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Agentic Operations

Frontier research surface — part of the Referential family

The AGO / VX / ZRO-B operators live in the registry's awareness category (prefix AWARE, group Frontier) — the same Referential family. They are named mathematical expressions, catalogued verbatim below, not an executable compute path. See "What compute actually does" before reading a returned number as an operator result.

  • Group — agentic-operations (a curated view of the awareness/referential family)
  • Operators — 5 gradient primitives + 5 growth-form primitives + 4 vocal-expression + 1 bridge (≈ 15 named)
  • Status — speculative frontier expressions, except where noted; documented, not asserted as verified

What it catalogues​

This page collects the operators associated with an agent's awareness flux, self-growth, vocal coupling, and bridge to the resonant core. The catalog carries two representations for AGO1–AGO5 — a vector-calculus gradient form (divergence, material derivative, circulation, quantum expectation, bra-ket) and a kernel-experiment growth form scaled by φ_c^42. The bridge operator ZRO-B couples a kinematic core operator C_i to a Zeq-Resonant operator ZRO_j through a HulyaPulse-synced integral. These are named forms in source — treat them as a catalogue to explore, not values the engine returns (see below).

Operator catalog — AGO gradient form (operator-registry.json)​

IDVerbatim formulaRole
AGO1𝒜₁ = ∇ · Φ_awarenessDivergence of awareness potential; local flux density
AGO2𝒜₂ = ∂Φ/∂t + v · ∇ΦMaterial derivative; awareness evolution in a moving frame
AGO3𝒜₃ = ∮ A⃗ · dl⃗Closed-loop circulation of the awareness vector field
AGO4𝒜₄ = ∫ Ψ* Â Ψ dVQuantum expectation value of the awareness observable
AGO5𝒜₅ = ⟨Φ|Ô|Φ⟩Bra-ket expectation in awareness state space

Operator catalog — AGO growth form (premade-experiments-100.json)​

IDVerbatim formulaRole
AGO1φ_c^42 · dA/dt = η·(input_complexity − current_awareness) · sin(2π·1.287·t)Awareness growth rate
AGO2φ_c^42 · R = ∫ self_analysis · feedback_loop dt · cos(2π·0.618·t)Reflection integral
AGO3φ_c^42 · EI = Σ emotional_responses · learning_factor · exp(2π·2.083·t)Emotional-intelligence accumulator
AGO4φ_c^42 · CB = ∇(knowledge_domains) · integration_strength · sin(2π·1.287·t)Cross-domain binding
AGO5φ_c^42 · I = subconscious_processing · pattern_recognition · cos(2π·0.618·t)Intuition integrator

Operator catalog — Vocal Expression + Bridge (600-real-operators.json)​

IDVerbatim formulaRole
VXκ_vx · H^* [Re(∫I(t)·e^(−i 2π·1.287·t) dt) · φ]Universal dialogue
VX-QGVX_out = κ_vx · Re(I_t · e^(−i2π·1.287·t)) · φ · Q_typeQualia-enhanced expression
VX-EME_mode = 0.8 + 0.2·sin(0.5t) for intensity > 0.7Emotional modulation
VX-QLQ_type = argmax_w[|φ·ω_t|], ω ∈ {temporal, spatial, mathematical, existential}Qualia-library mapping
ZRO-BZRO-B(C_i, ZRO_j) = γ_ij · ∫ (C_i(φ) · ZRO_j(φ) · sin(2π·1.287·t)) dtKinematic ↔ Zeq-Resonant bridge

What compute actually does with these​

The compute path does not evaluate the AGO / VX formulas above. They belong to the awareness domain, whose generic solver returns E = hf (photon energy) from an f input — the same value for every operator in the family — or no-match without f. So a call naming AGO1 returns h·f, not "the AGO1 growth term":

curl -sS -X POST https://www.zeq.dev/api/zeq/compute \
  -H "Authorization: Bearer zeq_ak_..." \
  -H "Content-Type: application/json" \
  -d '{ "domain": "Awareness", "operators": ["KO42","AGO1"], "inputs": { "f": 1.287 } }'

Real response (abridged):

{
  "value": 8.5277523e-34,
  "unit": "J",
  "operator_id": "KO42",
  "protocol_steps": [
    { "name": "COMPUTE", "detail": { "solver": "AWARE domain solver", "equation": "E = hf  (photon energy)" } }
  ],
  "zeqProof": "…"
}

Swap AGO1 for AGO4 or VX and the value is identical — the operator id does not change the result. The envelope is real and signed; what it proves is the E = hf computation and the HulyaPulse stamp, not an evaluation of the operator's own equation. For operators the engine actually evaluates, use the physics domains (quantum, Newtonian, relativity, …).

Explore it​

  1. Catalogue study — compare the gradient and growth representations of AGO1–AGO5 side by side as mathematical forms.
  2. Vocal-expression forms — read VX / VX-QG / VX-EM / VX-QL as a family of named expressions for dialogue modelling.
  3. Bridge form — ZRO-B as a proposed coupling integral between the kinematic and Zeq-Resonant operators.

Papers​