So i had and idea and looking over the rules it would seem to be legal unless i missed something.
"An arcanist can only cast a certain number of spells of each spell level per day. Her base daily spell allotment is given on Table: Arcanist under “Spells per Day.” In addition, she receives bonus spells per day if she has a high Intelligence score.An arcanist may know any number of spells, but the number she can prepare each day is limited. At 1st level, she can prepare four 0-level spells and two 1st-level spells each day. At each new arcanist level, the number of spells she can prepare each day increases, adding new spell levels as indicated on Table: Arcanist Spells Prepared. Unlike the number of spells she can cast per day, the number of spells an arcanist can prepare each day is not affected by her Intelligence score. Feats and other effects that modify the number of spells known by a spellcaster instead affect the number of spells an arcanist can prepare."
So a High ability score gives bonus spells that can be used by a caster. Normally though even if one had the bonus spell they would not be able to cast it because they both lacked the caster level and lacked the spell slot(ie spell knowledge).
Notice however that feats and other effects that modify spells known affect what the arcanist can prepare.
"This page is covered in densely-worded arcane or divine magical runes. It contains the knowledge of a single arcane or divine spell (chosen by the creator when the item is crafted). If the bearer is a spontaneous spellcaster and has that spell on her class spell list, she may use her spell slots to cast that spell as if it were one of her spells known. A page of spell knowledge is priced based on the spell's cleric or sorcerer/wizard spell level, unless the spell doesn't appear on either of those spell lists, in which case it is based on the highest spell level as it appears on any other spell list. For example, a spell that is on the 4th-level inquisitor list and the 2nd-level paladin list is priced as a 4th-level spell."
With this item the arcanist both have spell slots (thanks to high attribute bonus) and spells prepared thanks to the wording of arcanist's casting block and the magic item "Page of spell knowledge". But you still need a high enough caster level to cast the spell
"A spell's power often depends on its caster level, which for most spellcasting characters is equal to her class level in the class she's using to cast the spell.You can cast a spell at a lower caster level than normal, but the caster level you choose must be high enough for you to cast the spell in question, and all level-dependent features must be based on the same caster level.
In the event that a class feature or other special ability provides an adjustment to your caster level, that adjustment applies not only to effects based on caster level (such as range, duration, and damage dealt), but also to your caster level check to overcome your target's spell resistance and to the caster level used in dispel checks (both the dispel check and the DC of the check."
So your caster level is usually your class level but there are plenty of feats and abilities that can boost it above the class level. If one was able to meet the spell slot, the spell knowlege, and the caster level requirements, would anything prevent them from being able cast spells before they could normally access them?
— + 1 = —
Or, in longer form in this instance, — spells per day + 1 bonus spell per day from high ability score = — spells per day. It's also why if you cast bear's endurance on an undead, it still has — Con, among many other cases where — + stuff = —.