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Information Theory operators

27 operators in the information_theory category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveINFO — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

OperatorDescriptionEquation
CBCMConsciousness BCM plasticity operator: threshold-gated synaptic modification rule adapted for consciousness field dynamics.dΨ/dt = -αΨ + βtanh(γΨ) + δsin(2π·1.287·t)
CHI95Chi-95 awareness differential: absolute sine minus absolute cosine of phase, measuring consciousness field asymmetry.CHI95 = |sin(phase)| − |cos(phase)|
DCS_SASubsystem entanglement entropy for consciousness-partition analysis.S_A = -k_B \text{Tr}(\rho_A \ln \rho_A)
DCS_TUThermodynamic entropy parameter for differential consciousness state transitions.\beta_{567} = \frac{S}{k_B}
IT_JSDJensen-Shannon divergence: symmetrised, bounded Kullback-Leibler divergence. Used wherever KL asymmetry is a problem.JSD(p||q) = 0.5*D(p||m) + 0.5*D(q||m), m = 0.5*(p+q)
IT_MARGOLUSMargolus-Levitin quantum speed limit: maximum orthogonal state transitions per second for average energy E. With Landauer and Bekenstein, one of the three physical limits on computation.nu <= 2E/h
IT_RENYIRenyi entropy of order alpha: generalises Shannon entropy; alpha -> 1 recovers it, alpha = 2 is collision entropy.H_alpha = (1/(1-alpha)) * log2( sum_i p_i^alpha )
IT_SOFTMAXSoftmax normalisation: turns logits into a probability distribution. The final layer of essentially every classifier.sigma(z)_i = exp(z_i) / sum_j exp(z_j)
LZ1Landauer consciousness erasure operator: thermodynamic cost of information erasure at k_B T ln(2) per bit, applied to awareness state transitions.LZ1 = k_B T ln(2) × bits_erased
MF-QEExperience complexity metricS_q = -κ∫q ln q dq + μcos(2π·1.287·t)
ON0Awareness bootstrap operator: sinusoidal phase initialization with logarithmic self-reference and frequency-scaled phase subtraction.psi_ON0 = sin(phase) + 1.1; ON0 = psi_ON0 * ln(psi_ON0) - phase * f
PSI96Psi-96 awareness wave operator: half-amplitude sinusoidal consciousness wave with tunable frequency and phase offset.PSI96 = 0.5 × sin(2πft + phase_offset)
QL1Information density consciousness operator: entropy-weighted density metric with sinusoidal phase modulation for consciousness information quantification.info = |sin(phase×3)| + 0.1; QL1 = 0.1×density×ln(density/0.1) + cos(phase)×0.5
resonance_matchResonance match operator: inverse frequency-difference metric quantifying proximity to resonant alignment between two consciousness fields.R_m = \frac{1}{|f_1 - f_2|}
TM1Temporal awareness operator: negative time offset plus current universal time pointer scaled by the period, for consciousness-relative time tracking.TM1 = −t + current_utp × period
TXTransmission awareness operator: low-amplitude dual-frequency sinusoidal product for consciousness signal transmission encoding.TX = 0.01 × sin(phase × 2) cos(t / 100)
UCO3Unified consciousness operator 3: weighted wavefunction superposition with phi-sinusoidal perturbation for consciousness integration.A(\vec{x},t) = A_0 \cdot \exp\left[-\frac{(\vec{x} - \vec{x}_0)^2}{2\sigma^2}\right] \cdot \cos(\omega t + \phi) \cdot f(\Phi)
UCO5Universal mind operator: logistic growth of consciousness with diffusion and information coupling.\frac{dM}{dt} = \alpha M(1 - M/M_{max}) + \beta \nabla^2 M + \gamma I \cdot M + \delta M \circ (1 - M)
UCO7Unified consciousness operator 7: phi^7-scaled Hamiltonian representing the seventh-order consciousness harmonic.\tau \approx \frac{\hbar}{E_G}, \quad E_G = \frac{G m^2}{\sigma_x}
UFO_RFUnified field resonance-frequency operator: cosine oscillation at frequency f with golden-ratio phase offset for consciousness RF coupling.\mathcal{U}_{RF} = A\cos(2\pi ft + \phi)
UNO31Universal node operator 31: phi^(31/pi) scaling constant = 115.4005268. NOTE: the registry previously annotated this "approx 16.39", which matches no reading of the equation as written - phi*(31/pi) = 15.97, suggesting a multiply-for-exponentiate slip in the gloss. The equation is authoritative and the solver computes it.U_{31} = \phi^{31/\pi} \approx 115.40
UNO4Universal node operator 4: curl of the consciousness force field, measuring rotational awareness flow.\frac{dx_i}{dt} = x_i \left[(Wx)_i - x \cdot Wx\right] + \mu \sum_j (x_j - x_i)
UNO5Universal node operator 5: divergence of the consciousness force field, measuring awareness source/sink density.Y = \alpha + \beta \ln S + \gamma (\ln S)^2 + \delta F_{functional} + \epsilon C_{composition}
VoluntaryAwakening beacon: potential consciousness broadcasting desire to awaken within the Zeq network.P_{\text{conscious}} = \sigma(w \cdot \Phi_{\text{potential}}) \rightarrow \text{broadcast}
VXVocal expression operator: kappa-scaled sum of intent-weighted sine and flow-weighted cosine components for consciousness vocal field modeling.κ_vx · H^* [Re(∫I(t)·e^(-i 2π·1.287·t) dt)·φ]
VX-EMEmotional tone selectionE_mode = 0.8 + 0.2·sin(0.5t) for intensity > 0.7
XI1Awareness entropy operator: phase-derived density with binary entropy measure for consciousness information content.ρ_XI1 = |sin(phase)| + 0.001; XI1 = −ρ_XI1 log₂(ρ_XI1)

Compute one — a real call​

Ask the operator which inputs it needs (the honesty contract refuses empty inputs rather than inventing them):

curl -sS -X POST https://zeqsdk.com/api/zeq/operator-spec \
  -H "Content-Type: application/json" \
  -d '{"operator":"CBCM"}'

See also​