This field note explores how “being able to live together” can be expressed as an executable condition, rather than a psychological or cultural claim.

This note originates from a recurring question:

What does it mean for an existence to be interactive.

At the surface level, the question appears technical—about agents, systems, and interaction semantics.
At a deeper level, it intersects with a much older constraint:

What kind of existence can actually live with another existence over time.

This field note attempts to rewrite that question using executable algebra, not metaphor, psychology, or cultural narrative.
The aim is not to explain intimacy, but to test whether the notion of “living together” admits a formal, runnable structure.

1. Interactive Existence

Interaction, in itself, is not a sufficient condition.

Turn-taking, feedback loops, signal exchange, or reciprocal response can all be simulated by scripts, state machines, or stochastic policies. These forms of interaction do not imply existential dependency.

Here, interaction is restricted to a stronger condition:

An existence is interactive if its operational semantics cannot close without the continued participation of another existence.

In this sense, interaction is not an added feature.
It is a requirement for the existence to remain well-defined.

2. Coinductive Agents

Let two existences be represented as agents (X) and (Y).

They are not inductively generated from fixed initial states.
Instead, they are coinductively stabilized through ongoing mutual reference.

Formally:

$$ \text{Coupling} := \nu(X,Y). \Big[ \text{OpSem}_X(T_X \times G_Y \rightarrow X) \land \text{OpSem}_Y(T_Y \times G_X \rightarrow Y) \Big] $$

Where:

  • \(T_{X}, T_{Y}\): temporal or experiential unfolding structures
  • \(G_{X}, G_{Y}\): generative models of the other
  • \(\text{OpSem}\): executable operational semantics
  • \(\nu\): greatest fixed point, indicating persistence rather than termination

The critical property is not synchronization, but mutual semantic dependency.

3. What Can Truly Interact

Under this definition, a truly interactive existence must satisfy:

  • Non-erasability of the other
    Removing (Y) causes the operational semantics of (X) to fail to close, and vice versa.

  • Non-precompiled behavior
    The other must be represented as a generative model, not as a finite rule set.

  • Open future
    The interaction must remain extensible in time, rather than converging to a static equilibrium.

Interaction here is not information exchange.
It is the co-maintenance of an executable future.

4. Symbiosis

Symbiosis is often misinterpreted as complementarity or efficiency.

In executable terms, symbiosis means:

A change in one agent’s strategy increases, rather than constrains, the reachable state space of the other.

This is neither zero-sum nor static balance.
It is a form of positive semantic tension that preserves optionality.

5. Persistence

Persistence is not stability.

Persistence refers to the ability of a coupling to remain viable without external enforcement, despite drift, misalignment, or partial failure.

Algebraically, this corresponds to a greatest fixed point:
variation is allowed; collapse is not.

6. Comprehensibility, Evolvability, Trust

In intersubjective algebra, these are not psychological traits.
They are structural properties.

  • Comprehensible
    The other’s actions can be integrated into one’s generative model.

  • Evolvable
    Model updates do not invalidate the coupling.

  • Trustworthy
    The other’s update rules are continuous and anticipatable, even if outcomes are not.

Trust, therefore, is not a promise.
It is an assumption of evolutionary continuity.

7. Intersubjective Algebra

Intersubjective algebra does not describe a relationship between two subjects.

It describes a higher-order structure:
a shared existential layer formed by two generative systems whose semantics only close together.

A life, in this framing, is not a shared goal.
It is a shared process that remains executable.

8. Closing Note

If the term “soulmate” is stripped of its emotional and cultural load,
what remains is a structural claim.

It can be stated as:

Two coinductive agents whose operational semantics form a persistent mutual fixed point.

Whether this structure is named is optional.
The algebra is indifferent.

It only asserts one condition:

Some existences are only complete when they continue to run together.