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A Theory of Dimensional Information
By Lucien Lescanne

Abstract
This paper presents a unified theory of information, proposing that information is not an intrinsic property of a signal but a dynamic construction emerging from a receiver’s capacity to form relational links. We introduce a dimensional framework where reality is composed of "Object-Universes," whose stability and behavior are governed by a Principle of Dynamic Coherence, expressed as the product of internal and external coherence. This framework successfully models phenomena ranging from quantum measurement to social dynamics, offering a unified language for physics, cognition, and information science.
# Foundational Principle: Information is a Relation
The core axiom of this theory is a radical redefinition:

A Signal is a physical phenomenon.

Information is not the signal itself but a construction created by a receiver based on the signal and its pre-existing internal structure.

Information does not "travel"; it is instantiated locally by a receiver capable of interpreting the signal. This resolves the passive view of information in Shannon's theory, placing the active role of the receiver at the center.
# The Dimensional Architecture of Object-Universes
Any entity—a particle, an idea, a person, or a society—is an Object-Universe, defined by the triplet:

O
=
(
i
d
,
S
⃗
,
L
)
O=(id, 
S
 ,L)
i
d
id: A unique identifier.

S
⃗
S
 : The state vector, a hybrid structure 
S
⃗
=
(
P
⃗
,
T
⃗
)
S
 =( 
P
 , 
T
 ).

L
L: The set of relational links.

Dimensions:
Ψ (Psi - Dimension 0: The Origin): The core identity or "source code" of the object, represented by 
S
⃗
S
 .

Dimensions 1–3 (Space) & 4 (Movement): These classical dimensions are relative to the receiver’s frame of reference. Time is the measure of movement (Dimension 4).

Λ (Lambda - Dimensions 5: The "Related-To" Dimensions): An indefinite number (
n
n) of relational dimensions. Properties like mass, charge, or meaning are not intrinsic but specific types of links within 
L
L.
# Mathematical Formalization
3.1. Hybrid State Vector
S
⃗
=
(
P
⃗
,
T
⃗
)
S
 =( 
P
 , 
T
 )
P
⃗
=
[
p
1
,
p
2
,
.
.
.
,
p
m
]
P
 =[p 
1

 ,p 
2

 ,...,p 
m

 ] is the probability vector, where 
∑
i
=
1
m
p
i
=
1
∑ 
i=1
m

 p 
i

 =1. It represents uncertainty among mutually exclusive states.

T
⃗
=
[
t
1
,
t
2
,
.
.
.
,
t
n
]
T
 =[t 
1

 ,t 
2

 ,...,t 
n

 ] is the trait vector, where 
t
i
∈
R
t 
i

 ∈R. It represents continuous, co-existing characteristics.

3.2. Coherence Functionals
# Internal Coherence (
C
i
n
t
C 
int

 ):

C
i
n
t
(
O
)
=
−
(
α
⋅
H
(
P
⃗
)
+
β
⋅
δ
(
T
⃗
)
)
C 
int

 (O)=−(α⋅H( 
P
 )+β⋅δ( 
T
 ))
Where:

H
(
P
⃗
)
=
−
∑
i
=
1
m
p
i
log
⁡
2
p
i
H( 
P
 )=−∑ 
i=1
m

 p 
i

 log 
2

 p 
i

  (Shannon entropy).

δ
(
T
⃗
)
=
1
n
∑
i
=
1
n
(
t
i
−
t
ˉ
)
2
δ( 
T
 )= 
n
1

 ∑ 
i=1
n

 (t 
i

 − 
t
ˉ
 ) 
2
  (variance of traits).

Weights 
α
α and 
β
β are dimensionality-driven:

α
=
dim
⁡
(
P
⃗
)
dim
⁡
(
P
⃗
)
+
dim
⁡
(
T
⃗
)
,
β
=
dim
⁡
(
T
⃗
)
dim
⁡
(
P
⃗
)
+
dim
⁡
(
T
⃗
)
α= 
dim( 
P
 )+dim( 
T
 )
dim( 
P
 )

 ,β= 
dim( 
P
 )+dim( 
T
 )
dim( 
T
 )

# External Coherence (
C
e
x
t
C 
ext

 ):

C
e
x
t
(
O
)
=
1
∣
E
∣
∑
E
j
∈
E
strength
(
L
E
j
→
O
)
C 
ext

 (O)= 
∣E∣
1

  
E 
j

 ∈E
∑

 strength(L 
E 
j

 →O

 )
Where 
E
E is the set of pertinent external objects, and 
strength
(
L
)
∈
[
0
,
1
]
strength(L)∈[0,1] quantifies link intensity.
# Global Coherence (
C
g
l
o
b
a
l
C 
global

 ):

C
g
l
o
b
a
l
(
O
)
=
C
i
n
t
(
O
)
⋅
C
e
x
t
(
O
)
C 
global

 (O)=C 
int

 (O)⋅C 
ext

 (O)
The multiplicative relationship ensures viability requires both internal and external coherence.

3.3. The Evolution Equation
d
S
⃗
d
t
=
η
⋅
(
∇
S
⃗
 
C
g
l
o
b
a
l
(
O
)
)
dt
d 
S
 

 =η⋅(∇ 
S
 

 C 
global

 (O))
Where:

d
S
⃗
d
t
dt
d 
S
 

 : Rate of change of the state vector.

η
η: Learning rate/plasticity constant.

∇
S
⃗
C
g
l
o
b
a
l
∇ 
S
 

 C 
global

 : Gradient of global coherence, guiding the system toward higher coherence.
# Empirical Validation
The theory has been tested against diverse phenomena:

Bit vs. Noise: Discriminates stable bits (
C
g
l
o
b
a
l
C 
global

  high), random noise (
C
g
l
o
b
a
l
C 
global

  moderate), and superposed bits (
C
g
l
o
b
a
l
C 
global

  low).

The Couple in Crisis: Models relational stability via 
C
g
l
o
b
a
l
C 
global

 , which plummets during crises due to internal uncertainty and contradictory traits.

The Obsolete Craftsman: A perfectly efficient workshop (
C
i
n
t
≈
1
C 
int

 ≈1) fails when environmental demand collapses (
C
e
x
t
→
0
C 
ext

 →0).

Young’s Double-Slit Experiment: Reframes wave-particle duality as a coherence-driven transition. Wave behavior emerges without 
T
Which-Slit
T 
Which-Slit

  links; particle behavior emerges when such links force restructuration.
# Implications for Physics and AI
5.1. Resolving Quantum Paradoxes
Measurement Problem: "Wave-function collapse" is a coherence-driven phase transition. Creating a 
T
Which-Slit
T 
Which-Slit

  link makes superposition incoherent, forcing localization.

Non-Locality & Entanglement: Entangled particles form a single Object-Universe 
O
entangled
O 
entangled

 ; measuring one particle updates the global 
P
⃗
P
 , changing coherence conditions for the other.

5.2. A New Paradigm for Artificial Intelligence
Coherence-Driven AI: AI systems could optimize 
C
g
l
o
b
a
l
C 
global

  of their internal world models, balancing internal consistency (
C
i
n
t
C 
int

 ) and external utility (
C
e
x
t
C 
ext

 ).

Explainability by Design: Reasoning becomes transparent through coherence audits.

Learning as Coherence Ascent: The evolution equation generalizes gradient descent to a goal-driven search for coherence.

5.3. Ontological Shift: Relations Precede Objects
Reality is primordially a network of relations (Dimensions 5). "Objects" and "properties" are stable patterns (
C
g
l
o
b
a
l
>
θ
C 
global

 >θ) in this relational fabric.

Conclusion
The Theory of Dimensional Information proposes a Copernican shift: Reality is not a spacetime container but a dynamic network of relations, from which spacetime and object properties emergently derive. This framework unifies physics, cognition, and AI under a single principle of informational coherence, opening pathways to fundamental discovery and transformative technology.