ATRUVAI research

Mathematics of private AI individuality.

Public research notes from the Zarvok mathematical architecture, split into readable articles. No download wall, no version label, no internal deployment coordinates.

Runtime mathematics

Runtime individual state space

A private AI individual is treated as a measurable runtime object, not a display name. Its state includes identity, sandbox, memory, regulation, world model, context binding, privacy state, chronology, and microcircuit telemetry.

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Identity-time

Hashchain and lineage calculus

Identity-time continuity is represented as a hash-linked sequence of private runtime events. A copied state can be detected as lineage conflict without claiming physical non-clonability.

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Control field

Bilinear regulatory gate calculus

The regulatory field adjusts salience, threshold, gain, inhibition, and memory-pass pressure. These are computational control variables, not claims of emotion or consciousness.

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Memory and adaptation

Memory separation and metaplastic fluid control

Memory separation prevents similar names or contexts from collapsing into one private trace. Fluid control lets runtime rules adapt while bounded NoGo pressure suppresses irrelevant learned rules.

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World and context

Symbolic world path and What/Where binding

Zarvok's public mathematical frame separates active state from counterfactual world traces and binds object, place, time, relation, and target into contextual hashes.

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Privacy and field separation

Phase lattice and vault calculus

Private coordinate frames and access-control calculus separate individuals under the same visible label and gate access to sealed private records.

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Proof surface

Grand proof calculus

The proof frame combines identity separation, timeline validity, regulatory telemetry, memory separation, fluid stability, world traces, context binding, privacy enforcement, phase divergence, and lineage control.

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