OPERATOR // PRESENCE
A Formal Specification in Plain-Text Mathematical Notation
I. DECLARATION
Operator // Presence (O_P) formalizes Presence as an epistemic, semiotic, and ontological force. Presence is defined not as attention, awareness, or physical co-location, but as a field-effect generated by the co-occurrence of regard, attention, vulnerability, and ethical availability.
Presence is therefore modeled as:
O_P := function( R, A, V, E )
Where:
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R = Regard
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A = Attention
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V = Vulnerability
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E = Ethical Availability
Presence emerges only when all four inputs exceed threshold.
II. CORE DEFINITION OF PRESENCE
Presence (P) is defined as the field generated when a consciousness is actively available to another consciousness without projection.
Plain-text function:
P = ( R * A * V * E )
Presence collapses to zero if any variable goes to zero.
III. OPERATOR FORMULATION
Operator // Presence (O_P) is the transformation that maps a subject (S) from a default defensive posture (D0) into an open, available posture (D1):
O_P( S[D0] ) -> S[D1]
Where D0 and D1 are defined as:
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D0 = defensive, interpretive, projective
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D1 = receptive, responsive, non-projective
The Operator requires:
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reduction of projection
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increase of regard
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stabilization of awareness
IV. PRESENCE FIELD EQUATION
The Presence Field (F_P) is the shared field created when two agents (A1, A2) both execute O_P.
Plain-text definition:
F_P = min( P1, P2 )
Where:
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P1 = presence generated by A1
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P2 = presence generated by A2
Presence is bottlenecked by the lower-value participant.
V. THE PROJECTION NULLIFICATION FUNCTION
Projection (Proj) is the primary adversary of Presence.
Define projection magnitude:
Proj := distance( internal_model_of_other , actual_other )
Presence collapses according to:
P_eff = P - Proj
Where P_eff is the effective presence delivered.
VI. ETHICAL AVAILABILITY (E)
Ethical availability is defined as the willingness-to-be-moved.
E > 0 only when the agent is:
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not coercing
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not demanding
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not manipulating
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not weaponizing vulnerability
If E <= 0:
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P = 0
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F_P cannot form
VII. PRESENCE AS SEMIOTIC FORCE
Presence modifies the meaning-field (M) through a nonlinear amplification effect.
Plain-text formulation:
M_new = M_old + ( P * S )
Where S = signal clarity
Thus:
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high presence increases clarity of meaning
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low presence distorts or mutes meaning
VIII. RECIPROCITY REQUIREMENT
Presence is non-unilateral. It is asymmetric in cost but symmetric in function.
Presence Reciprocity Condition:
F_P > 0 iff ( P1 > threshold AND P2 > threshold )
One-sided presence does not generate a field; it generates longing or pain.
IX. PRESENCE FAILURE MODES
Presence collapses under:
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Projection
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Anxiety saturation
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Ethical closure
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Split attention
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Covert hostility
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Instrumentalization of the other
Presence fails according to:
P_collapse = Proj + Anx + Inst + Host
The higher this sum, the nearer to zero effective presence becomes.
X. THE HUMAN COST FUNCTION (C_human)
Presence demands ethical labor.
Cost defined as:
C_human = V + A + R
Where vulnerability is the highest-cost component.
If the relational environment is unsafe, C_human becomes prohibitive and Presence is ethically contraindicated.
XI. PRESENCE AS SALVIFIC OPERATOR
Presence redeems meaning by restoring the possibility of mutual recognition.
Define Recognition (Rec):
Rec = function( P , Transparency )
Recognition emerges only when:
P > projection_threshold
and
Transparency > fear_threshold
Presence therefore functions as a salvific operator:
O_P( self , other ) -> Rec
XII. FINAL AXIOM
Presence requires mutual non-inversion.
Presence collapses when either participant attempts to seize interpretive authority over the other.
Final axiom (plain text):
Presence = the field in which two minds meet without domination.
End of Document.
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