[3.x] TO-complete

[Chronos]

Note: This thread deals entirely with theoretical optimization. Nothing in this thread should be considered appropriate for a real game, under any but the most permissive of DMs.

I: What is TO-complete?

In computer science, there is a very large class of problems called NP, containing almost all interesting computing problems. Some problems are said to be NP-complete: This means that any NP problem can be easily converted into a problem of that type. This means that any program that can solve any NP-complete problem can also be easily modified to solve any NP problem at all. Historically, once one specific problem (called the Boolean satisfiability problem) was proven to be NP-complete, any other problem could easily be proven to be NP-complete by showing that the BSP (or any other already known NP-complete problem) could be converted to a problem of that type (and hence, any other NP problem could be converted to a problem of that type by first converting it to the BSP).

Here we define a similar concept, that of TO-completeness. A TO problem is any problem which can be solved via an arbitrary number of spells of arbitrary caster level. We will show that there are a number of spells, items, and other game options that are TO-complete: That is to say, a single use of any of these game options can be converted to solve any TO problem. Following the example of NP-complete, we will first demonstrate that one particular spell (specifically, Wish) is TO-complete, and then show that other options are TO-complete by showing how they can be used to gain a Wish.

II: List of TO-complete options

A: Wish (spell)
1: (see section IV)
B: Lawful Evil Candle of Invocation (item)
1: Gate in an Efreet for immediate service.
2: Immediate service is for the efreet to grant three wishes (reduced to A).
C: Shapechange (spell), CL and HD at least 16
1: Shapechange into a Zodar (FF)
2: Use the Zodar’s (su) Wish ability (reduced to A)
D: Planar Binding, Greater Planar Binding, Planar Ally, Greater Planar Ally (spell)
1: Call an Efreet
2: Bargain or compel it to grant a Wish (reduced to A)
E: Shades (spell)
1: Emulate Planar Binding (reduced to D)
F: Miracle (spell)
1: Emulate Planar Binding (reduced to D)
G: Greater Metamorphosis (psionic power)
1: Metamorph into a Zodar
2: Use the Zodar’s (su) Wish ability (reduced to A)
H: Reality Revision (psionic power)
1: Depending on interpretation of transparency, a Candle of Invocation is either a psionic item, or a nonpsionic item of less than 25,000 GP value. Either way,
2: Reality Revise for a lawful evil candle of invocation (reduced to B)
I: Simulacrum (spell), CL at least 10, components bypassed:
1: Emulated creature is an Efreet, advanced to 20 HD.
2: Simulacrum of the Efreet has abilities appropriate to a 10 HD efreet.
3: Order simulacrum to grant Wishes (reduced to A)
J: Ice Assassin (SC) (spell)
1: See Simulacrum.
K: Simulacrum (spell), CL at least 8, components bypassed
1: Emulated creature is a Sylph, advanced to 8 RHD, with 8 class levels, and with Planar Binding as a spell known.
2: Simulacrum has abilities appropriate to an 8 HD sylph, including casting as a sorcerer 12.
3: Order Simulacrum to use Planar Binding (reduced to D)
L: Lesser Planar Binding, Lesser Planar Ally:
1: Call a Mirror Mephit (Expedition to the Demonweb Pits)
2: Mirror Mephits have Simulacrum as an (sp) ability (hence no components) at CL 8
3: Bargain or compel the mephit to use its Simulacrum ability (reduced to K)
M: Limited Wish (spell):
1: Emulate Lesser Planar Binding (reduced to L)
N: Two castings of Fey Ring (http://archive.wizards.com/default.asp?x=dnd/fw/20040710a) (spell):
1: Call a Ruin Chanter (MM5).
2: Call a siabre (http://archive.wizards.com/default.asp?x=dnd/fw/20020817a).
3: Direct ruin chanter to use Inspire Greatness on siabrie, which now has 17 HD.
4: Direct siabrie to shapechange into an illumian with the Krau sigil.
5: Siabrie now has +1 to caster level, up to its HD, so CL 17 for its SLAs.
6: Siabrie re-casts Shapechange, with 17 HD and CL 17, to turn into a Zodar
7: Zodar uses Wish supernatural ability (reduced to A)
O: Gate (spell):
1: Call an efreet for immediate service
2: Immediate service is for the efreet to grant three wishes (reduced to A)
P: Metamorphosis (power) or Polymorph (spell), with ML 15, and the Metamorphic Transfer feat:
1: Turn into a phasm
2: Use Metamorphic Transfer to gain phasm's alternate form ability
3: Use phasm's alternate form ability to turn into a zodar
4: Use Metamorphic Transfer to gain the zodar's wish ability
5: Use wish ability (reduced to A)

Lowest-level TO-complete spell known: 4 (Lesser Planar Ally/Lesser Planar Binding)

III: Doesn’t quite work

A: Polymorph Any Object (spell)
OK, maybe you can polymorph yourself or something else into an efreet or zodar, but it’s really not clear what you get from that. Let’s just assume that you don’t get spell-like or supernatural abilities.
B: Summon Mirror Mephit (Expedition to the Demonweb Pits) (Spell)
Summoned creatures refuse to use any spell that costs XP, or any spell-like that emulates such a spell. Simulacrum costs XP, so a summoned mirror mephit won’t use it.
C: Bend Reality (psionic power)
Can emulate lower-level powers, but there do not appear to be any TO-complete powers below level 9. Explicitly cannot emulate spells, though there might be a loophole in the “any other effect whose power level is in line with the above effects” line.
D: Greater Shadow Conjuration (spell)
Can emulate 4th-level conjuration spells, but only from the (summoning) or (creation) subschools. Lesser Planar Binding is (calling).
E: Fey ring (http://archive.wizards.com/default.asp?x=dnd/fw/20040710a):
Can call a siabrie (http://archive.wizards.com/default.asp?x=dnd/fw/20020817a), which has Shapechange as a spell-like ability… but siabrie only have 15 HD and CL, so they can’t turn into a zodar

[Chronos]

IV: Proof that Wish is TO-complete

A: A single Wish can produce an unlimited number of Wishes unlimited by XP cost.
1: Wish for a Lawful Evil Candle of Invocation.
2: Use Candle to gate in an efreet for immediate service.
3: Immediate service is for the efreet to grant three wishes. Note that as a spell-like ability, the efreet’s wish is not limited by XP cost, so even very expensive magic items can be wished for.
4: Use one Wish for another Candle of Invocation.
5: Use other two wishes as desired.
6: Repeat

B: An unlimited number of Wishes unlimited by XP cost can produce any effect that can be produced by spells of arbitrary caster level
1: Wish for and use a Tome of Leadership and Influence +5.
2: Wish for and wear a Cloak of Charisma +6.
3: Wish for and use a Tome of Understanding +5.
4: Wish for and use a Periapt of Wisdom +6
5: Wish to emulate Owl’s Insight, for a +8 insight bonus to Wisdom
6: Between B1-B2, you now have at least a 12 Cha. Between B3-B6, you now have at least a 20 Wis.
7: Wish for a CL 17 divine scroll of Shapechange
8: Wish to emulate Wieldskill (PGtF), choosing Use Magic Device. You can now use the skill as if trained.
9: Wish to emulate Divine Insight.
10: Wish to emulate Guidance of the Avatar.
11: Use UMD to use the scroll of Shapechange. Your wisdom is high enough to meet the ability score requirement, and Divine Insight, Guidance of the Avatar, and your +1 or greater Cha modifier mean that your minimum roll is 37, enough to guarantee success on a CL 17 scroll.
12: Wish for a scroll of any spell desired, of the desired caster level.
13: Repeat 13 for all desired spells.
14: Use Shapechange to turn into a Lilitu (FCI)
15: Use the Lilitu’s Item Use (ex) ability to use all scrolls

[georgie_leech]

I guess at this point the interesting challenge would be finding problems that can't be solved by an arbitrary number of spells at arbitrary caster levels. :smallbiggrin:

[Chronos]

Eh, that'll be tough, given that you can achieve Pun-Pun ascension via spells. And of course, I'm also interested in any TO-complete things that I missed.

[eggynack]

E: Fey ring (http://archive.wizards.com/default.asp?x=dnd/fw/20040710a):
Can call a siabrie (http://archive.wizards.com/default.asp?x=dnd/fw/20020817a), which has Shapechange as a spell-like ability… but siabrie only have 15 HD and CL, so they can’t turn into a zodar
I'm not infinitely versed in shapechange options, but are you sure there isn't some lower form with a resource that's wish convertible? It seems plausible, given the breadth of monsters out there, and it's vaguely possible that there are lower convertible forms for other things.

[Kazyan]

I think Fey Ring is TO-complete, if the following steps check out.

1: Call a siabrie.
2: Order the siabrie to shapechange into a Dusk Giant.
3: Allow the Dusk Giant to use Cannibalize 5 HD of living creatures, such as chickens or goats. (Is spending a few gp to acquire these animals allowed?) This gives the siabrie another Hit Die.
4: Order the siabrie to shapechange into an Illumian with the Krau sigil. This increases its caster level by 1.
5: The Siabrie now has 16 HD and 16 CL, so it can shapechange into a zodar. Order it to do so.
6: Order the siabrie to use its wish (Reduced to A).

[Chronos]

I think that the Dusk Giant's extra HD would go away when you switch to a different form, but I'm not sure about that. We could still make it work, though, if we could find some other form that has an ability that boosts caster level which isn't limited by HD, because once you've cast Shapechange you don't need the CL-boosting ability any more.


Quoth eggynack:

I'm not infinitely versed in shapechange options, but are you sure there isn't some lower form with a resource that's wish convertible? It seems plausible, given the breadth of monsters out there, and it's vaguely possible that there are lower convertible forms for other things.
Nope, I'm not sure of that. If you find something else that'll work, post it. It's a bit tricky, though, in that Shapechange only gives (ex) and (su), not (sp), and most interesting monster abilities are (sp).

[Kazyan]

I can show that two castings of Fey Ring is TO-complete, but not that only one is, for the moment.

1. Fey Ring up a Ruin Chanter.
2. Fey Ring up a Siabrie.
3. The Ruin Chanter uses its Inspire Greatness on the Siabrie, and keeps doing so until step 6 is complete.
4. The Siabrie Shapechanges into a Krau Illumian.
5. The Siabrie uses Shapechange again so that it operates at CL 16.
6. The Siabrie Shapechanges into a Zodar.
7. Wish (reduced to A).

[Gralamin]

Mostly right, some inaccuracies.


Some problems are said to be NP-complete: This means that any NP problem can be easily converted into a problem of that type. This means that any program that can solve any NP-complete problem can also be easily modified to solve any NP problem at all.
It means that any NP-complete can be converted into another problem in the set. NP-complete does not let you solve NP-hard problems that are not NP-complete. This matters for some cases.


Here we define a similar concept, that of TO-completeness. A TO problem is any problem which can be solved via an arbitrary number of spells of arbitrary caster level.

For problems that can't be solved by this, you likely need to go to the realm of undecidable problems. The classic example is the halting problem: will an arbitrary program end.

[Forrestfire]

C: Bend Reality (psionic power)
Can emulate lower-level powers, but there do not appear to be any TO-complete powers below level 9. Explicitly cannot emulate spells, though there might be a loophole in the “any other effect whose power level is in line with the above effects” line.



Metamorphosis with ML 15 into a Phasm
Metamorphic Transfer its Alternate Form (Su) ability
Alternate Form into a Zodar
Metamorphic Transfer its Wish (Su) ability
Wish (reduced to A)

Thus, Metamorphosis, and by extension, Bend Reality, are TO-complete when used with Metamorphic Transfer at ML 15 or higher.

This same logic applies to Polymorph and Alter Self (if using Reserves of Strength and are an Elan), as long as you can qualify for and take Metamorphic Transfer.

[nothingforyou]

Craft Wondrous Item can be used to create universal Turing machines. To brute force a proof:

Step 1) Align magic traps in a lattice.
Step 2) Order traps to output ON or OFF signals (via illusions or whatnot).
Step 3) Order traps to obey the rules of Conway's game of life.
Step 4) It is known that Conway's game of life can be used to create a universal Turing machine.
Step 5) Laugh at puny mundanes.
Step 6) Skip the industrial and nuclear ages, kickstart the information and nanotech age.

[Chronos]

Quoth Gralamin:

It means that any NP-complete can be converted into another problem in the set. NP-complete does not let you solve NP-hard problems that are not NP-complete. This matters for some cases.
NP-hard problems that are not NP-complete are not in NP. An NP-complete problem does let you solve all NP problems.

And it looks like metamorphosis + metamorphic transfer checks out. Two fey rings probably does too-- Where is Ruin Chanter from? I'll add them later today.

[Gralamin]

NP-hard problems that are not NP-complete are not in NP. An NP-complete problem does let you solve all NP problems.

And it looks like metamorphosis + metamorphic transfer checks out. Two fey rings probably does too-- Where is Ruin Chanter from? I'll add them later today.

Ah I had terms conflated in my head. This is what I get for not double checking. You are correct.

[Kazyan]

Ruin Chanter is from MMV.

[Irk]

Lady of Pain is not a TO problem. Interesting proposition, Chronos.

[Vaz]

In regards to Bend Reality, with the existence of a Spell to Power Psion (preferable 17+), any and all Arcane Spells are available to become Psionic Powers - and any Divine Spell can become an Arcane Spell through several ways - such as Wyrm Wizard 2. This gets around the limitation of powers only.

If you're going to the trouble of getting a Fey Ring for a Siabrie, could you not hire a/use your Bard to improve its HD?

[Kazyan]

If you're going to the trouble of getting a Fey Ring for a Siabrie, could you not hire a/use your Bard to improve its HD?

You could, but doing it with Fey Ring alone seems a stronger proposition.

[nothingforyou]

NP-hard problems that are not NP-complete are not in NP. An NP-complete problem does let you solve all NP problems.

Which is also why, counter-intuitively, you only need one example of an NP problem in P to show that P=NP. As opposed to showing that the implication that X\in NP\to X\in P is true and vice versa.

Edit Speaking of which, I'm guessing that P=NP in the DnD universe.

[Urpriest]

...so did you come up with this concept completely independently, or were you inspired by one of my posts? Because I've been working on this concept for quite some time, and occasionally alluding to it, and I haven't seen anyone else mention it at all.

Edit: Not trying to be confrontational, just very puzzled.

Also, you left out Gate itself. And the Shadow seed. Probably the Mythal seed too.

[Chronos]

I remembered that someone else had mentioned it, but couldn't remember who (must have been you). But it's a concept I had been thinking about before, and "TO-complete" is a succinct way to put it-- I think you might have been the origin of that term.

As for leaving off Gate... d'oh! That's kind of an important one. Epic seeds, though, seem kind of overkill-- They're epic; they're supposed to be ludicrously overpowered.


EDIT:
Added double-fey-ring, metamorphosis/polymorph with metamorphic transfer, and Gate.

Is there any reason that the metamorphic transfer trick wouldn't work with a changeling as the intermediate form, instead of a phasm? Minor change shape is only limited in choice of forms by basic body shape and by size, and zodars are medium and basically humanoid-shaped. That would remove the high caster level requirement, and open it up to Alter Self for humanoids, and without Reserves of Strength cheese.

[Jack_Simth]

For problems that can't be solved by this, you likely need to go to the realm of undecidable problems. The classic example is the halting problem: will an arbitrary program end.Commune can be duplicated via Wish, and results in a true yes/no answer for any given arbitrary program. Alternately, an arbitrarily large number of castings of Contact Other Plane (Greater Deity - a different one each time) (also duplicatable via Wish) will give you an arbitrarily high probability of getting the correct yes/no answer for any given arbitrary program.

[Douglas]

Probably the Mythal seed too.
Definitely, the Mythal seed can trivially grant at-will Wish as I recall.

[Gemini476]

Commune can be duplicated via Wish, and results in a true yes/no answer for any given arbitrary program. Alternately, an arbitrarily large number of castings of Contact Other Plane (Greater Deity - a different one each time) (also duplicatable via Wish) will give you an arbitrarily high probability of getting the correct yes/no answer for any given arbitrary program.

Commune isn't strictly limited to binary yes/no answers, you know.

You contact your deity—or agents thereof —and ask questions that can be answered by a simple yes or no. (A cleric (http://www.d20srd.org/srd/classes/cleric.htm) of no particular deity contacts a philosophically allied deity.) You are allowed one such question per caster level. The answers given are correct within the limits of the entity’s knowledge. “Unclear” is a legitimate answer, because powerful beings of the Outer Planes are not necessarily omniscient. In cases where a one-word answer would be misleading or contrary to the deity’s interests, a short phrase (five words or less) may be given as an answer instead.


The spell, at best, provides information to aid character decisions. The entities contacted structure their answers to further their own purposes. If you lag, discuss the answers, or go off to do anything else, the spell ends.



Contact Other Plane is similar, although it's limited to one-word answers.

(All questions are answered with “yes,” “no,” “maybe,” “never,” “irrelevant,” or some other one-word answer.)

[In the footnote for "True Answer":] You get a true, one-word answer. Questions that cannot be answered in this way are answered randomly.
[In the footnote for "Random Answer":] The entity tries to lie but doesn’t know the answer, so it makes one up.


And both of these are limited by the knowledge of the deities themselves, who are not omniscient even within their portfolios.

[Erik Vale]

Contact Pun Pun.

[Forrestfire]

Or the Omniscificer.

[Gemini476]

Contact Pun Pun.

How? He's pretty much undetectable through any means unless he wants you to know about him, due to various effects. Vecnablooded, for instance.

I also don't remember the Omniscifier having divine ranks, but I could almost certainly be wrong about that.

[Forrestfire]

Well, there's always the option of being the Omniscificer. Alternatively, use a trick to get divine ranks yourself, put knowledge in your portfolio, then go pull the guy out of his bucket of water thanks to future sight.

[nothingforyou]

Uncanny Forethought an epic spell slot allows you to cast a massive-cast-time-to-DC-mitigation spell (approx. -220 DC) with a full round action.

Develop all the 0 DC spells you want immediately, so that you "know" them, reserve Uncanny Forethought on your epic spell slot, then cast epic spells with -220 DC mitigation in 1 turn. Absolutely ridiculous insta-solution to everything.

Want a wish mythal? A bunch of ice assassins from shadow seed (so no XP cost)? It's all available, for the low low price of Epic Spellcasting + Uncanny Forethought.

[Shadowquad]

While I appreciate and enjoy the initiative, I think you need a proper definition of TO-reduction (i.e. the equivalent of polynomial reduction in the case of NP-hardness). Otherwise, we could really say that Commoner 1 is TO-Complete: you just have to kill CR-appropriate things and take 17 levels of wizard, then cast Wish.

A good idea might be to bound the number of rounds within which you may reduce the TO-hard problem to the condidate one, but how many rounds would make sense ?

[Sith_Happens]

While I appreciate and enjoy the initiative, I think you need a proper definition of TO-reduction (i.e. the equivalent of polynomial reduction in the case of NP-hardness). Otherwise, we could really say that Commoner 1 is TO-Complete: you just have to kill CR-appropriate things and take 17 levels of wizard, then cast Wish.

"Leveling up" should obviously be disqualified (as should "Hiring someone else to do it for you, excepting spells whose explicit purpose is to let you do so"), but I'm not seeing what other restrictions there need to be.

[Shadowquad]

Well, time still remains a problem. With sufficient time, you can always break WBL (at least with profession skill rules) and buy a custom item of wish. I agree it's inappropriate for actual play of course, but we're talking TO here.

Also, we can't fix an arbitrary time within which the reduction must occur, because one of the fundamental properties of reduction is that it has to be transitive (i.e. A reduces to B and B reduces to C implies A reduces to C). An arbitrary fixed delay would not obey that transitivity property.

[NichG]

Maybe the best restriction is something along the lines of 'nothing exists in the universe except that which you can create using the ability being evaluated and that which is necessary for the problem being solved'. So, e.g., if a technique requires hunting down some particular monster in addition to casting a spell, then it's not TO complete unless that spell also has the ability to summon/create the necessary monster, or that necessary monster is specified as a component of the solution.

So, e.g., 'Level 1 Commoner' is not TO-complete because it cannot level without challenges that are worth XP existing in the world, nor can it summon Pazuzu. However, 'Level 1 Commoner + Pazuzu exists' is TO-complete, as is 'Level 1 Commoner + Adventure path granting enough xp to level to Lv8' (for Planar Binding).

[Svata]

Wall of Salt/Iron should be listed. Sell Salt/Iron from wall, buy LE Candle of Invocation, reduce to B. Hell, add in Flesh to Salt while you're at it.

[Shadowquad]

This implies the existence of NPCs who are willing to buy salt/iron from the PC, and others that are willing to sell you candles of invocation. If such NPCs exist, then 1 profession or perform rank is enough to gain money and buy that candle

[Gemini476]

This implies the existence of NPCs who are willing to buy salt/iron from the PC, and others that are willing to sell you candles of invocation. If such NPCs exist, then 1 profession or perform rank is enough to gain money and buy that candle

Well, salt is a trade good. And a Candle of Invocation costs 8,400gp, so it can be found and bought in any small city with more than 5,000 inhabitants.

Not necessarily through a magic mart, fluffwise, but through various small magical knick-knack shops and dusty old rooms with dusty unknown items and churches of lawful evil dieties and whatnot.

This changes if you change the setting, of course, but if you're arguing from a RAW standpoint (which most TO is) you're probably either going by the rules of a certain setting or trying to make your build as setting-independent as you can. Pun-Pun only exists in settings that have the Forgotten Realms, for instance, while the Omniscifier is mostly limited to Eberron and non-WotC settings (which may include homebrew).
By the DMG, there are actually people who are willing to buy salt/iron from the PCs and others that are willing to sell them candles of invocation.

And yes, 1 profession or perform rank is enough to gain that money. I'm not really sure where you start getting a profit when you subtract your living costs from your income, but yeah that's certainly a way to get a Wish. Maybe. It might take longer than you live unless you're the right race, so I'd need to double-check that before I comment on it.

[Shadowquad]

The point I'm trying to make here is that the very notion of TO-completeness is ill defined, because the notion of TO-reduction is unclear. If we keep this unclear definition, one can argue that any build is in fact TO-hard, which clearly defeats the point of TO-completeness in the first place.

I think NichG drew a first guideline when he said that

nothing exists in the universe except that which you can create using the ability being evaluated and that which is necessary for the problem being solved

So, it's actually "Wall of salt + people who sell/trade/have candles of invocation and are willing to deal with the PC" which is TO-complete, but the main point of TO-hardness here is that people are selling candles of invocation, not the mean to acquire money to buy them.

[Chronos]

Hm, that's a good point. My inclination is to say that the candle is TO-complete, but that means of earning money (which can be used to buy a candle) are not. But I can't think of any good definition off the top of my head which would allow one but not the other. Any ideas?

[Urpriest]

Hm, that's a good point. My inclination is to say that the candle is TO-complete, but that means of earning money (which can be used to buy a candle) are not. But I can't think of any good definition off the top of my head which would allow one but not the other. Any ideas?

Hmm...

The goal here is to have a definition which highlights game elements that give you access to everything. That way, a DM wanting to ban TO-complete gameplay can ban just those elements, while a DM wanting to run a TO-complete game (some Tippy games for example) would encourage players to make sure they have access to something on the list.

This suggests a certain concept of minimal-ness: wealth is not on the list, because Candle of Invocation covers it.

That's not a sufficiently precise definition, because it gets rid of your ability to reduce things at all, when the whole goal is to reduce things to Wish in most cases.

For the moment, I'm going to suggest that we simply use a heuristic metric of interesting-ness and relevance. WBL shenanigans to get access to a Candle in the end are a separate sort of trick that just boils down to getting a Candle. Similarly, leveling-up is its own part of the game. If we try to stick to entries that are characteristic of TO-completeness, that pop up in many potential TO-complete ascensions, then we'll be closer to achieving what I (and presumably Chronos) envisioned.

And of course if someone has a good precise definition that would be welcome!

Incidentally, Planar Shepherd's Wild Shape should be included, since it grants Efreet SLAs among other things. And we should probably include exploitable monster abilities, like Manipulate Form and the Shaedling's Shadow Gossamer.

[nothingforyou]

You can appeal to a notion of analycity: it's analytic if and only if it is seemingly necessary.

So, more or less, the candle of invocation is analytically TO-complete because it is necessary to use the candle of invocation trick. Money is not analytically TO-complete because it is not necessary, i.e., you can formulate the candle of invocation trick without introducing money.

[Urpriest]

You can appeal to a notion of analycity: it's analytic if and only if it is seemingly necessary.

So, more or less, the candle of invocation is analytically TO-complete because it is necessary to use the candle of invocation trick. Money is not analytically TO-complete because it is not necessary, i.e., you can formulate the candle of invocation trick without introducing money.

I like this idea. It'll have some subjectivity, but that's not a huge issue.

Incidentally, I'm assuming you're referring to this (http://en.wikipedia.org/wiki/Analytic_proof) when you call it analytic?

[nothingforyou]

I like this idea. It'll have some subjectivity, but that's not a huge issue.

Incidentally, I'm assuming you're referring to this (http://en.wikipedia.org/wiki/Analytic_proof) when you call it analytic?

No, mathematical analycity is a different notion. I'm referring to epistemic analycity, a la Kripke.

http://www.uvm.edu/~lderosse/courses/nnn/analyticity.pdf

If you are rigorous and robust in its application, then subjectivity should not be an issue. Of course, from the definition I've given, there's a lack of rigor, but it's more than sufficient for our purposes.