Poincaré conjecture’s first certifier is regarded as Grigori Perelman formally at mathematics academic circle.
By the way, its originally exercised certification was done at concretely made materialized model, and that each momentary try and error certification must have been so a posteriori procedural process.

Nevertheless, once some ever unidentified outcome dragging own procedure was certified as we all are used to deliberate in expectation of being truth, from that moment on, we’d regard it just “truth” having not questionable skepticism.

Then, first not certified truth must swtich into strictly fixed knowledge, and consequnence of these certifying processes must become totalized in only previously fixed truth.

Though, essentially, a priori must be at least according to the notional systematic reason which must be “gotten a priori gone through a posteriori exercize or certifying practice".

At the dimension of notional definition, certified “a priori” must be versus concept accoring to the principle of existance.
However, at our reality abiding order or procedural systematically given, one “empirical” way of existing must be a posteriori.

Though, as the last certification by Perelman, what we’d acknowledged must be shown in some so twisted truth like next.

Since his last certification, many a posteriori experiments was done by many mathematicians. And necessarily, their own process as all of them in running around certifying must have no dualism dragging own complicated stepping and stepped footprint as road to certifying completion.

In conclusion, a priori and a posteriori making own dualism is just only one answer derived from the consequential theory.

If those all assumptions are corret, certainly, dualism’s credibility is only plainly jaxtaposed with first enigmatic suggestion and its answering through vertification.

Though, notinally, and conceptually easily regarded duality must depend on our own economizing own expediency.
In other words, that dualism dependent comprehension is only expediently given only facts’ refference. Thus, necessarily, any certified simply expressable formula must have each very diffrentiated law or rule’s articulating route with so twisted and never so easily divisionary each very unique nature.

E.g. there shown exampled “Poincaré conjecture” must be one of so complexed articulating process, because from Poincaré’s age, prpbably accoding to each certifying effort’s applicalbe angle, each experimental act must be so diversely interpreted and analyzed at so assorted methods.

These all processes stepped truth must mean that any certified truth in which simply arranged duality reliant comprehension could be possible must have each very exceptional form and appearance as one chance in permanent time span, that nature must be equipped.

Though, that’s why mathematics must have so interacted relevance with physics dealing nature world’s complicated composites and compositionally organized system and character.

In this regard and in terms of mathematics’ definition, it is strictly entangled with nature world, though, otherwise, mathematics showing and displaying own rationalized and economized view could have been derived from many accidentally made only one chance gotten some unidentified, in other words, a chance compositional order that cannot be quantified, and the only equilibrium beauty in that composition can be discovered in not a priori provable, certified only “absolute balance” could be discovered.

Though, all just seen previously given articulated formulation and certified mathematics’ truths could have been only accidentality leaned some “not certified with that accidentally given event”, and that factual regarding by itself could be certified with some so credible formula we can easily comprehend, couldn’t it? That questionable interpreting must be convincing explainable approach.

Upper those interpretable systematic process could be displayed by next diagram and equation.

GIVEN ALREADY CERTIFIED TRUTH (replaceable with own fixed equation) = Ⓒ

UNIDENTIFIED REASON to COMPOSE OWN FIXED OUTCOME in realized reality= Ⓞ

　Ⓒ ⇒ certifying Ⓒ in Ⓞ

Now that once Ⓒ was certified, that’d be nothing but Ⓞ comes up to us.

Nevertheless, only Ⓞ was never given through certifying. Because “tool for certifying” must never be certified.

In other words, between Ⓒ and Ⓞ, there must be some JOINT for ONLY ACCIDENTALITY and NECCESSITY though BRIDGE for deduction.

By the way, that BRIDGE is so stark REALLY GIVEN MATERIALIZED SUBSTANCE otherwise, ONLY NOTIONAL EQUATIONAL awareness or recognition.

And to it, how we can regard the QUESTION by mathematics, or physics, or both possibly dealt?

(Irregularly to be continued)

Aug. 15th. 2022