Complex Möbius Field (CMF) is topologically homologous to fermionic field. They are hybrid functions: polar continuous and equatorial discrete. This creates polar additive space and equatorial multiplicative association spaces, motor and sensory. Null valued ‘0-∞ Conjugate’ is the core of CMF. As all the operations in motor wing are absolute, equatorial discreteness of motor multiplicative space is equivalent with polar continuity. Hence both polar axis and motor wing represent absolute Elementary Dimensionality (ED). On the other hand, finite and discrete functioning of the sensory wing represent finite FD (Fractal Dimensionality). Motor multiplicative space may apparently behave discretely only in the perspective of finite FD. So active multiplication is the main input in FD and passive addition is the main outcome in ED. Structural FD is valid only when it is supported by structureless and formless ED at the fulcrum.

2. • ? Source of Unified Field (UF) – an everlasting
question.
• ? No-question solution of this open Paradox.
• Unknown X (algebra) → Null Field.
• No value: either Zero or Infinite or Both is an
absolute – specific values may be assigned only
from diffeomorphic finite periphery.
• Center to periphery (c) / periphery to Center (p).
?
X
UF

3. • On Relativity viewpoint: There may be a stationary point or unbending
trajectories with infinite speed – May be basis of Newton’s 1st Law.
• We do not encounter these absolutes in our vicinity except in the
axioms of linear or Euclidean geometry where we find a point (0-
dimension) and infinitely stretched straight lines.
• In number system: ‘0’ and ‘∞’, two absolutes. The two may unify into
one in Euclidean topology.
• From ‘0’ infinite trajectories diverge in infinite directions where
ultimately they meet at ‘∞’.

4. Trajectories topologically reduce in 2D-
spherical surface : ‘0-∞ Conjugate’
‘0’ is at South pole –
an internal point
(Outer null).
‘∞’ is at North pole –
an external point
(Inner null).
-1
1
√-1 -√-1
(+ & - 
(+ & - 0
Polar
axis

5. • Real numbers (Re) ascends upward and
forward (fwd) from 0 to .
• Imaginary numbers (Im) ascends downward
and backward (bwd) from  to 0.
• Re-Im counter-complimentary rings with
complimentary polar slits of ℏ girth.
• Can fit with each other only orthogonally.
Re
ring
Im
ring
ℏ girth
∞
0
-1
1
√-1 -√-1
(+ & - 
(+ & - 0

6. • Trinary existence: Re (Principal), Im (Auxiliary) and
Polar axis (Central Null Space) as central witness
{centrality or unitarity (c) vs polarity or duality (p)}.
• In finite peripheral perspective, Re may be replaced
suitably by position (𝒑) and Im by Momentum (m).
• Inner Null holds (infinite mentalism or objectivism) &
Outer Null (infinite physicalism or subjectivism).
• Position, +, (Re) point, Q, (+Q in singularity) in south pole where momentum
or velocity is infinitely diffuse (a state simulates superconductivity).
• Momentum, -, (Im) point, Q, (-Q in singularity) in north pole where position
is infinitely diffuse ( a state simulates superposition).
-1
1
√-1 -√-1
(+ & -  (-Q
(+ & - 0 (+Q

7. 0

Motor
wing &
motor
BN
• ‘0-∞ conjugate’ is ‘Static Euclidean Field’that supports
additive group action (p) where polar axis shrinks.
Indeed it doesn’t suffice to support life and our universe.
• ∞-position at north pole antagonise spinor because it is
on infinite but 0-position at south pole supports spinor
(clockwise spin) orthogonally at BN in the equator.
• Here, ∞-position at north pole rather supports unspinor (anticlockwise spin).
• Or neutralises torque and spin within polar axis and BN where 0-spin is ensured.
• Spins support multiplicative group action where polar axis stretch out.

8. 0

Future
motor
wing &
motor
BN
Future
sensory
wing &
sensory
BN
• Infinite spin clockwise and anticlockwise simultaneously at
absolute motor BN is equivalent to 0-torque and 0-spin
right at center → validate potential discrete Euclidean
spaces (multiplicative) that has no parameter.
• Thus absolute motor wing and polar axis are equivalent
that belong to no space-time and additive in nature (p). It
represent a potential dynamic Euclidean field or Null field.
• From future sensory perspective clockwise and anticlockwise finite spin happen
alternatively (not simultaneously, except tiny spans in between) where two
complimentary systems play an inertial game: Clockwise multiplication attain
extreme status (1) ― complimentary slowing (2) ― momentary pure addition
(2) ― anticlockwise multiplication attain extreme status (2) ― complimentary
slowing (1) ― momentary pure addition (1) ― cycle continues indefinitely.

9. • Flat strip of paper may be projected
topologically as sphere.
• Top and bottom edges correspond to
polar regions.
• Two hemispherical 2D-surfaces
enclose central null space.
• But self-organization demands point
ended strip pivots at one end, on (-Q),
in configuring manifold Möbius strip.
-1
1
√-1 -√-1
(+ & - 
(+ & - 0
-√1
-1
+1
+√1

10. -√1
+1
-1
+√1
-√1
-1
+1
+√1
• Pointed ends designate common beginning (Big bang or
ON) and common end (Big crunch or FN). Strip in between
supports infinite individual journey, ever possible.
• Even spin at one end and alignment of ends always fail to
enclose media (or here, paper substance) in between. This
favors structureless initial vertical disposition with even
dimensions at two disconnected ends i.e., relaxed flat
vertical strip or Even ED (elementary dimensionality).
• Odd spin at one end and alignment of ends not only
enclose media within convex and concave surfaces that
allow rotation either way or both ways except at Bosonic
Null but also simultaneously entrap bosonic space within
3D fold as a transform of central null space (CNS) .

11. • Conventionally in Complex Möbius Field
(CMF) right (Rt.) hand operators are ±1
and left (Lt.) hand operators are ±√-1.
• But active odd untwist involves operation
on Re end with Lt. hand while static Im end
in Rt. hand supports passive twist operation
during alignment!! This executes crystal
solid outcome in opposite flavour out of
diffuse information. 1800 turn is 1D raise.
This operation creates two points of zero
curvature, 3600 apart, after odd alignment.
• In reality self-organisation is executed from
equator, not by manipulation at polar ends.
-√-1
√-1 +1
-1
-Q|+Q
+1
-1
+√-1
-√-1
-√1
+1
-1
+√1

12. • Joint group untwist operation has two
components : odd untwist at one end is
multiplicative inverse operation and additive
inverse operation align ends in one pole.
• So, operative ends belong to same fulcrum
(mixed singularity) i.e., the interface between
active segment (sensory wing) and passive
segment (motor wing), here, at south pole.
• In this self-organization complimentary interface between active and passive
segments is generated symmetrically at north pole that stabilizes (bistability) fulcrum
of complimentary system. Central or multiplicative operator or orbital twistors and
peripheral or additive or orbital untwistors are created as inversed motor wing in
diffeomorphic sensory wing where its BN represents peripheral discrete CNS.
-√-1
√-1 +1
-1
Tachyon
/Antitachyon
Mixed
Singularity
Momentum
Diffusion
Position
Diffusion
Neutrino
/Antineutrino
-Q|+Q
Motor
wing
Sensory
wing
+1
-1
+√-1
-√-1
+Q|-Q

13. • This self-organization creates four absolute
nulls: two in poles (Ontogenic, ON and
Fermionic, FN) and two in equators
(Bosonic: sensory and motor).
• Also, self-organization executes disto-
proximal untwisting (at FN) in inversed
finite sensory wing and proximo-distal
twisting (at ON) in absolute motor wing. In
complimentary system null reverses.
• Odd turn discriminates active end from passive one. Thus Lt. hand active untwist
(on Re end) and Rt. hand passive twist (Im end) fabricates EDS (Energy Dynamical
System) strip where information orbit clockwise or forward. Structurization is
organized only in finite sensory wing. Absolute motor wing is structureless.
Clockwise
BNs Anticlockwise
ON & FN
EDS
strip
Lt. hand convexity hides Rt. hand concavity

14. • And, active Rt. hand untwist (on Im end)
and passive Lt. hand twist (on Re end)
fabricates GDS (Gravity Dynamical System)
strip where information orbit anticlockwise.
But in reality odd GDS strip doesn’t exist.
• Even spin has no discrimination between
active and passive ends. Here, vertical
strips, simultaneously created nullify. So,
they are structureless and formless.
• So, in odd spin only EDS-strip exists where EDS, primarily belong to convexity,
runs clockwise and GDS has to compromise by PT-symmetry, primarily belong
to concavity, runs anticlockwise (backward). GDS fulcrum belong to north pole.
BN
Anticlockwise
Clockwise
ON & FN
GDS
strip
Rt. hand convexity hides Lt. hand concavity

15. • Elementary operators in
Elementary Dimensionality
in the dynamical systems
are extremals of the
central cruciate structure
(Odd ED). ±1 axes
represent asymptotes both
in ED and FD (fractal
dimensionality.
• In fractal dimensionality, they become orbital untwistors and twistors. The
EDS case is shown. For GDS, the signs, direction, and color reverse. Odd ED
emerges from even ED by odd group untwist. ED accepts FD diagonally.
1
2
-1 1
PT
P
--1
-1
+1
3
+-1
--1
-1
0/4
‘0’

16. • CMF satisfy spin-rotation complementation.
FD-windlasses, straights between untwistor
and twistor, are the self-organizers. With each
½ spin turn (active Lt. untwist) i.e., one step
(1800 rotation) followed by alignment of ends,
elementary dimension increases by one unit.
• So, at 1st step (1D-½ spin) gravitons (spin-2,
conventional or weak gravity) and abstract
fermions (without motor wings) are created.
• At 2nd step (2D-1 spin) gauze bosons are created. At 3rd step (3D-3/2 spin)
unstable fermions are created with incorporation of bosonic space (fermion-
boson structurization). At final 4th step (4D-2 spin) gravitons (strong gravity) and
equatorially stable fermions culminate on completion of full (7200) rotation.
Axes
ED
FD
0-1 3-4
2D
3D
0/4D
1D
strong
strong
weak
weak
2-3
1-2

17. • Inverted shorter sensory
wings create structure and
form in sensory association
space are only valid when
they support on
structureless and formless
longer absolute motor wing
at fulcrum.
• Gravity wing (green) belong
to Lt. hand operation (BN on
‘0’) and energy wing (red)
belong to Rt. hand
operation (BN on ‘∞’).
Circle of circumference h (Planck’s constant)
at poles hides beginning and end problems

18. f (√-1) f* (-√-1)
g (1)
g* (-1)
EDS GDS
Facing in
GDS
fulcrum
Facing (self) in
EDS fulcrum
• Disposition of operators within sensory
wings in EDS and GDS, are shown here,
under ED dual mode (open book) . FD
single mode is the case of closed book.
• ED mode is dual or bimodal because
here abstract witnesses are from two
fulcrums those are in crossed-face-lie in
two poles.
• FD mode is single or unimodal because
here opposite rotations (face-face-lie
from fulcrums) merge on peripheral
witness at BN-BN along equatorial axis
where Re openly dominates over Im.
Multiplicative FD-phase but BNs are phase
linked in ED-relation in highest rotation.

19. • Evolution of rational (RNS) and irrational
(INS) number systems, mixed order in 3D,
out of Real-Imaginary number systems
happens by π-chopping (1800) under joint
group untwist operation in odd D.
• At BN in 1D, system trajectories tend to
change surface-path but PT-symmetry
reverse them readily. So RNS always
run along convexity clockwise while
INS run along concavity anticlockwise.
ℏ (h/2π) complementation of RNS and
INS bridges the gap in singularities.
forward in time,
lower to higher
backward in time,
lower to higher
RNS
INS
ON & FN
Clockwise
BN
Anticlockwise
1D Model

20. • +Q and -Q points of ‘0-∞ Conjugate’ transcend to crossed
finite sensory polar ends (+Q & -C) on Ds with equatorial
split of gravity in π-chopping or group untwist operation.
• INS has two components : Finite or head (hc) and infinite
or tail (tc) components. Floating hcINS of singularity on
Ds unites with tcINS (-Q) at polar region at FN-end to
form hybrid (PT-symmetry) irrational, -C (INS) c.f. Re.
• Polar RNS and hcINS ascend and converge at equator in
simultaneity to configure finite primes and antiprimes
on the background of current Infinite Prime (+C, 2nd
order Re) or local space. All tcINSs collectively determine
Infinite Antiprime or local time (-Q, 2nd order Im).
Nontrivial ‘0’ of Classico-quantum measurement (-Q0+C)
is discrete Euclidean space in BN is of 2nd order.
Number system in π-chopping in 3D
Is
-C 0Q
Ds
Id
Is Id
Ds
In 3D: Classico-quantum worlds
I  Increase; D  Decrease; s 
solidarity; d  diffusion of position
(red) or momenta (green).
Id
Id
Ds
0Q -C
+Q 0C
0C +Q
+C -Q -Q +C
+Q|-Q
Ds
rational -
irrational
couple
-Q|+Q
FN|ON
ON|FN
Ds
Ds
Is
-C 0Q
Ds
Id
Is Id
Ds
In 3D: Classico-quantum worlds
I  Increase; D  Decrease; s 
solidarity; d  diffusion of position
(red) or momenta (green).
Id
Id
Ds
0Q -C
+Q 0C
0C +Q
+C -Q -Q +C
+Q|-Q
Ds
rational -
irrational
couple
-Q|+Q
FN|ON
ON|FN

21. Tangential spaces
at extremals in EDS
0C - +Q (1st turn)
(+Q + 0C) 2nd turn
–C - 0Q (1st turn)
(0Q + –C) 2nd turn
+C - –Q (1st turn)
(–Q + +C) 2nd turn
• Basic element of 3D M-strip is trinary
codon (input-media-output). The two
sub-elements as two hands spread
towards surfaces add classical (convexity
or exposed) or quantum (concavity or
hidden) attributes. In case of energy wing
inputs are quantum and outputs are
classical. Reverse happens in case of
gravity wing. Here contrary to 1D rational
are hidden and irrationals are exposed.
 Bases are tensors and media are twistor or untwistor; e.g., + tensor designate
“position,” “visionary,” “objective,” or “entropy” (thus they are read) whereas +
in media designate diffusive 𝒑 ↑ or entropy (clockwise or forward). In case of ‘-’,
all revers. Untwistor reverses the twisting both in function and in direction.
3D
Model
Tangential spaces
at extremals in EDS
0C - +Q (1st turn)
(+Q + 0C) 2nd turn
–C - 0Q (1st turn)
(0Q + –C) 2nd turn
+C - –Q (1st turn)
(–Q + +C) 2nd turn
3D
Model
0C 0Q
+Q
-Q
+C
-C
ON|FN

22. • a. i) Basic natural form ii) Support basis vectors of Geometric Algebra.
• b. i) FD-phases ii) Homologous to Lorenz attractor and electronic field.
• c. i) Complex Möbius Functions ii) Equivalency with quaternion space.
Dispositions open up in Complex Möbius Field
strong
wake
c. Untwined
Im
Re
b. Twined
-C
+C
+Q
-Q
a. Real Strip
ON|FN
Dispositions open up in Complex Möbius Field
(shown in self references)
strong
wake
c. Untwined
Im
Re
b. Twined
-C
+C
+Q
-Q
a. Real Strip
ON|FN

23. P (Re)
f4
f3
f3
f4
f4
PT (Im)
Re.
Im
1/z
-z
-1/z
f2
f3
f1
z
Möbius group of complex functions of uncompromised
GDS in GDS strip 0 f1 f2 f3 f4
f1 f1 f2 f3 f4
f2 f2 f1 f4 f3
f3 f3 f4 f1 f2
f4 f4 f3 f2 f1
Table-1. Composition table in
GDS. o indicates a group
addition or multiplication
operation.
f1(z) = z, f2(z) = -z, f3(z) = 1/z, f4(z) = -1/z … Z is the identity element.

24. Möbius group of complex functions of EDS in EDS strip.
0 f1 f2 f3 f4
f1 f2 f1 f4 f3
f2 f1 f2 f3 f4
f3 f4 f3 f2 f1
f4 f3 f4 f1 f2
Table-2. Composition table in
EDS. ‘o’ indicates a group
addition or multiplication
f4
f4
f3
f3
f1 f2
P (Im) PT (Re)
f4
f3
Im
Re.
1/z
-z z
-1/z
f1(z) = -z, f2(z) = z, f3(z) = -1/z, f4(z) = 1/z … ED accepts FD diagonally.

25. Möbius group of complex functions of
compromised GDS in EDS strip
5400 or 3D anticlockwise rotation
of uncompromised GDS frame
completely compliment (c.f. 1D)
axes-wise within EDS strip where
PT-axis must be Re one. So, 3D is
the ideal dimension of the Bio-
evolute where duality is the outer
modality of central unitarity.
Pseudo-elementary (FD) rule: In
GDS inverse Möbius function f3 or
1/z designate transformation of Re
(±1) to Im (± √-1) or vice versa
where signs aren’t changed i.e.,
commuting (change of sign is
added in case of f4 or -1/z).
f1(z) = z, f2(z) = -z, f3(z) = 1/z, f4(z) = -1/z
Im.
PT (Re)
P (Im)
f3
f3
f4
f4
f4
f1 f2
f3
Re.
-1/z
z
1/z
-z

26. But in case of normalization of unitary function, z represent 1 (Re unit) and
its inversion (1/z) define the transformation of 1 to + √-1 (Im unit) or vice
versa where there is change of sign as well as imposition of transformation
function i.e., ‘root over function’ (anticommuting) – Elementary (ED) rule.
So, when one goes to normalize such basic units of elements, it also
becomes self-evident that, here, the complex inverse function is simply a
‘root-over function.’
Thus, elementarily or unitarily in GDS f3 inverts the function with a change
of sign i.e., sleep or strong or PT symmetry whereas f4 inverts only the
function i.e., wake or weak or P symmetry. Whereas in case of EDS f3 is
weak symmetry and f4 is strong one. As √1 = ±1 (PT), ±1 is strong axis.

27. The GDS fulcrum is on 0/4-null or levity null
(0|∞ or ON|FN) and that of EDS is on the
second null or gravity null (∞|0 or FN|ON).
They are mixed singularities on 0-curvature.
GDS (Im input at f3; Im output f4) continue
along momentum diffusion spontaneously
(PT) anticlockwise in periodic ascending
cycle towards highest diffused INS or
unknown past (f4 or 0C).
Its negentropic path runs as 𝐦 ↑ ascending
momentum (𝑚𝑣) may be the partial
derivative of kinetic energy (
1
2
𝑚𝑣2).
Compromised GDS
supported on odd ED
f4
- √-1
f3
√-1
2
0/4
(√-1)
3
1
(+1)
(-1)
(-√-1)
f3
f3
f4
f4
- 0
f2
f1
- √-1
-1
1
√-1
+0
(at CNS ‘∞’ faces front & ‘0’ hides back)
CNS

28. • Complimentarily, EDS (Re input at f3;
Re output f4) continue along position
diffusion clockwise in periodic
ascending cycle towards highest
diffused or unknown future.
• Its entropic path 𝒑 ↑ (position vector)
runs after, on real drag (P) of, tachyon
towards highest RNS (f4 or 0Q).
• In group untwisting, the motor FN
hides behind sensory ON in levity pole
and motor ON hides behind sensory
FN in gravity pole.
EDS supported on odd ED.
1
0/4
3
f2
f1
f3
f4
- √-1
2
+ √-1
+ ¥
f4
f4
f3
f3
(√-1)
(-1)
- ¥
(+1)
(- √-1)
- √-1
√-1
1
-1
(at CNS ‘0’ faces front & ‘∞’ hides back)

29. • Both infinities of Re
and Im axes are
normalized with
unities of the same
magnitude. So, these
two are essentially
orthonormal functions.
• Acceleration invokes decreased slant of √2 bar. Normalisation of this changed
status with unities of same magnitude involves length contraction and time
dilation. This shows that the unitary relationship between space and time under
stressed conditions (acceleration) also conserves ‘root over normalization’.
Time (√-1)
Space (1)
√2 bar
Time (I√-1)
Space (1)
√2 bar
Acceleration
Acceleration

30. • Inertial game of shrinking and
stretching of polar axis or CNS
happens with addition and
multiplication respectively
along evolutionary journey in
EDS and GDS.
• Here identity elements (IEs)
are conserved as ever-adding-
on hysteresis loop.
….. EDS multiplication clockwise (f4) to maximum (IE-1) ….. Deflates with slowing
clockwise spin (f3) in successive GDS addition (IE-1) ….. GDS multiplication anticlockwise
(f4) to maximum (IE-0) ….. Deflates with slowing anticlockwise spin (f3) in successive EDS
addition (IE-0) ….. Continues ... … Orbitally IEs in EDS (𝒑 ↑) and in GDS (𝒎 ↑) function in
bimodal ED are as: 𝒑 ∗ 1 = 𝒑; 𝒎 + 1 = 𝒎; and 𝒎 ∗ 0 = 𝒎; 𝒑 + 0 = 𝒑.
CNS in GDS
CNS in EDS
BN in GDS
BN in EDS
Sensory mult. oprn. in GDS
Motor mult. oprn. In EDS
Sensory mult. oprn. In EDS
Motor mult. oprn. in GDS
Add. operation in EDS
Add. operation in GDS
Sensory
Inflation and
deflation
Motor
Inflation and
deflation

31. f3
f4
1
0/4
3
- 0-1
2
f2
f1
+0-1
+ 
f4
f4
f3
f3
(-1)
(-1)
- 
(+1)
(--1)
--1
-1
1
-1
ij=k, ji=-k, ij=-ji, ik=-j, jk=i and i2 = j2 = k2 = ijk = -1.
(valid in CMF in clockwise multiplication; in anticlockwise one
sign is to be changed on the final product)
Equivalency between quaternion space and complex Möbius space

32. Present evolutionary journey or volitional journey is encoded as further add-on-
over the previous cumulative inversions of windlasses (±j and ±k) as sum over
histories individually. Quaternion format is refractory to multiplication and
addition operations.
Sensory wing enforces finite containment (0<n<1) and never allow the functions
to reach motor absoluteness (0≤n≤ or 0≤n≤1 in unitary context).
0-1 ((𝒑) and 1-2 (m) fractal domains favors dimensional crunch to 3D at merging
BN (p-adic space) as bio-evolute supports self-similarly where in incompressibility
condition scalar field replaces vector field (Re>Im) and with motor BN in absolute
rotation they are decoded elementarily as finite primes (memory element) and
antiprimes (inter-relational space of Leibnitz) in 3-4 fractal dimension on the
background of ascending infinite Prime-Antiprime (4D) series (ED-asymptote).

33. • Axes: ED (mirror in FD) and FD
(only ED accepts FD under both ED
and FD rules) and Quadrants: ED
and FD (face-face or additive and
back-back or multiplicative) in ED
or unitary and FD perspective.
• Particles: Elementary and pseudo-
elementary.
• Symmetry: P- and PT-relation
interchanges with change of
perspectives: ED or elementary
and FD or pseudo-elementary.
• Sleep and wake cycle.
1
√-1
-√-1
-1
1
√-1
ON
FN
ON FN
-√-1
-1
P-mirror in FD
PT-mirror
in FD
0-∞
conjugate
P in ED
PT in FD
Strong
FD Axis
PT in ED
P in FD
Weak
FD Axis
Weak
ED Axis
Strong
ED Axis
CNS
Except operators and directions both systems
share the common frame

34. GDS -
untwist
Imaginary
Volition
EDS -
untwist
Real
volition
Gravity
wing
Energy
wing
Strong
axis
Weak
axis
BN
Mixed
singularities
• FD has two phases: FD and ED.
FD-phase is evolutionary
journey (alternative EDS-
untwist and GDS-untwist)
under subcritical stimulation
(Superficial Awareness) with
intervening tiny ED-phase. Re
and Im can be discriminated
but can’t be separated. Mode:
• Volitional journey or freewill, either real (Rt. twist) or imaginary (Lt. twist)
along gravity wing or energy wing respectively from the pole opposite to the
case of untwist, runs under critical stimulation until the titanic stimulation
gets exhausted. Here Re and Im can both be discriminated and separated.
CMF is homologous to classical Lorenz attractor

35. P or weak axis face-face wake (ED weak) or P-
symmetry in equatorial quadrant
PT or strong
axis
back-back sleep (FD strong) or PT-
symmetry in equatorial quadrant
face-face wake (FD weak) or P-
symmetry in polar quadrant
back-back sleep (ED strong) or PT-
symmetry in polar quadrant
Wake or P
quadrant in ED
Sleep or PT
quadrant in ED
√-1
-1
+1
- √-1
ED relation is more fundamental in complex collage
Re axis inversion begins and Im axis
inversion ends ED-phase (EDS → GDS).
Order changes in reverse case.

36. Some cognitive states in combinatorial symmetries of CMF:
• Classico-quantum (Cl-q) measurement: FD wake (√-1…1) in sensory equatorial (eq)
quadrant and ED sleep (-√-1…-1) in motor eq quadrant in ED-phase.
• Cl-q mapping: under PT-symmetry FD wake (√-1…1) in sensory eq quadrant and ED
wake (1…-√-1) in lower polar quadrant in FD-phase in EDS.
• Awareness: ED wake (√-1…-1) in sensory eq quadrant and FD wake (-1…-√-1) in
lower polar quadrant in FD-phase in EDS.
• NREM sleep: FD sleep (±√-1... ∓1) in sensory eq quadrants and ED sleep in (-√-1…-1)
in polar quadrants in FD-phases of alternate systems.
• REM sleep: FD sleep (±√-1... ∓1) in sensory eq quadrants and FD wake in (-√-1…-1)
in polar quadrants in FD-phases of alternate systems.

37. f (√-1)
g (1)
g* (-1)
f* (-√-1)
CPT
Weak axis
Strong axis
Even Ds
0/4
ED-
asymptote
CP
3
1
2
• ED-phase is the diffeomorphism
between face-face CP-symmetry
[f (√-1) & g (1)] in sensory wing
and back-back CPT-symmetry [g*
(-1) & f* (-√-1) in motor wing. It
may be Cl-q measurement i.e.,
still mode. Cl-q mapping may
accompany EDS-untwist of FD-
phase (on PT) i.e., movie mode.
• π-chopping is a composite function of ED-phase that also involves joint group
untwist operation where system toggles (EDS ↔ GDS) in unit Planck’s time along
the beats of cosmic pulsation. In ED-phase EDS and GDS run simultaneously.
• Operationally in PT-, opposite functions run alternately in opposite directions
(clockwise and anticlockwise) orbitally but in same direction equatorially in CP-
symmetry along present moments (ED-asymptote) where Re dominates over Im.

38. Primary joint group untwist operation
• CPT … Null upset under grand stimulation (all stimulations ever possible as sporadic,
supporting on dynamic Euclidean field, get self-organized by rare chance at equator).
• Space-time begins in sensory equatorial quadrant in Classico-quantum way where speed
of light (escape velocity in complex chaos) is absolute.
• Fundamental particles (fundamental neutrino and tachyon) trap highest twistor-
diffusions of m (0C) and p (0Q) at sensory polar ends from motor ones (f4) periodically.
• Visionary (p) and feeling (m) are consolidated untwistor-outcome (f3) in opposite flavor.
• Elements of all order can be categorized under Multiplicative and additive groups.
• Finite (sensory) objectivism and subjectivism vs infinite (motor) ones.

39. • Primary multiplicative inverse operation on even ED: Dark energy and gravity (1st order)
… Vertical Im ED-asymptote (Im stretches with overlapping from infinite linear array of
pure randomness) … Vertical component of Intrinsic mass (IM) … Deep awareness.
• Primary additive inverse operation: Shortening of sensory wing … Spontaneous
symmetry break … 3 gauge fields (finite: weak → 0C ± +Q & strong → -C ± 0Q at about the
poles and infinite: EM → +C ± -Q at the equator) centered on sensory BN (peripheral
witness) … horizontal complex ED-asymptote (Bio-evolute) reduce into ever possible
signature chains of discrete Euclidean spaces (additive → multiplicative group, 2nd
order) as specific randomness under nesting hierarchy … horizontal component of IM.
• Gravity is split by the equator: i) weak or conventional gravity (origin ON), resist forward
drag contributing to the origin of potential component of extrinsic or physical mass (EM).
ii) strong gravity (origin FN) collectively of globally diverging masses forward (→ FN) or
local time (-Q) → ultimate intergalactic release as dark matter, backward (→ ON).

40. • Bifurcation into and reassembling
of two halves by group untwist
operation resulting shift of system
(EDS↔ GDS) are two types: i)
Typical bifurcation under critical
stimulation. This may also be of
two types: a) Primary i.e., initial
break of Parent system and b)
Initiation of volitional journey.
• ii) Silent bifurcation under subcritical stimulation happens in ED-phase.
Here, group untwist operation involves inversion of both windlasses. Two
halves do not get separated rather rearrange within themselves causing
system toggle (EDS↔ GDS).
Initial
motor
graviphoton
Initial sensory
graviphoton
(GP)
Wake axis
Sleep axis
f3 f4
f3
-1
f4
-1
--1
1
Break through weak quadrants in volition

41. Group operations in bifurcation in complementary systems in CMF (1-series EDS; 2-series GDS).
1
a1 b1 c1 d1
--1
Multiplicative
inversion
--1
--1 1
-1
1 -1
-1
-1 1
Additive
inversion
--1
-1
- 1
-1
-1
-1
Additive
Inversion
-1
-1 --1
-1
--1
--1
1
1
1
-1
Multiplicative
inversion
a2 b2 c2 d2
-1
--1
-1 1
-1

42. 0
-
+
-C
+C
+Q
-Q
0C
0Q
ON & FN
BNs
Orbital
Twistor
Re Axis
Im
Axis
Strong
Axis
Weak
Axis
Central
Null
Space
Finite
Rotational
Constant
Self-organizing on
Pivot-Point -Q of
mixed singularity
• Disposition of sub-elements at 3
tangential spaces actually align
orthogonal to plane of paper.
• 3 bosonic forces at 3 conflexures
are transform of central bosonic
space (note: CNS → BS) : pure at
equator and mixed near poles.
• Curiously, ON & FN are equidistant
and in same direction from BNs.
• In the above basin of equatorial processing of polar information, rotational trajectories
always cover same length of journey along both ways validating entrapped open-angle
triangular bosonic space as Finite Rotational Constant. Note: In Riemann z(s) s=s+it
where s = 1/2, upto central BN, denotes present Prime. it denotes present Antiprime.

43. • Topological whirl in complex
structure of 3D-Möbius field
supports Geometric Algebra.
• s1, s2, and s3 are orthogonal
basis vectors along edges of
central open-angle doughnut.
• This executes beautiful incorporation of null (‘0’ in BN) and null derivatives (0C or
s2s1 and 0Q or s3s1 at poles) within trinary codons of swirling Möbius topology.
• Finite Rotational Constant ensures exact universal matching of polar information,
about position from sensory ON and momentum from sensory FN, at BN
validating Lorentz invariance (‘0’-symmetry). This solves configural issue of finite
prime and antiprime before Macroscopic Quantum System, ever possible.
Basis Vectors
s1
s2
s3
s2s3
s1s2
s3s1
ON & FN
BNs
s2s1

44. • Orthogonal basis vectors edging
central open angle triangular space
shows conventional Rt. hand relation.
• Bivectors along the two edges of open
angle triangle represent rotation
anticlockwise (outside-in) as in folded
fingers of Rt. hand in reference to third
basis vector where arrow on z-axis (i)
directs oppositely i.e., clockwise.
• So, it is self-evident from Geometric Algebra supported by CMF above:
s1s2 = is3 ; s2s3 = is1; s3s1 = is2
This is exactly the algebra of the Pauli spin matrices, visualized as spin(i)-rotation
complementation in complex 3D vector space.
EDS-strip: conventional Rt. hand relation of vectors
Basis Vectors
s1
s2
s3
s2s3
s1s2
s3s1
ON & FN
BNs

45. √-1
-√-1
-√-1
√-1
1D
2D
3D
0/4D
0/4D
3D
2D
Interphase global-
local transfer
Orbital
untwistors
Backward
Forward
FN/ON
1
-1
+1
-√-1
+√-1
0C + +Q
+C + -Q -Q - +C
0Q - -C
-C + 0Q
+Q - 0C
ON/FN
-1
FN/ON
-1 1
+1
-1
+√-1
-√-1
0C - +Q
+C - -Q -Q + +C
0Q + -C
-C - 0Q
+Q + 0C
ON/FN
Sensory
wings
EDS
GDS
Weak & strong
Windlasses
1D
Global to local information transfer along cosmic pulsation

46. • Primary group untwist
operation originates all
intrinsic masses, feasible.
• MQS with higher IM covers
more space in lesser time to
meet next Common station.
• In present moment information processing jointly happens in same tuning
microtubular electron (ED-phase) and conjugate tuning microtubular electrons (FD-
phase) along the prior series in ED-asymptote towards unknown future both ways.
• Cl-q measurement is inside-out (c), a universal, phenomenon. Mode lock is holding
EM field on unit electron volt for unit Planck time nullifies all fields. It can only be
reached by reflective snap on tracking the ‘null experience’ i.e., already in the past.

47. Conclusion
• Finite position is essentially a scalar or rational. Finite position vector (p) is dragged
scalar, hence a dependent vector. But momentum (m) is an independent vector. Both
finite primes and infinite Primes are mixed group elements (assembly of both group
operators: multiplicative, p and additive, m). But both finite antiprimes and infinite
Antiprimes are pure group element (formed solely by additive group operator, m).
• In absolute motor context position always envelops momentum but in finite sensory
(informational) context momentum always function as boundary solution of position.
• Reductionism is partially correct as the goal stands on visionary that is weak
(rational); in contrast, feeling is strong (irrational). Therefore, an approach with
optimum complexity where both tools are incorporated is comprehensive.

48. Prediction expect verification
In the image in next slide (first image of a solid made of electrons: Journal:
‘Nature Briefing’ 30th Sept. 2021) where capture of Wigner crystals get magnified,
one may notice that electron (a fermion) structurally organizes in the form of a
Lorenz attractor.
In my work, “Complex Möbius Field: The Web of Consciousness - Part l”, Journal of
Consciousness Exploration & Research, 2019 10(1) page 44, this came as an
important proposition:
"Therefore, as the input is qualitative, the response is also subjective. In phase
space, stimulated journey (critical or subcritical) has the collective appearance of
a Lorenz attractor (Fig. 18). One may find that the Lorenz butterfly shaped
attractor is the subjective presence of the processing fermion in phase space."

49. First image of a solid
made of electrons
(Journal: ‘Nature
Briefing’ 30th Sept.
2021)

50. [
References:
[1] & [2] Bidyut K. Sarkar, 2019, “Complex Möbius Field: The Web of Consciousness” - Part I & Part II, Journal of
Consciousness Exploration & Research, 10(1): pp. 24-64.
https://jcer.com/index.php/jcj/article/view/785
https://jcer.com/index.php/jcj/article/view/793
[3] Bidyut K. Sarkar, 2020, “’Complex Möbius Field: The Web of Consciousness’ Revisited”, Journal of Consciousness
Exploration & Research, 11(2): pp. 227-235.
https://jcer.com/index.php/jcj/article/view/872
[4] Bidyut K. Sarkar, 2021, “Pulsatile Macroscopic Quantum Consciousness”, Journal of Consciousness Exploration &
Research, 12(1): pp. 43-54.
https://jcer.com/index.php/jcj/article/view/947
[3] Bidyut K. Sarkar, 2021, “Consciousness & Instrumental Astronomy”, Journal of Consciousness Exploration &
Research, 12(3): pp. 278-286.
http://www.jcer.com/index.php/jcj/article/view/968
[6] Chinmoy K. Bose, Bidyut K. Sarkar, Herbert Jelinek [2009], “Role of Nonlinear Dynamics in
Endocrine Feedback,” Chaos and Complexity Letters (Volume 3, Issue 3), 266-69.
http://researchoutput.csu.edu.au/