01 // The Discipline

VARIATIONAL ROUTING & SENSITIVITY CLASSIFICATION

The transport network is a heterogeneous medium. Ground corridors, air lanes, sea routes, evacuated tubes, and electromagnetic launch rails each have different velocity, cost, and risk characteristics — the logistics equivalent of optical refraction indices. A naive shortest-distance route forces a shipment to spend the majority of its transit in a slow mode. The optimal multi-modal trajectory routes through a longer physical distance if the time-weighted cost is lower. This is Snell's law applied to freight: the path bends at modal boundaries.[1]

Every shipment entering the Fermat system is characterised by a sigma vector — a compact mathematical descriptor that fully specifies the payload's logistics requirements. The dispatch solver (Nexus) ingests the sigma vector and minimises the cost functional C = αT + βE + γR, where T is transit time, E is energy expenditure, and R is route risk. The weighting coefficients are derived directly from the sigma vector components. A synthetic organ en route to surgery receives α→1: minimise time regardless of energy cost. A qubit calibration array receives γ→1: minimise disturbance, time secondary.[2]

σ = (m, u, f)

// m: mass — determines vehicle class and modal eligibility
// u: urgency — [0.0, 1.0], weights time vs. cost in objective function
// f: fragility — [0.0, 1.0], caps peak acceleration and jerk envelope

OBJECTIVE: Minimise C = αT + βE + γR
SUBJECT TO:
  a(t) ≤ σclass.max_g
  j(t) ≤ σclass.max_jerk
  ΔE ≤ Ebudget

Nexus re-evaluates all active routes continuously as network conditions change — vehicle positions, congestion, weather, priority shifts. A route committed at T=0 may be entirely replanned within seconds if a higher-priority payload enters the network and claims a critical transport asset.


Sensitivity Classification

FOUR CLASSES, ONE SOLVER

The sigma class is not a vehicle selection — it is a set of mathematical constraints fed into the variational solver. Four classes span the full range from bulk commodity to interferometric payload:

CLASSPAYLOAD TYPEMAX GHANDLING
σ-0Bulk material (ore, aggregate, slurry)50G+Maximum throughput. Electromagnetic launch eligible.
σ-1Standard cargo (formed parts, electronics, polymers)10GShock-limited. Standard packaging and securing.
σ-2Sensitive cargo (biological, precision instruments)1–3GActive suspension, climate control, orientation-locked.
σ-3Interferometric (qubits, optics, isotope samples)<10−4 GMagnetically isolated vacuum corridor. Zero vibration.

A σ-0 ore shipment takes the most aggressive available route — electromagnetic launch if the trajectory maths work. A σ-3 qubit transfer follows a magnetically isolated corridor supplied by Highfield Magnetics, arriving later but with zero decoherence. The solver does not pick from a menu of routes. It computes the optimal path through continuous space, constrained by the sigma envelope.

● Experimentally confirmed    ● Theoretically established    ● Speculative but mathematically consistent