I am assuming you are referring to assumptions here. In that case lets focus in on decay rates and the assumption they have been constant through their history. Please tell me why this is not an assumption and i will need more than saying "this is a lie"
Certainly.
When I was in the military, I worked with electronic test equipment. People from other units would bring their equipment to us to be tested for accuracy...or calibration, as it is termed. So the standards set forth by the military that each piece of equipment has to be calibrated by another tool that is at least 4 times as accurate. So the equipment that we used had to be 4 times as accurate as the equipment being brought to us. This equipment with the higher accuracy is what we call the
standard. So we would adjust, or calibrate, the other unit's equipment to match our standard. In turn, we would have to send our equipment to Redstone Arsenal, Alabama, where they had equipment used as standards for our equipment. And so on, until it was eventually traceable to NIST (National Institute of Science and Technology) in Colorado.
Of course, sometimes it wasn't always possible to obtain these proper calibrations, such as when we were deployed in mobile vans. So, we did something called "cross-checking." The idea is basically that we test our equipment against each other, in several different ways. So let's say we were testing the output voltage of a piece of equipment. We might measure that output voltage on an oscilloscope, a multimeter, and whatever else we had which was capable of it.
So, if we get the same measurement on each of the three measurement tools, we could be reasonably certain that all of those pieces of equipment were functioning normally, even though we didn't have access to standards. Because the more methods you have for making a measurement that agree with each other, the less likely it is that the measurement is wrong. The odds are pretty slim that the voltage output was incorrect, and the measuring tools were wrong in JUST SUCH a way that they all gave the same wrong answer, which just so happened to coincide with the expected value of output.
This idea is called consilience.
So, this is how we know that the decay rate of carbon has been consistent for at least the last 40-50k years. Carbon dating is calibrated primarily using dendrochronology (over the last 11-12k years). It is the science of counting the tree rings of specific types of trees which have been observed to grow one ring per year to determine how old the tree is. So tree rings are the standard by which we adjust the carbon dating (more on why it needs to be adjusted in a minute...it debunks one of your other "assumptions"). Yes, I know you have issues with dendrochronology too, but let me finish.
So now you may be asking. Ok, so what is the standard for dendrochonology? This is where the "cross-checks" come in. We don't really have a standard by which to test dendrochronology (at least not directly), so we have to test it against other methods. So this is what we do:
We have multiple tree chronologies (in different parts of the world) which go back to more than 10k years. If we carbon date a section of those chronologies, we can determine what the atmospheric carbon content was at that time (because it does change...we know this...we never assume that it didn't) by comparing the raw (uncalibrated) carbon date with the tree ring counts. So we use this knowledge to calibrate the carbon date.
From there, we do several things. 1. We test these calibrated carbon dates against items of historically KNOWN age. 2. We test the calibrated dates against annual sediment layers, called varves, deposited in a couple of lakes throughout the world (most notably Lake Sujitsu in Japan) 3. We test them against annual layers of ice cores, like has been spoken of here, in Greenland. 4. Against speleothems 5. against coral bands. 6. Against known volcanic eruptions with embedded ash layers within the varves, and cores, and against the abnormal tree rings during that time.
And we can plot all of these data points on a graph, and show how well they match with each other.
The results are remarkable.
So the question you are left with is, which is more likely? 1. That the carbon dating is accurate, or 2. that somehow tree rings grew remarkably fast AND carbon decay rate vastly increased AND pollen was produced and deposited ridiculously often every year in the lakes, AND unknown volcanic eruptions just happened to occur at precisely the right time during those hundreds to thousands of pollen laying events AND the KNOWN volcanic eruptions somehow didn't leave a layer in the ACTUAL correct sediment layer AND a dozen other things happened JUST SO....
...we got the expected result of carbon years which matched all the (equally) wrong answers?
