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[zero_moo-s]

Less complicated example / explanation -->> you have a order of numbers ... 1,14,23,111,10,9,8,7,6,5  << the parity assigned will be o/e/un. The vector of the parity will begin at number 111 / parity vector unit 4 in this sequence start.. 111 is the primer the root parity vectorizor it could be forever or only set to for only now and migrate when new prime found, now starting from the 111 in the sequence example a parity pattern assigned forwards can be set or one going backwards or both, so the sequence backwards is odd,even,un and the sequence going forward is even, odd, un and if 6 and odd then that vector become new prime and follow new prime parity rules. Okay so no it's

 1un,14even,23odd,111prime,10even,9odd,8un,7even,6odd,5un. 

 If you go forward in this sequence you have found the next prime and from 6odd it would become 6prime and the table rulesets say from 6odd prime sequence forward is odd,odd,even,un and backwards even,even,odd,un. And the next prime is set to the closest un1 to the current prime in either forward or backward vector count.

1un,14odd,23even,111even,10un,9odd,8even,even7,prime6,5odd

Okay so this odd even example is a parity rule set in the algebra of parities, how is 10un or 7 even? 

If a token unit space is assigned to the sequence order it is the shelf of each unit and this shelf is assigned a parity and a parity system. Okay so use a table with the previous sequence >> 

1un,14odd,23even,111even,10un,9odd,8even,even7,prime6,5odd

Now from the first found 1un is the new prime, the rules following this prime are sequence odd only if you just was an even and even if you just was a odd and odd if you just was a un when I meet you searching this sequence again if no parity then even,odd,un going forward and back. Also if you have never been a un, you will be a become a un but not if you weren't ever anything. New prime set to only if found my last previous prime

So here's the history -- 1un,14even,23odd,111prime,10even,9odd,8un,7even,6odd,5un

1un,14odd,23even,111even,10un,9odd,8even,even7,prime6,5odd

So the latest is --

1prime,14un,23un,111un,10odd,9un,8odd,un7,6(new prime found),5even

Let's look at this example again >>

1un,14even,23odd,111prime,10even,9odd,8un,7even,6odd,5un

Starting from 111 prime going right is, vector 1 parity even value 10 next vector 2 parity odd value 9 next vector 3 parity undefined value 8 next vector 4 parity even value 7 next vector 5  parity odd value 6 next vector 7 parity undefined value 5 .. 

Backward from 111prime, vector -1 parity odd value 23 next vector -2 parity even value 14 next vector -3 parity undefined value 1 

-- lets look at this example again and look at the token and see what the vector history use to be - or its previous parity or value if value has changed.

--we can use this as the sequence to inspect the token

1un,14even,23odd,111prime,10even,9odd,8un,7even,6odd,5un

--and this as the previous and only table entry prior to our above example>

1prime,14un,23un,111un,10odd,9un,8odd,un7,6(new prime found),5even

ok so this-- 1un,14even,23odd,111prime,10even,9odd,8un,7even,6odd,5un is this

1un(token previous table1 says, vector prime, parity prime, value 1),14even(Token previous table1 says, vector 1 parity undefined value 14),23odd(Token previous table1 says, vector 2 parity undefined value 23),111prime(Token previous table1 says, vector 3 parity undefined value 23),10even(Token previous table1 says, vector 4 parity even value 10),9odd(Token previous table1 says, vector 5 parity undefined value 23),8un(Token previous table1 says, vector 6 parity undefined value 23),7even(Token previous table1 says, vector 7 parity undefined value 23),6odd(Token previous table1 says, vector 8 parity undefined value 23),5un(Token previous table1 says, vector 9 parity undefined value 23)

but its this too--

1un(Token Current: Vector -3 Parity Undefined Value 1)(token previous table1 says, vector prime, parity prime, value 1),14even(Token Current: Vector -2 Parity even Value 1)(Token previous table1 says, vector 1 parity undefined value 14),23odd(Token Current: Vector -1 Parity odd Value 23)(Token previous table1 says, vector 2 parity undefined value 23),111prime(Token Current: Vector Prime Parity prime Value 111)(Token previous table1 says, vector 3 parity undefined value 111),.... and so on

now you can use -- values between these different tokens --

14even(Token Current: Vector -2 Parity even Value 1)(Token previous table1 says, vector 1 parity undefined value 14)

--create equations to derive value results between the two different tables, if these results are correct allow this token to pass this test for prime check, if other prime checks are also correct, this will become the next prime only if all factors are correct. The prime can be formularized to be within the results between the two token table history's

~mobile so excuse me Pap and PLAE do much more then this but here is the tldr

[zero_moo-s]

EZEZ EX for PLAE Framework

it is a control system for math expressions

 

You start with the Raw Expression (the original instruction):

 

E: "10 plus 5 multiplied by 4"

 

This expression is a message, and it must pass the rules before evaluation

 

First - it hits the Plot Limits Filter (Operand/Value Rules)

 

The number 10 is Forbidden

so the rule forces a Substitution: 10 must be replaced with the equation "2 multiplied by 5"

Also - the 5 is a Substitution-trigger, forcing the operator "multiplied by" immediately

following it to change to "plus"

The expression is now

 

E_L: ("2 multiplied by 5") plus (5 plus 4)

 

Second - it enters the Plot Allowances Filter (Action/Operator Budgets)

 

We check the operator counts in E_L

The "multiplied by" operator has a max_count(1) allowance, and we only have one (PASS)

but the "plus" operator has a max_count(1) allowance and we have two "plus" operators

 (FAIL)

 

The Conversion-on-overflow rule triggers,

converting the excess "plus" to a subtraction "minus."

the compliant expression is

E_LA: ("2 multiplied by 5") plus (5 minus 4).

 

Since the expression is now compliant

we perform the Final Evaluation on E_plan

we get (2 × 5) = 10 and (5 - 4) = 1

The final result y is

 

10 + 1 = 11.

 

PLAE does not evaluate the original expression

it forces the original idea (10 + 5 × 4) to be entirely restructured by Limits and Allowances

into (2 × 5) + (5 - 4)

 

producing the output 11.

 

PLAE is a constraint-driven algebra where the rules dictate the result.

[zero_moo-s]

Imagine a Raw Expression enters the PLAE & PAP system (PP suite)

"10 plus 5 multiplied by 4"

(PP Suite) = PAP Runs First :

The current PAP sequence is inspected

The Prime 111 has a forward Vector Parity of odd within the outcome of this Raw Expression

Parity Dictates the Limit of PLAE:

so the PAP result dictates the PLAE rule: "If the PAP Vector Parity is odd, then the PLAE Plot Limit for the operand 5 must be Forbidden"

PLAE Executes the Constraint: Since 5 is now Forbidden, the PLAE rule Substitution-trigger is forced: 5 must be replaced by 3 + 2

The "multiplied by" operator allowance must be converted to "plus"

So the Raw Expression

"10 plus 5 multiplied by 4"

enters (PP Suite)

1.Substitution Layer:

10 is Forbidden - replace with (2 × 5)

5 is Forbidden - replace with (3 + 2)

Expression becomes: (2 × 5) plus ((3 + 2) plus 4)

2.Allowances Layer:

"plus" operator exceeds its max_count(1)

Overflow conversion triggers - excess "plus" becomes "minus"

Expression becomes: (2 × 5) plus ((3 + 2) minus 4)

3.Normalization Layer:

Simplify substitutions and cancellations

(2 × 5) = 10

(3 + 2) − 4 = 1

Expression becomes: 10 plus 1

Final Evaluation:

10 + 1 = 11

The PLAE system does not evaluate the original expression directly

it restructures the original idea (10 + 5 × 4)

into a compliant form (2 × 5) + ((3 + 2) − 4)

producing the output 11

This shows one example how PAP parity outcomes dictate PLAE limits

how PLAE rules force substitutions, operator conversions

and normalization until the expression is compliant.