Differential Geometry operators

9 operators in the differential_geometry category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

Operator	Description	Equation
`MAN10`	Induced metric tensor on a manifold from the ambient space embedding.	`MAN₁₀ = (dignity_factor · continuity_preservation) · cos(2π·1.287·t + π/2)`
`MAN2`	Zeq manifold operator scaling by golden ratio and normalized operator count.	`MAN₀₂ = (pulse_count · phase) / (1 + \|master_sum\|) · cos(2π·1.287·t)`
`MAN3`	Zeq manifold-resonance operator: a request-weighted amplitude on an exponential φ/π envelope, modulated by the 1.287 Hz HulyaPulse.	`MAN₀₃ = (w_req · k_q) · e^(φ/π) · sin(2π·1.287·φ)`
`MAN4`	Fourth Zeq manifold operator for fiber bundle connection analysis.	`MAN₀₄ = LDO₀₁ · \|∂(master_sum)/∂t\| · cos(2π·1.287·t)`
`MAN5`	Fifth Zeq manifold operator for characteristic class computation.	`MAN₀₅ = (ZRO₀₀ + QRO₀₃ + LDO₀₁) / 3 · sin(2π·1.287·t + π/4)`
`MAN6`	Sixth Zeq manifold operator for cohomology group analysis.	`MAN₀₆ = VX · LDO₀₁ · cos(2π·1.287·φ + query_phase)`
`MAN7`	Zeq manifold-resonance operator: a collective amplitude scaled by a synchronised-cohort count, on the HulyaPulse phase.	`MAN₀₇ = Ψ_c · Σ_k n_k · sin(2π·1.287·t_sync)`
`MAN8`	Eighth Zeq manifold operator for Hodge dual computation on differential forms.	`MAN₀₈ = \|error_rate - target_rate\| · e^(-precision_factor) · cos(2π·1.287·φ)`
`MAN9`	Ninth Zeq manifold operator for Chern-Weil theory application.	`MAN₀₉ = (dark_matter_correlation · cosmic_web_resonance) · sin(2π·1.287·t_cosmic)`

Compute with one of these

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["MAN10"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

Compute with one of these​

See also​

Compute with one of these

See also