Causality-respecting FTL: A primer

Basic, rough operational understanding

In our world, travel in space is always proportional to travel in time. This means that when we accelerate in space, in a sense we trade speed in time to gain speed in space. Slower-than-light (STL) travel means we move greater distance in time than in space; at lightspeed travel our motion through space and time become equal; and at FTL speed we begin to move greater distance in space than in time.
When we say FTL "travel" what we usually mean is something like "instantaneous travel". However, in a world where motion in space modifies our motion in time, the definition of "instantaneous" becomes complicated. All travel through space incurs some passage of time. Therefore, the goal of FTL (travel back in time) is to cancel out the forward time incurred by STL travel.
This means that all FTL travel has two halves: an STL leg, and an FTL leg.
The STL leg always comes first because FTL travel requires the creation of a spacetime tunnel: a wormhole, or a Krasnikov tube. It should be clarified here that "true FTL" travel in the sense of, say, a warp bubble accelerating past the speed of light never occurs. The reasons for this are covered in Reactionless Propulsion.
A spacetime tunnel is a link between two points in spacetime: in a wormhole, for example, time passes at an equal rate for both gates of the wormhole, because inside the wormhole, they are not moving relative to each other.

Example: Wormhole linelayer

Say a wormhole Linelayer (a type of Metric Utility Ship) deploys a destination gate 1LY away at 80% lightspeed. The trip takes 1.25 years relative to observers on the homeworld. The shipboard time dilation factor (inverse of the Lorentz factor) is 0.6x outside time, making the journey last 0.75 years to the wormhole gate aboard-ship. The wormhole therefore links between the ship 1.25 years after departure to the homeworld at 0.75 years after departure (0.5 years in the past).
This does not create a time paradox. On one hand, time passes at the same rate through the wormhole, so no paradox is created by moving information through the wormhole. The potential trouble comes when information from normalspace enters the wormhole (which links to the past in the destinaton-to-homeworld direction). The central tenet of chronology protection is that information from an object's future must never reach its past. When it can, this is called a closed timelike curve (CTC).
Maybe the trouble comes if information from in normalspace can enter the wormhole and travel back in time. Our linelayer traveled at 0.8 c and took 1.25 years total, but experienced only 0.75 years, and receives homeworld light-info from 0.25 years after-departure. This means Normalspace info from H is always 0.5 years in the past compared to the Wormhole connection to H. This does not create a paradox, since all information flow is still past-to-future.
This means 1 - 0.5 = 0.5 LY is the absolute minimum distance the two wormholes can approach one another again, assuming extremely slow transport speed (further relativistic travel and time dilation would increase it). We can call this the minimum paradox radius.

Network Architecture

There are a few ways around this problem.

Slow linelayers

One is to deploy stargates at a slow speed from the beginning. At sub-relativistic speeds, the paradox radius drops drastically. A linelayer traveling 1 LY at 0.2 c, for instance, incurs a travel time of 5 years, and dilated ship/wormhole time of 4.9 years. Meanwhile, normalspace light-info from Gate H arrives at Gate D from 4 years after departure, a total of 0.9 years of difference. The paradox radius then becomes 1 - 0.9 = 0.1 LY.
Paradox radii become mostly negligible at interplanetary deployment speeds - say, 40 km / s for a high example (0.0001334256 c). The Lorentz factor is 1.0000000089, inverse is 0.9999999911. If we wanted to deploy a wormhole over 1 light-hour (3600 light-seconds, about 1e9 km, or 4.7x the semi-major orbital radius of Mars), our travel time is ~2.698132122e7 sec (~312 days).
Dilated time is ~2.698132097e7 sec. Normalspace light-info arrives from Gate H to Gate D from 2.697772112e7 sec after departure, yielding a difference of 2.698132097e7 dilated time - 2.697772112e7 light-info time = 3599.85 sec. The paradox radius then becomes 3600 - 3599.85 = 0.15 light-seconds, or about 12% the Earth-Moon distance.

Gravitational time dilation

General relativity offers the possibility of inducing time dilation using tremendous masses. Specialty, high-power metric drives, such as those employed by Metric Utility Ships, are capable of summoning the requisite energies from the NSET brane for such purposes. Slowing down the wormhole's subjective experience of time on the destination end allows the homeworld gate to "catch up", and vice-versa. This can be used to modify the network architecture to allow placement of gates that would otherwise threaten causality violation.

Midpoint deployment

Another way to lessen the problems of relativistic deployment on the network is to initiate two stargates at the midpoint between two systems. This ensures that both gates experience dilation effects into the future as they are separated.

Robustness & failure modes

Spacetime tunnel networks that rely on the NSET brane are quite robust against causality violations. The reason for this, predicted by Hawking in the 20th century, is that gravitational fluctuations arise between any two structures that are approaching close enough to violate causality, which would form what is known as a Cauchy horizon. The gravitational fluctuations push the two structures apart, preventing the Cauchy horizon from forming, and causing a shift in the overall structure of the network if many tunnels are involved.
The true failure mode of a tunnel is called Visser collapse, and it occurs only under fairly extraordinary circumstances; in this case, the formation of a Cauchy horizon is prevented by quantum fluctuations that destabilize the tunnel and cause it to detonate. Due to the mechanics of the NSET brane this explosive power is dampened from what it would otherwise be using negative stress-energy tensors indigenous to our branes, but it can make a formidable weapon.

Network architecture

In the absence of gravitational time dilation devices, the default form of a tunnel network laid at relativistic speeds takes the shape of a directed acyclic graph, or a star network. Midpoint deployment and GTD allow for more distributed interstellar network structure.
Sometimes, polities see fit to disrupt the network for military purposes. Metric utility ships called super-interdictors are equipped for heavy duty work in this regard.

Type

Natural