If I recall correctly (don't have references in front of me), the Art of Terram also covers the aspect of "solidity" in materials (unless I am conflating with 4th Ed)
Presuming it does, would using a InTe spell, built off the Base 2 guideline "examine visual properties", be able to recognize a crown carved from Ice, Bone, Wood, or laurel leaves?
(The appropriate skill would be Hermetic Magic Theory, as it has baked in Shape bonuses for a Crown)
Terram can be used for interacting with inanimate objects, as several of the spells in the core book show and the first line in the core book on Terram spells specifically states "...in addition to covering earth, stone, clay, metal, and glass, can sometimes affect inanimate objects in general" (AM5, p152).
However when used on something that does not traditionally fall under Terram most of these spells note that they require a Requisite of the appropriate Form.
Spells that can be used on non-Terram targets from just the Core Book include:
Eyes of the Eons (targets any nonliving object)
Eyes of the Treacherous Terrain (targets any natural terrain)
Tracks of the Faerie Glow (Will work on tracks left in grass, etc)
Supple Iron & Rigid Rope (works on any inanimate, appropriate Form Requisite)
Object of Increased Size (works on any inanimate, appropriate Form Requisite)
Fist of Shattering (works on any inanimate, appropriate Form Requisite)
Stone to Falling Dust (works on any inanimate, appropriate Form Requisite)
Unseen Arm (works on any inanimate, appropriate Form Requisite)
Wielding the Invisible Sling (works on any inanimate, appropriate Form Requisite)
The Unseen Porter (works on any inanimate, appropriate Form Requisite)
Hermes' Portal is of special interest here, since it uses Terram to affect everything. However it is not a standard Hermetic spell and thus should not be taken as an example.
Directly relating to your question, the first three spells on the list are InTe (one Base 2 and two Base 4) which learn properties of an object. Of further note the Intelliego spells are the ones which do not have the "appropriate Form Requisite" text.
If I recall correctly "Eyes of Treacherous Terrain" is Base 2, and thus "Eyes of the Eons" must be Base 4.
I could probably use "Eyes of the Eons" in another thread to indicate that visual properties don't reveal the information that "Eyes of the Eons" does (the age of an item I suspect).
Hmm, Terrain can have ground cover, so theoretically "Eyes of Treacherous Terrain" can detect treacherous bits of terrain underneath a field of grass. (though how about a log under the grass?)
This seems to lend support to the question if InTe could recognise the shape of a crown in a solid ice carving of a crown, or in a carved wooden crown.
The Base 4 learns any one mundane property of an object, while the Base 2 learns any one visible property with the note that a visible property is "a property that someone with appropriate skills could determine just by looking".
That is the difference between the two spells. Eyes of Treacherous Terrain gives information that someone with an appropriate skill could see ("How is this terrain unsafe?") while Eyes of the Eons gives information that is not visible ("How old is this object, +/- 10%").
Age usually leaves some visible clues (at least on people).
So as I understand it Base 2 InTe could probably tell that a 100 year old crown is older than a brand new crown made by identical means, but you would need the Base 4 InTe to tell how much older, no?
The Base 4 allows the spell to tell the age without visual clues. It is also a lot more accurate than the "guess'timate" you would get from visual clues if it was even possible.