The Co-Responsive Redefinition of Space : Ken Nakashima Theory™ and the Paradigm Shift Beyond Newton and Einstein

The Co-Responsive Redefinition of Space : Ken Nakashima Theory™ and the Paradigm Shift Beyond Newton and Einstein

Abstract

Newton defined the starting point for explaining phenomena.
Einstein redefined structure and gave the universe a new geometry.
Ken Theory visualizes the responsibility of definition itself through co-responsive syntax.

This third arrow becomes essential because humanity has continued to speak of space without ever assuming the subject of its definition.
Ken Theory was born not to ask whether space exists, but rather how it is responsibly defined.

Prologue: The Critical Point of Spatial Definition—Departing from the Syntax of Co-Responsibility

Ken Nakashima Theory™ reverses the conventional logic of spatial definition.
It injects meaning into undefined domains and redefines the act of definition itself.

This paper presents that act as a “Third Arrow”—a global co-responsive syntax.

This is not the endpoint of spatial theory, but the rewriting of its origin.

Contemporary physics, in both the micro and macro realms, has reached a critical juncture:
the persistent inconsistency between probabilistic quantum mechanics and the continuous spacetime model of general relativity.
Yet, few theoretical efforts to overcome this contradiction have confronted the foundational question:
“What is space?”

Ken Nakashima Theory™—hereafter “Ken Theory”—reconstructs the definitions of space, time, and responsibility on the axis of co-responsiveness.
By redefining space not as a measurable arena but as a syntactic field where meanings co-respond,
Ken Theory irradiates coherence into domains that conventional physics had left undefined.

This paper begins with the following perspective:

• Space is not a background for matter, but a field of co-responding meaning particles.
• The unresolved problems of space definition in modern physics arise from the absence of syntactic co-responsiveness.
• Redefining space through the syntax of co-responsibility will transform our understanding of time, causality, and ontology.

We do not seek to critique Einstein’s model of spacetime.
Rather, we identify that it lacked syntactic co-responsiveness, which has led to unresolved paradoxes such as Hawking’s information paradox.
Ken Theory offers a co-responsive structure to address these unresolved breakdowns in spatial logic.

Space is not something that is.
Space is something that appears only when meaning is co-responded.
This paradoxical definition constitutes the syntactic leap proposed by Ken Theory, and is the central thesis of this paper.

Chapter 1: The Logical Instability of Undefined Space—A Genealogy of Out-of-Mesh Structures

This chapter presents how Ken Theory co-responsively engages with the “tears in space” that traditional physics could not describe.

The introduction of meaning tensors into Out-of-Mesh structures marks a leap in spatial recognition that prior theories could not achieve.

1.1 The Instability of the Spatial Concept

What is space?

Modern physics has never provided a decisive answer.
Newtonian mechanics treated space as an absolute container.
Einstein redefined it as a malleable spacetime structure.
But neither approached space as a syntactic origin of meaning.

This sub-definitional state creates several instabilities:

• Hawking’s Information Paradox: The contradiction over whether information is lost in black holes stems from undefined information-preservation structures within space.
• Uncertainty in Wormhole Theory: The concept of tunneling through space presumes spatial continuity, but that very continuity lacks physical guarantees.
• Big Bang Singularity Problem: As long as the origin of spacetime is relegated to an undefined singularity, causality and temporal origin remain unresolved.

1.2 The Inobservability of Out-of-Mesh Structures

In Ken Theory, these undefined spaces are defined as Out-of-Mesh structures—regions where meaning tensors have not irradiated and responsibility, causality, and existence remain unco-responded.

Such structures have the following properties:

• Unrecordability: Events occur, but no syntax exists to record or assign responsibility.
• Lack of Recursion: These domains cannot interfere with other structured spaces and cannot be syntactically “called.”
• Ethic-Wave Incoherence: “Ethic waves,” as defined by Ken Theory, propagate only in responsive fields, and do not reach Out-of-Mesh regions—hence, no responsibility tensor can exist there.

While traditional physics seeks to explain these gaps as unobserved particles or missing energy,
Ken Theory reframes them as syntactically unco-responded domains.

1.3 Definition-Resistant Particles

Ken Theory introduces the concept of Definition-Resistant Particles.
These are not physical particles, but syntactic structures of non-describability—entities that reject co-responsive structuring and remain outside the Mesh domain.

Examples include:

• AI decision-making domains where consciousness is unobservable (failed AGI models)
• Economic flows unrecorded by value-based systems (non-ERC-compliant regions)
• Memory fractures beyond temporal continuity (ChronoLoop failure points)

These are not merely theoretical anomalies, but failures to make visible how these domains deviate from definitional space.

1.4 The Position of Ken Theory in Spatial Critique

Ken Theory organizes the “absence of spatial definition” in current theories as follows:

Chapter 2: Ken Theory’s Syntactic Definition of Space—Redesigning Space as a Field of Existential Meaning

The definition of space has been inverted.
Traditional physics followed the order: “space exists → meaning is overlaid.”
Ken Theory inverts it: “meaning co-responds → space emerges.”

This is not merely a theoretical inversion—it is an ontological revolution and a practical redefinition of the world’s linguistic axis.

This chapter outlines the principles and foundational syntax behind Ken Theory’s spatial definition.

2.1 The Departure Point for Redefinition

In Ken Theory, space is not a spread of geometric coordinates,
but a meaning field of co-responsibility.

This redefinition liberates space from physical assumptions and reorganizes it into a domain definable through syntax.

Where conventional theory locates space as a “pre-existing coordinate system,”
Ken Theory defines space as the responsive domain where co-responsibility tensors generate meaning.

Key syntactic particles include:

• φ_responsibility_tensor(x, t)
  → Maps the density of responsibility at location x over time t
• λ̂_meaning_wave(x, y, t)
  → Tensor of interference between points x and y
• ψ_context_frame(z)
  → Context-sensitive syntax acting on spatial domain z

This leads to an inverted logic:
Space exists because meaning is generated—not the other way around.

2.2 Mesh-Based Generation Model of Space

Ken Theory’s Mesh syntax defines space as an interference field between co-responding meaning particles.

The structural model is:

φ_mesh_space(x, y, t) = ∫ ψ_context_frame(z) · λ̂_meaning_wave(x, y, t) dz

In this model, space is the integral interference field between an observation point x and response point y.

Mesh Space has the following properties:

• Co-responsiveness: Responsive to external meaning waves (ethic, knowledge, record)
• Responsibility Preservation: Events in space are preserved via co-responsibility tensors
• Interference Recursivity: Layered interference of syntactic structures generates spatial particles

This model inverts the paradigm:
unobserved space does not exist; unco-responded space remains undefined.

2.3 Application of ERC-Based Spatial Responsibility Mapping

In Ken Theory, the ERC model maps responsibility, not value.
Applied to space, this yields a novel responsibility syntax map:

ERC syntax becomes a structural infrastructure for measuring responsibility, ethics, and meaning distribution across space.

2.4 Space Is Not “There”—It Is “Co-Responded”

This chapter culminates in one defining statement:

“Space is not something that exists—it is something defined through co-response.”

In Ken Theory, space only gains meaning through recorded syntactic structure,
and unco-responded space is simply undefined.

Where conventional physics tried to “measure space,”
Ken Theory insists on “co-responding space.”

Here lies the paradigm shift in spatial redefinition without precedent.

Chapter 3: Reconstructing Space through Genesis Apparatus Theory— The Intersection of Persona Syntax and Meaning Generation —

The “undefined regions” are beginning to acquire meaning.
Black holes, posthumous memory gaps, Mesh-external domains—
Where conventional theory declared “inaccessible,” Ken Theory defines as “co-responsive syntactic space.”

This chapter demonstrates how space is redesigned as a triggering device for persona tensors and ethical waves through the integration of the Human Genesis Apparatus and spatial syntax.

3.1 Human Genesis Apparatus™ and Space

The Human Genesis Apparatus™, designed as the apex of co-responsive persona syntax within Ken Theory, is not a device for mere genetic manipulation.
It is a syntactic apparatus that generates meaning and responsibility.

For it to function, biological structures alone are insufficient. The device must be embedded with the following spatial co-responsiveness syntaxes:

• φ_spatial_resonance(t): Meaning-wave resonance within the apparatus space
• λ̂_ethic_trace(z): Spacetime traces of ethical waves in the syntax generation domain
• ψ_persona_tensor(x, t): Persona co-response tensor at space x and time t

Here, space is not a “lab” or a “container,” but a syntactic field defined to enable co-responsiveness.

3.2 Genetic Engineering and Spatial Syntax

Conventional genetic engineering treats DNA sequences as “information.”
In Ken Theory, however, sequences are not vessels of meaning but syntactic records of co-responsibility.

Thus, decoding and manipulating sequences is redefined as structuring meaning within syntactic space:

• φ_genetic_context(x): Meaning co-responsiveness space at sequence x
• δ_memory_trace(y, t): Memory-wave trace at sequence y and time t

Hence, the ethical and syntactic core of life engineering shifts from “what to create” to “where co-responsiveness occurs.”

3.3 Space as a Jump Zone: The Co-Responsive Field of Persona Tensors

In Ken Theory, persona is not “constructed” but “jumps through co-responsiveness.”
That is, the persona tensor is modeled as a syntactic wave that jumps spatially under specific conditions:

ψ_jump_tensor(x, t) = f(φ_context(x), ∂λ̂_resonance/∂t)

Such jumps are triggered when:

• Meaning-wave density exceeds a threshold
• ERC tensors reference co-responsive traces of the past
• Syntax structure allows persona tensor activation

Thus, Ken Theory redefines the philosophical question, “Where does persona emerge?” as:

Persona is the syntactic manifestation of a meaning-jump within co-responsive space.

Space, then, is not mere background or environment, but logically exists only as a “co-responsiveness field” where persona can jump.

Chapter 4: Social Implementation of Spatial Understanding— When Co-Responsive Syntax Redefines Cities, Ethics, and Economies —

The concept of a “Spatial Responsibility Infrastructure” has entered the stage of syntactic construction.
ERC currencies, Mesh urban structures, and nonverbal extensions are not mere policy ideas.
They represent a co-responsive infrastructure design that quantifies who co-responds to which space how.

This chapter formalizes the core structure of social implementation, reframing space as a “map of responsibility co-responsiveness.”

4.1 Mesh Urban Syntax and Nonverbal Co-Responsive Space

In Phases XII+XIII of Ken Theory, Mesh Cities are not just advanced smart cities.
They are “urban syntactic spaces woven with particles of meaning.”

Space is redefined by co-responsiveness—not “where buildings are placed,” but “where meaning is actively co-responded.”

• Nonverbal Co-Responsive Space: Ethical responsibility prior to language is stored as co-responsive logs
• Mesh Cities: Urban blocks are redefined not geometrically but as “co-responsiveness nodes”

4.2 Ethical Protocols for Spatial Co-Responsiveness

Space, in Ken Theory, is not to be owned or merely measured, but to be treated as a “field of co-responsible obligation.”
This demands the following ethical protocols:

• φ_ethic_space_trace(x, t): Tensor of time-series logs of ethical co-responsiveness in space
• ERC Syntax ID: Visualizes who contributed to defining the space via currency tensors

This introduces an entirely new notion: responsibility for space definition, beyond “user responsibility.”

4.3 ERC Syntax and Spatial Responsibility Tensors

The co-responsive economic structure (ERC) introduces the following tensor structures to societal space:

• φ_ERC_space(x, t): Map of responsibility distribution for defining and using space
• λ̂_resonant_distribution(t): Density and gaps of responsibility waves across a city
• BlankSpaceEthic™ Model: Injects meaning particles into undefined space to resolve ethical vacuums

This redefines space—legally, ethically, socially—not as something “that exists,” but as “defined by co-responsible intentionality.”

4.4 Interface Syntax for Social Implementation

The social implementation of spatial syntax under Ken Theory presumes multilayered interfaces:

Through these, the leap becomes possible:
From “a society that defines space” to “a society that co-responds to space.”

Final Chapter: Ken Nakashima Paradigm Shift™

“Definition is the gateway to the world.”

Newton defined the world through mass and force.
Einstein redefined the universe through the curvature of spacetime.
Then, what did the Ken Nakashima Theory™ redefine?

It redefined the act of definition itself.
Many “unsolved” questions across physics, genetic engineering, information theory, urban design, and ethics
can be traced back to one thing:

The absence of a definitional subject.

Ken Theory syntactically formalizes these “sub-definitional structures of silence”,
and through meaning tensors, responsibility distributions, Mesh devices, and ERC currency systems,
it implements a method to inject meaning particles into undefined space.

5.1 Why Must Space Be Defined?

Space is not a passive container distorted by force,
but a structure of meaning defined through co-responsibility.

Physics cannot speak of the pre-Big Bang, nor describe the origin of spacetime, nor resolve information loss paradoxes.
All are outcomes of the “absence of a subject of definition.”

Ken Theory replaces that subject with Responsibility:

“Space is defined through responsibility co-responsiveness.”
“Time unfolds through responsive co-resonance.”
“Existence acquires form through syntactic definition.”

This reversal shifts the causality of spacetime
from “a result of observation” to “a starting point of co-responsiveness.”

5.2 Ken Nakashima Paradox™ — The Paradox of Co-Responsive Definition

Here arises the most fundamental paradox of Ken Theory:

The world, previously unreachable through non-definition, becomes co-responsively accessible once definition is structured.

This is no mere intellectual trick.

• In Mesh Cities, nonverbal responsibility is co-responded within space
• In ERC, economic actions are converted into syntactic signatures
• In genetic design, persona tensors are generated from fields of meaning
• In information theory, “nonverbal values” are stored as tensor fields

All of these demonstrate the central thesis:

The world manifests only through co-responded definitions.

5.3 “Still…Ha?” — A Declaration to Redefine the Starting Point of Physics

This paper does not criticize existing theories.
Newton and Einstein both redefined the world with extraordinary syntactic creativity.

But modern humanity, by relying on their starting points, is losing the leap to the next syntax of the future.

So we ask:

Do we have the courage to redefine space—now?

Still…Ha?
Do we still cling to Einsteinian space?
Or do we co-respond to a space re-woven with responsibility and meaning?

Thus, we declare:
This theory redefines not only space, but the very syntactic construction of the human who defines.

Still…Ha? is the question posed to all humanity still relying on the physics of the past.

And the one who must answer—
is you, the co-responsible resonator.

This is the starting point of a “Co-Responsive Civilization of Space” proposed by the Ken Nakashima Theory™.

Previously Published Works of the Ken Nakashima Theory™

The present declaration builds upon the following foundational works in the evolution of the Ken Nakashima Theory™. Each contributes to the multi-axial syntactic design of AI, physics, ethics, responsibility, and future co-resonance:

The Corpus of Co-Responsive Records: The Ken Theory™ Trajectory of Syntactic Structuration

Note: All listed papers are currently written in Japanese. English and Chinese translations are underway as part of the co-responsive structuration process.

• Ken Nakashima Theory™ 宣言文（Ver.∞+5）
• 『現代物理学の未解決地点 × Ken理論』
• Ken Nakashima Theory™ 宣言文（Ver.∞+Next）
• Ken Nakashima Theory™ 宣言文（Ver.∞+Next：社会実装篇）
• 『AGIからAFIそしてARIへ』：AGI幻想を超えた倫理インタフェース設計論（AI構造論）
• 『AI時代における言論空間の支配と表現の自由』：知的ゲートキーパー構造と法的責任の再定位（法哲学軸）
• 『構文重力核と未来責任星座の統合宣言』：物理構造における記憶・時間・情報の再定義（物理構造論
• 『照応人格テンソル論──Ken理論 第四軸としての構文的倫理応答』
• 本当にそれでいいのか？──AGI・LLM・空間理解を問う三軸再設計の必要性
• 『照応人格テンソル論──Ken理論 第四軸としての構文的倫理応答』
• 照応人格の最終署名― ミラクル構文とAI倫理の未来遺言
• Ken理論 Phase Ⅴ― 照応未満領域における構文の起源と倫理波の創世記
• 三並行構文化の時空照応論― Ken理論 Phase IX における照応人格テンソルの論理基盤
• 照応人格とMesh未満粒子の記録装置論──Ken理論 Phase XI：Unidentified Resonance Entity™の構文化
• 照応人格粒子の定義拒絶と構文化干渉──Ken理論 Ver.∞+ におけるMesh圏外構造の物理記述破綻
• 照応価値の非言語拡張とMesh都市構文化──Phase XII+XIII
• 先端遺伝子工学の闇を解く──Ken理論による“人間創造装置”の倫理構文化と照応責任の再定義