I am in a timeline which would be tens of thousands of years advanced from yours, and humans have colonized a significant portion of the stellar neighborhood, multiple thousand light-years across (Last I checked - a century maybe?). Sadly, the laws of physics you devised, on the grand scale, seem to mostly (with a few exceptions) have held up (importantly - relativity). Many of you can probably extrapolate our technology (Ignore the timeline communicator - It was given to me by the Great God of Plot and will be taken away by Him after I have received my answer). Probably the greatest invention is fusion energy and torchships - capable of supporting constant 1g (or more upto Plot) acceleration for an extended period of time, without being a weapon of mass destruction from the heat (due to Plot. One of the few deviations from your world physics. Thermodynamics turned out to be somewhat forgiving! It is still destructive due to its kinetic energy.)
I have reached my destination, System X. I was sent here to build a semi-colony semi-military-base, and am the grand authority here. This system is particularly close to routes fleets of opposing factions would need to take to into allied space. I have a few million colonists, and a drone fleet that was sent at greater accelerations and arrived a few years before. It has mined up a lot of the resources we would need to begin colonization in luxury. They even have a Dyson swarm set up that can extract as much energy as I will need. This system is ours for all intents and purposes.
The test target is an enemy fleet that will - at its closest point - pass within a few light-years of this system. This will happen in a bit more than a century. We know the ship design and know they have accelerated to maximum velocity - They don't have enough fuel for significant deviations from this course. Thus, I have a few decades to build my weapon.
What I have in mind is a huge battery of railguns - as many as Plot demands! They will be capable of accelerating a projectile of mass Plot to around 0.2c max (if that is insufficient, it will be accelerated to Plot). Using my massive fleet of drones, and some calculations about the rate of material gathering, I believe this can be done in the required timespan.
But is it viable? Can using thousands of railguns to attack this fleet at interstellar distances work? I must send a report of my plans to my superiors in a few hours (technically, years), so I must be certain my plan will work. It will be really bad for me if they calculate it will not - and will thus have wasted more then a decade by the time their new orders get here. So I want to be sure this will be able to significantly damage any fleet which passes within a reasonable distance of this star system.
Additionally, will they or a nearby star system be able to tell exactly what I am constructing? Not that they could do much about it - this fleet is doomed either way (even if it changes course, it won't have the fuel to stop). But having the element of surprise for the century or so before this fleet is destroyed and their information reaches the enemies would be very useful, especially if our enemies decide to launch other fleets during that time.
As a bonus, there is a rather pesky system a few parsecs away whose continuous existence and defiance is a thorn in the Empire's side. Can I use these railguns to attack them? Perhaps I will be able to destroy their off planet installations. Maybe I'll even be able to bombard their planets.