Proof of the Poincare Conjecture

This proof was copyrighted to the early 1990s,
and especially of the use of infinite iteration
of roots of any
positive Real number always converges to the number 1.

Later on, circa 1993-1994 I would find out that p-adics also
have infinite iteration of roots that converges to both 0 and 1.

There are many reasons why PC is so easy to grasp as
a conjecture but
tremendously difficult to prove and why it was
outstanding for 100
years. Here to enumerate a few.

(1) Math definition of dimension has never been
understood nor resolved
to this date. In physics only the 3rd dimension makes
sense where
experimentation has shown that any dimension other
than 3rd leads to
the wrong physics of Newtonian Classical. That alone
should have
alerted the math community that there definition of
higher dimensions
were pure illusions, fire breathing dragons.

(2) As if dimension definition was not enough of a
bugaboo, but the
concept of "completion with a point at infinity" to
make the Eucl plane
into a sphere. Math people once they hear this idea
they sheepishly
accept it as clear as broad daylight. But we should
require a proof of
this. Prove that the Eucl plane can be point
compactified for it to turn
into a sphere? Point deletions are always possible,
but point
compactification is silly. Where do Plane
compactifiers propose to put
that point? I ask you, where do you attach it?

(3) The idea that the Euclidean plane can be infinite
in reach is not a
true idea. One must prove it first if it is true. I
believe it is false
by the following argument on Reals or the Complex
plane. The infinite
Euclidean Plane is a contradiction in terms. The
Euclidean Plane to
exist must exist as a finite plane. Proof. The
Euclidean Plane is
represented by Descartes coordinate system of Real
numbers. For an
Infinite Euclidean Plane implies that there exists at
least one Real
number which is both infinite string leftwards and
rightwards of the
decimal point. No individual Real number exists which
is an infinite
string both leftwards and rightwards simultaneously
of the decimal
point. Hence, no infinite Euclidean Plane. When
the Euclidean
Plane is made to be infinite, it automatically reverts
into a
Riemannian sphere because it is my claim that Adics =3D
Riem geometry and
that Reals are finite leftwards but Adics are infinite
leftwards.

POINCARE CONJECTURE (PC) PROVED

Brief description of proof. PC rests on the
fact that the
infinite iteration of roots of any positive Real
number always
converges to the number 1. And for ADICS the infinite
squaring of any
ADIC when converted to base 2 converges to 2 points,
both ...00. and
...01. These convergences are the SIMPLY CONNECTED.

NOTE: All topological objects of the sphere are
determinable as
Riemannian geom objects OR, as positive Real number
objects. In this
way the iteration of roots or the squaring of any Adic
in base 2 is the
simply connected.

The statement which I claim is not a
well-formulated statement
of the Poincare Conjecture1 is this. The 3-sphere, the
space obtained
by completing R3 by a point at infinity, is the only
closed
3-dimensional space whose fundamental group is
trivial. I assert this
Poincare Conjecture is not a well-formulated
conjecture, it is a fuzzy
idea, only the notion of a conjecture.

I give a well-formulated Poincare Conjecture
as follows:
Riemannian geometry is the only geometry which is
simply connected
where positive Reals forms a positive Gaussian
curvature or the Adics
are Riemannian geometry.

PROOF OF THE WELL-FORMULATED POINCARE
CONJECTURE.

All topological objects of the sphere are
determinable as
Riemannian geom objects or, as positive Real number
objects. In this
way the iteration of roots or the squaring of any Adic
in base 2 is the
simply connected. It is
easily proved that a function built on the infinite
iteration of roots
of any positive Real number always converges to the
number 1. For
example, you take any positive Real number, then you
take successive
square roots, successive cube roots, successive
quadratic roots and so
on, of that number, then the convergence of all of
these iterative
roots sequences, all of these iterative roots, is to
the number 1. But
the iterative roots function does not work with any
negative numbers,
since imaginary numbers come into action, and negative
numbers occur in
all geometries except Riem. Where Riem. geom is
positive gaussian
curvature and so no negative curvature (no negative
number) can occur
in Riem. geometry. Thus the iterative roots sequence
is the simply
connected concept of every loop shrunk to a point,
which means there
are no holes in the geometry. So for Riem. geom, every
loop can be shrunk
to the number 1. But every other geometry except
Riem. geom has negative
numbers and thus there exists loops in them which are
impossible to shrink
to a point. Q.E.D.
------------

--- quoting Wikipedia on Perelman's proof method of Poincare
Conjecture ---
Perelman's proof

In November 2002, Perelman posted to the arXiv the first of a series
of eprints in which he claimed to have outlined a proof of the
geometrization conjecture, a result that includes the Poincar=E9
conjecture as a particular case. See the Hamilton-Perelman solution of
the Poincar=E9 conjecture for a layman's description of the mathematics.

Perelman modifies Richard Hamilton's program for a proof of the
conjecture, in which the central idea is the notion of the Ricci flow.
Hamilton's basic idea is to formulate a "dynamical process" in which a
given three-manifold is geometrically distorted, such that this
distortion process is governed by a differential equation analogous to
the heat equation. The heat equation describes the behavior of scalar
quantities such as temperature; it ensures that concentrations of
elevated temperature will spread out until a uniform temperature is
achieved throughout an object. Similarly, the Ricci flow describes the
behavior of a tensorial quantity, the Ricci curvature tensor.
Hamilton's hope was that under the Ricci flow, concentrations of large
curvature will spread out until a uniform curvature is achieved over
the entire three-manifold. If so, if one starts with any three-
manifold and lets the Ricci flow work its magic, eventually one should
in principle obtain a kind of "normal form". According to William
Thurston, this normal form must take one of a small number of
possibilities, each having a different flavor of geometry, called
Thurston model geometries.

This is similar to formulating a dynamical process which gradually
"perturbs" a given square matrix, and which is guaranteed to result
after a finite time in its rational canonical form.

Hamilton's idea had attracted a great deal of attention, but no one
could prove that the process would not "hang up" by developing
"singularities", until Perelman's eprints sketched a program for
overcoming these obstacles. According to Perelman, a modification of
the standard Ricci flow, called Ricci flow with surgery, can
systematically excise singular regions as they develop, in a
controlled way.

It is known that singularities (including those which occur, roughly
speaking, after the flow has continued for an infinite amount of time)
must occur in many cases. However, mathematicians expect that,
assuming that the geometrization conjecture is true, any singularity
which develops in a finite time is essentially a "pinching" along
certain spheres corresponding to the prime decomposition of the 3-
manifold. If so, any "infinite time" singularities should result from
certain collapsing pieces of the JSJ decomposition. Perelman's work
apparently proves this claim and thus proves the geometrization
conjecture.

--- end quoting Wikipedia ---