archimedes

That is correct, there is no free vis for advancement and labs in Rome, getting any vis in Rome is a struggle, due (at least in part) to the overwhelming presence of dominion auras. It is probably the only tribunal where divine vis is easier to get ahold of than magical.

Almost makes me want to roll up a divine character instead, but you wanted us to be non-divine searching for a magic aura, and I've had versions of this guy in my head for a while.

I will reshuffle the seasons a bit. The Verditius discount for opening was always an afterthought but this actually makes it matter quite a bit. So basically have to rent for a season to extract and rent for another season to open an item? Or is there a way to earn vis by assisting parens or opening items for him? (I know it's a loss of status to assist other magi after gauntlet but that doesn't count for parens, right? Or does it?

No, it does not hurt your standing to "submit" to a parens, who is already acknowledged as a superior.
In terms of payment for verditius to assist a parens I'm going to say MT pawns of vis per season, up to 2 seasons per year- average. Your parens may have a long project they want to contract your assistance with that covers several seasons in a row before a dry spell. You also get 1 season/year that you can use their lab (again, on average) while they read books or undertake non laboratory activities, during the time you contract with them.

I have a 10 point discrepancy in the experience point values:
45 points early childhood
120 points pre-apprenticeship
300 points apprenticeship

total 465 points at gauntlet
4 years full advancement 120 points
1 teaching for 12 points
1 quest for 5 points
6 exposure experience for 12 points (affinities are calculated at a later stage in my process)

final point total:614

also noting that by RAW there is no exposure xp when advancing a character in abstract. quests and teaching are not even touched upon in RAW, but setting that aside for a moment:

I show 474 points in general abilities and 150 points in arts, for a total of 624 points.

I came up with a discrepancy of 5 which I took off finesse. Also took away the exposure xp. The Divination virtue gives a free point in the ability, were you accounting for that?

yes, I have taken the free 5 points of divination into account, here is my ability/cost list chart:
Sardinian 0
Area Lore:Sardinia 5
Craft:Goldsmith 15
Craft:Mechanism 5
Craft:Weaponsmith 5
Craft:Stonecarver 15
Craft:Jeweler 15
Craft:Bookbinder 15
Craft:Woodcarver 15
Craft:Tailor 15
Verditious Cult Lore 15
Artes Liberales 50
Latin 75
Philosophae 30
Code Of Hermes 5
Faerie Lore 15
Finesse 5
Infenal Lore 5
Magic Theory 76
Parma Magica 10
Divination 0
Neoplatonic Cult Lore 48
Concentration 5
Jewelry Sympathy Trait 30
and arts:
Creo 15 Animal 15 Ignem
Muto 15 Aquum Imaginem
Intelligo 15 Aurum mentem 15
Rego 15 Corpus 15 Terram 15
Perdo 15 Herbem Vim 15

note this values are before your most recent changes, so the 5 points is still in finesse and the exposure points are present

apparently I missed when you dropped infernal lore

approved

Thanks. Sorry it was such a headache.

no problem

1st inspiration (male figure): soul jar- the enchantment of a object to contain a human soul- this does violate known hermetic capabilities but not Hermetic limits as it doesn't seek to actually create a soul. Mu(Te)Me- imbue a clay or stone figuring to hold a human soul - this is a base 15 effect, +1 magnitude for touch, +2 magnitudes for duration:day and +4 levels for trigger (sunrise and sunset) for a level 34 imbued effect. No further inspirations may be gained in developing this mystery ability until this device is invented. The base effect cannot be used outside of the gained inspiration at this time.
2nd inspiration (female figure): The frozen womb (ancient magic p. 56) MuCo:40- prevents a fetus from developing in the womb, holding it at its current level of development. for 1 year- ritual (the version in ancient magic assumes fertility magic has been learned and can include unborn child as a target- current version uses target:part to achieve the same effect)

I haven't advanced Archimedes at all post-tribunal.

How is the correspondence re Verditius Lore working? The normal +1 xp on top of other seasonal activity, or something different that takes up seasons?

Any season that you advance Verditius Lore you add +1 to your SQ.

but main source needs to be teacher, right? or practice? or are there books on it?

There may be books or tractatus but they would not be traded over the redcap network. Exposure would also count.

He would open correspondence by asking for such a book, or for a season or two of teaching; offering vis as payment.

Understanding that most verdituous are not great writers, he is willing to let you have a Level:4 SQ:8 summae for 4 pawns of vis and a pledge to never let it be seen outside the house.

archimedes agrees to that, and has the vis sent. (I will note on wiki).

Note that it will require 1 season to arrange the deal, payment, and delivery

Advancement caught up.

I took Intrigue for tribunal even though I didn't roll it, is that ok?

That fits, you didn't roll it but you were certainly involved in it...