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Wicht , I'm curious how pemerton's usage of "regeneration" is incorrect or politically expedient or duplicitous (or whatever the particular indictment is)?
1 - Regeneration just means that
something (in this case HP) is being restored or replenished.
2 - Within D&D's 3e and 4e mechanics, that merely means HP pool replenishment on a scheduled basis (every round at start of turn) until trigger condition is met (eg end of encounter, etc).
3 - HP component parts are contentious. Pemerton gave you the 4e definition of HP and Regeneration and made (IME) the most reasonable inference out there based on all of the above.
I don't see the issue that you feel is self-evident enough to not explain it. Are you loading 3 with your own interpretation of HP and saying he is being disingenuous for using the system's specified definition (which is provided for reference); eg "HP pools can only be meat pools > therefore, regeneration of meat pools must mean actual tissue restoration > therefore he is being disingenuous"?
I don't see what is self-evident. Certainly not enough to challenge integrity on.
On the Martial power source and "not traditional magic"; I think this is explainable within the fiction and mechanically easily enough.
1 - Traditional magic in 4e is accessed via the Arcane, Divine, and Primal power sources. Arcana lets you discern magic effects related to those power sources (others came about later). Arcana lets you discern nothing about the Martial power source outside of "there is no magic afoot here" (meaning no conduit to or latent energies of the Arcane, Divine, or Primal power sources).
2 - As it leaves it open for the specific table to decide, my guess is the default would be merely "this person's martial capacity is so far beyond my own that I have no ability to comprehend how (s)he is doing this; (s)he's a magician." This is a very common response given the extreme diversity of martial capacity in the general populace. You talk to your average person and running 5 miles straight to them is borderline awe-inspiring. They can barely get their head around it. You talk to your average runner and 5 miles is nothing to them but they're in awe of people who do 26 miles and change. You talk to your average marathon runner and they're in awe of people who do ultras (100 m). You talk to an ultra and they're probably in awe of the folks who are running marathons when they're 90 years old.
Then there is the aspect of the disparate understanding of the various component parts of the science of physical activity and the upper and lower bounds of human capacity. To someone who doesn't understand the mechanics of something physical very well, and is limited in their own physical capacity, they will consider someone who is an extreme alpha in the discipline/activity as a borderline wizard. I'm very athletic and I understand the various component parts of the science of physical activity. Nonetheless, I'm still mystified by the incredible athleticism and mental and physical fortitude of dozens of athletes at the pinnacle (to date) of human accomplishment (from free runners, to downhill skiers, to any other number of gymnasts and professional athletes). For all intents and purposes to me, they're magicians. And, unfortunately, they're capable of feats far more mythical (in our own world) than anything most people expect possible for mundane characters in D&D. It seems like most people expect your average D&D Fighter to be about as athletic as I am (which is to say above average with respect to the general populace but nothing mythical or special - even by the mundane standards of our world).