Is head space a minimum or maximum dimension?

It bugs me that they always say things like - 1/4" headspace.  But they never say if that's a maximum or minimum.   Depending on how precisely you measure, you'll never get it EXACTLY to 1/4".  So if you're going to be off by a tiny bit, is it better to be less full (more head space) or more full (less head space)?  Or if you're doing something like soup and you have 2/3rds of a jar at the end of the stockpot, is that fine to can with excessive headspace?

I've tried to think through the fluid and thermo dynamics of the process without luck.

Does anyone know?  And especially, can anyone explain the science of it?  Thanks!

I'm guessing it's both. I believe that the mechanics of boiling liquid causes pressure to build in the jar that when cooling shrinks and seals the lid. I believe too little liquid would mean you wouldn't get enough hot/ wet sustained pressure to create a seal. Based on my instant pot experience where I've added too much contents and it just steamed all over my counter and wouldn't seal, I believe the opposite would be true with jars that were too full. They'd also be more prone to exploding since it's glass or boiling the contents out and contaminating the rubber so they wouldn't seal.

I've done a lot of canning and I never measure exactly. I basically fill to the top of the shoulder (give or take). There's a rough sweet spot.

Note all the "believes." I don't KNOW all that to be true but it's my best stab at answering your question

When I can food, I tend to leave a bit more head space than too little. I don't measure it exactly and it's always worked out fine.

As the contents in the jar heat up, they expand.  So if there isn't enough head space the contents will leak out of the lid and prevent a good seal.

As far as canning 2/3 of a jar, that's a lot of head space. Any partial jar I just put in the fridge and use up in a day or two.  Or freeze it.

I assume it is an approximate.  Like most measurements in my life, I eyeball it and run with it.

Considering you can pressure can raw pack meat safely with no liquid, and it makes it's own broth but it's not THAT predictable where it will end up as a level,  I have a hard time worrying about being precise.  I think overfilling can lead to food/oil under the seal.   I try to get it 'roughly' where it's suggested, but a little less is fine with me, especially if it means I can get another jar done without a lot of leftover that I have to use right away.   So far so good.

I can't help explain any of the reasoning behind any of it, and I've only canned a few things, but I left about an inch and didn't have any problems at all.  

I think the assumption is that you want to get as much food into each jar as possible and so it's the minimum clearance required to try to prevent your produce from bubbling out into your canner and potentially leaving crap on the rim that compromises the seal. On the other hand, I almost always end up with food migrating from jars to canner and have only once had a seal fail, so...I guess I'm not sure either. One could try canning two jars, one overfull and one with just an inch of whatever in the bottom, and see what the results are. Maybe if one of them fails spectacularly, it'll make clear what's intended.

It seems to me that you want to stay at or lower than the headspace due to stuff squirting out under and then affecting the seal.  But since I'm not sure, that's why I'm asking.  I keep hoping a food safety expert weighs in with something a bit more...  official sounding.

My understanding, which seems to be backed up here

https://www.healthycanning.com/the-role-of-headspace-in-home-canning/

is that the headspace recommendations are there to ensure a good seal. If you get a good seal, regardless of how much food is in there, you should be fine.

From https://www.healthycanning.com/safety-margins-in-home-canning-recipes/

Home canning recipes that have been tested to USDA standards (which includes those by Ball and Bernardin) are written for people even with a flawed or incomplete understanding of health and safety, and allow, frankly, for a high level of stupidity, distraction, and stubbornness.

Independent researchers tested some of the various recipes and recommended processing times in the 2009 USDA Complete Guide to Home Canning. . .  They found an extremely wide margin of safety that far surpassed any usual safety requirements.

While you should always give the seal on your jar a final test before opening, and give the contents a quick sniff once opened, if you have followed tested recipes based on USDA procedures, and the jar stayed sealed, experts say that contents of that jar will never be unsafe. You can reach for it with confidence from your pantry shelf:

“If you follow a tested recipe, a properly sealed canning jar will never become unsafe.”  [7]

I do raw pack tomatoes, pulsing them in the blender before dumping into jars. I always let them sit for a while and stir a few times, but there's a lot of air in the mix when I put them in the canner. The first time I did them that way, they boiled over badly. The jars all still sealed well, despite tomato bits under the lids. We used the last jar probably five years after canning. Now I leave extra headspace, just about two inches, to avoid boiling over.

Thanks Jan, that first link you shared was very detailed.  I never knew that we were trying to drive the air out of the jars by replacing it with steam.  

I guess I'll continue to try to be accurate to the recipe and err on the side of more headspace than less.