In Vernor Vinge's "Zones of Thought" series, is it possible to detect anomalies related to the zones' boundaries from the Earth using contemporary astrophysics instruments?I.e. if you are violating the fundamental laws of nature (speed of light) there ought to be profound consequences that can be seen from afar.
Almost certainly not. At least not with any technology slow zone humanity ever discovered.
All humans in the beyond were descended from a single human colony that accidentally found its way out of the slow zone. Said colony had no record of the spacefaring Queng Ho and additionally had artifacts from old earth (as seen in "the blabber" short story) so must have descended from a very early human colony. So undoubtably the Queng Ho came about much later. In fact, Earth has been fully depopulated and resettled at least four times well before the events of deepness in the sky and to repopulate an entire planet multiple times must take thousands of years. Several thousand more years have elapsed between deepness in the sky and fire upon the deep. So we at least have a few thousand years of spacefaring humans in the slow zone with none of them noticing anything worthwhile to investigate in the beyond.
Additionally, it was stated that it is completely unknown whether humanity still exists in the slow zone at all and that if they do they would be completely ignorant of what happens in the beyond implying they would have no ability to find out about it, or at least humans on the beyond don't believe they would develop any ability to find out about it.
The main reason I don't think so is Pham Nuwen himself had access to the best tech humanity has ever produced accross hundreds of civilizations in the slow zone and spent his entire life searching for any sign of a more advanced society or something unexplained to explore. If there were unexplained observations on the outskirts of the galaxy then he would have been all over it with his expedition.
Note that the speed of light isn't higher in the beyond, it is just that there is a fundamental limit on the fastest possible computation or density of information that can exist within a volume that is zone dependent. The mechanism that allows FTL travel is extremely computationally intensive, at some point a computer fast enough to perform those computations cannot exist at which point you lose the ability to FTL. But as seen in "the blabber" and somewhat implied by the on-off star, FTL communication at least can happen in the slow zone with the expendenture of enormous resources (like the entire output of a star for 200 years, or dimming of a planets sun by a few percent just to send a single bit of information FTL) so whatever fundamental physical laws allow FTL still exist in the slow zone, they just cannot be exploited. Both artifacts originated in the transcend so it is unlikely they could be constructed with slow or even beyond technology.
The criterion "related to zone boundaries" is too vague.
For example, the "on/off" star in Deepness was anomalous, and was presumably detectable by anyone pointing a sufficiently sensitive telescope at it. But it was anomalous partly because it was ignoring zone boundaries. So detecting it would not tell you anything about them.
edit: Why anomalous? It was cycling between dim and bright on a regular 250 year cycle, contrary to any known physics. Any slow zone physics, to be more precise. In the larger context of the Zones universe, this was probably because it was engineered or modified by transcendent technology to carry out its function (whatever that was) even in the slow zone. So if you already knew about the zones, and then saw a star located in the slow zone behaving like that, you would immediately suspect a violation of the zone boundaries. But if you did not know about the zones at all, it would if anything be taken as counter-evidence to a hypothesis that certain physics could happen only in other parts of the galaxy.