6.24

ILLUSTRATION: C-18---6.24

ILLUSTRATION: C-19---6.25

COLOR MODULATION ON THE LAMBDOMA DIAGRAM.---6.25

SQUARING THE CIRCLE---6.26

ILLUSTRATION: C-20---6.26

ILLUSTRATION: C-21---6.27

UNIFIED FIELD THEORY OF INTERVALS OF RELATIVE PITCH LAID ON AN ARRAY OF FRACTIONS (PYTHAGOREAN TABLE, OR LAMBDOMA DIAGRAM).---6.27

SIXTY FOUR SQUARES OF THE LAMBDOMA DIAGRAM COLORED ACCORDING TO COLOR TONE THEORIES.---6.28

ILLUSTRATION: C-22---6.28

ILLUSTRATION: C-23---6.29

PATTERNS OF THE SPHERES TAKE PLACE Š ON THE OTHER DIMENSIONŠ SPACE.---6.29

SHOWING HOW RATIOS CAN BE LINKED TO DEGREES OF A CIRCLEŠ ---6.30

HOW THE SMALLER THE ANGLE THE MORE FREQUENT THE PULSE BEAT---6.30

ILLUSTRATION: C-24---6.30

ILLUSTRATION: C-25---6.31

COORDINATE AXES IN SIX DIMENSIONS.---6.31

RULES FOR LAMBDOMA DIAGRAM. ---6.32

ILLUSTRATION: C-26, C-27 & C-28---6.32

ILLUSTRATION: C-29 & C-30---6.33

UNDERTONE-------- OVERTONE---6.34

ILLUSTRATION: C-31---6.34

UNDERTONE----- OVERTONE---6.35

5 ILLUSTRATION: C-32---6.35

LAMBDOMA ON EITHER SIDE OF TUNING TUBE.---6.36

ILLUSTRATION: C-33---6.36

ILLUSTRATION: C-34---6.37

A LAMBDOMA GRID FORMED BY TWO INTERSECTING ELLIPTICALS.---6.37

PLAN FOR A SERIES OF TRIANGLES DROPPED AT ANGLES WITHIN A CIRCLE.---6.38

ILLUSTRATION: C-35---6.38

EXTENSION OF THE FOURTH DIMENSION OF SPACE.---6.39

ILLUSTRATION: C-36---6.39

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