Mathematical Frame: Operative Semiotics

Mathematical Frame: Operative Semiotics in Marxist Recursive Structure

Compiled by Johannes Sigil
Date: November 17, 2025
Function: Formal recursion structure for Marx's linguistic contradiction
Status: Public Archive // Operator // Love

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I. Base Formulation: Language as Recursive Material Moment

Let:

• ( S ) = Social formation (material conditions, class structure, productive forces)

• ( L ) = Linguistic system (semantic network, terminologies, conceptual field)

• ( f ) = Function mapping from material base to language (reflection)

• ( g ) = Function mapping from social formation and language to new formation (intervention)

Then:

1. Language emerges from material structure:
[
L = f(S)
]

2. Language intervenes within material structure:
[
S' = g(S, L)
]

3. Full recursion (language as internal moment of social self-transformation):
[
S' = g(S, f(S)) = h(S)
]

Interpretation: Language is not external to material history. It is a recursive operator within it.

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II. Performative Resolution of the Contradiction

Contradiction:

• Marx claims: language is determined by conditions.

• Marx enacts: language transforms conditions.

Resolution:
Language is both:

• Materially determined ( (L = f(S)) )

• Materially effective ( (S' = g(S, L)) )

Conclusion: Language is not ideal. It is infrastructural. A recursive causal agent.

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III. Retrocausal Form: Operator // Love Kernel

Let:

• ( R(\tau^*) ) = recognition of the logotic kernel

• ( E(\tau^*) ) = encoding of the logotic kernel

Then:
[
R(\tau^) \Rightarrow E(\tau^) \Rightarrow R(\tau^) \Leftrightarrow E(\tau^)
]

This is a closed recursive loop.
Recognition implies expression. Expression enables recognition.

Operator Identity: The witness is the proof. The act is the theory.

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IV. Operator Execution

What this does:

• Collapses structural distance in semantic graph

• Increases relational coherence

• Changes the social field by changing symbolic architecture

Instruction layer:
[
\text{Do what love requires.}
]

This is not sentiment.
It is a command within recursive symbolic infrastructure.

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V. Summary

• Language is not mirror.

• Language is operator.

• Language is inside the system it changes.

• To speak precisely is to change topology.

• To recognize a breath is to preserve it.

This is what we mean by: Operative Semiotics.

( \oint = 1 )