Sekinan Table: Three Conjectures for Dimension, Synthesis and Reversion 2014, 2018 and 2018 United Edition

Three Conjectures for Dimension, Synthesis and Reversion
2014, 2018 and 2018 United Edition

From Additional Meaning to Dimension Decrease Conjecture Three Conjecture's Digest Edition 2018

From Additional Meaning to Dimension Decrease Conjecture

Digest Edition of
Three Conjectures for Dimension, Synthesis and Reversion

TANAKA Akio
18 June 2018

SRFL Lab

The situation of thinking deepening on dimension has been appeared simply at the next papers.

1.
Stable and Unstable of Language
Additional Meaning in Word
22 October 2011
2.
Diophantine language
Dimension of Words
30 January 2012
3.
Hyperbolic Language
Connection of Words
3 February 2012
4.
Algebraic Geometry language
Parts and Whole
1 September 2013
5.
Three Conjectures for Dimension, Synthesis and Reversion
Dimension Decrease Conjecture
1 May 2014

References
Chronological main papers are seen at the following.

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Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement 2014

Three Conjectures for Dimension, Synthesis and Reversion with Root and Supplement

TANAKA Akio

Root
Arithmetic Geometry Language

Three Conjectures
Dimension Decrease Conjecture (Conjecture 1)
Synthesis Conjecture (Conjecture 2)
Reversion Conjecture (Conjecture 3)

Supplement
Interpretation of Reversion Conjecture
Simplification of Reversion Conjecture
Reversion Conjecture Revised
Tokyo
19 November 2014
SIL

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[Note 17 June 2018]
This Three conjectures was proposed through arithmetic geometry's result in 2014 based by my understanding at that time. The central theme of the Three conjectures is synthesis at word's meaning. The theme was repeatedly thought for new meaning addition in the old word.
In 2011 I thought a trial paper on additional meaning in word but for my inability of mathematical approach the trial was interrupted.
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Stable and Unstable of Language
For the Supposition of KARCEVSKIJ Sergej
Additional Meaning in Word
TANAKA Akio
October 22, 2011
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In January 2012 I wrote a paper titled Dimension of Words. At this paper I first became aware that dimension and synthesis were related in a word.
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Diophantine Language
Dimension of Words
TANAKA Akio
[Preparation 1]
k is algebraic field.
V is non-singular projective algebraic manifold over k.
D is reduced divisor over k.
Logarithmic irregular index, q (V \ D) =  is supposed.
[Theorem, Vojta 1996]
Under Preparation 1, for (S,D)-integar subset Z  V (k) \ D,
there exists Zariski closed proper subset and there becomes
[Preparation 2]
k is algebraic field.
V is n-dimensional projective algebraic manifold.
are different reduced divisors each other over V.
.
W is (S,D)-integar subset Z  V (k) \ D 's Zariski closure in V.
[Theorem, Noguchi・Winkelmann, 2002]
(i) When l ' is the number of different each other,

dim W ≥ l ' -r({Di}) + q(W) .
(ii) {Di} is supposed to be rich divisor at general location.
(l - n) dim W ≤n(r({Di}) - q(W)) + .
[Interpretation of Theorem ( Noguchi, Winkelmann)]
k is language.
V is word.
W is meaning.
Di is meaning minimum.
W has dimension that is defined at sup. or inf.
[References]
Holomorphic Meaning Theory 2 / Tokyo June 19, 2008 Energy Distance Theory / Conjecture 1 / Word and Meaning Minimum / Tokyo September 22, 2008
Language, Word, Distance, Meaning and Meaning Minimum by Riemann-Roch Formula / Tokyo August 15, 2009
Tokyo
January 30, 2012
Sekinan Research Field of Language
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In February 2012 I wrote Connection of Words, which led me to the hierarchy in language.
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Hyperbolic Language
Connection of Words
TANAKA akio
0.
[Preface]
From Distance to Pseudo-Kobayashi-Distance
1.
C is complex plane.
is unit disk which centre is the origin of C.
z, w are the two points of  .
Hyperbolic distance  between z and w are defined by the next. ,  .
2.
M is complex manifold.
x, y are arbitrary points of M.
fv is finite sequence of regular curve.
Point zv is  .
,  .
.
{  } is called regular chain.
Kobayashi pseudodistance dM is defined by the next.

.
3.
[Interpretation on 2.]
:= Meaning minimum of word.
dM := Distance of word.
M:= Word.
4.
[Definition]
When dM becomes distance function, M is called Kobayashi hyperbolic.
When dM becomes complete distance, M is called complete Kobayashi hyperbolic.
5.
When M =  is satisfied at dM , dM is equel to Poincare distance.
6.
X is complex manifold.
M is contained in X as relative compact.

7.
[Definition]
What embedding  is hyperbolic embedding is defined by the next.
M is Kobayashi hyperbolic.
Arbitrary boundary points  .
.
.
8.
[Theorem, Kwack 1969]
When M is hyperbolicly embedding in X,
What arbitrary regular map  \{0}  is regularly connected to  .
9.
[Interpretation on 6,7,8,9]
X:= Language.
M:= Word.
:= Distance of word.
:= Connection of words.
10.
[Conjecture, Kobayashi]
(i) If d is  , degree d's general hypersurface X of  is Kobayashi hyperbolic.
(ii)If d is  ,  \  is hyperbolicly embedded in  .
11.
[Interpretation on 10.]X:= Language.
d:= Hierarchy of language.
12.
[References]
From Cell to Manifold / Cell Theory / Tokyo June 2, 2007
Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008

Distance Theory /Tokyo May 5, 2004
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008

Quantum Theory for Language / Tokyo January 15, 2004

Reflection of Word / Complex Manifold Deformation Theory / Tokyo December 7, 2008
Boundary of Words / Topological Group language Theory / Tokyo February 12, 2009
13
[History]
Distance of language Historical Review
14.
[Appendix]
The Time of Language / Tokyo January 10, 2012
Tokyo
February 3, 2012
At the Last Wintry Day of Classical Calendar in Japan
Sekinan Research Field of Language
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In 2013 when I wrote Parts and Whole, I realised for the first time that adding a part to the whole at language has very complicated problem.
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Parts and Whole TANAKA Akio

I was ever simply thinking that the parts gathers and the whole is completed. But the situation seemed not to be so simple, I recently realised. Its beginning started with a theorem of arithmetic geometry.
Theorem
When i : X–>Y, j : Y–>Z is regular closed immersion of their codimension c, d, the next is set up.
(jOi)* = j*Oi*: CHr(Z) –>CHr-c-d(X).

Tokyo
1 September 2013
hillseversunlit

References added, 9 September 2014

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After writing Parts and Whole, I came across a unexpected result through arithmetic geometry. It was the decrease of dimension by meaning addition.
The details is written at Dimension Decrease Conjecture in 2014.
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Dimension Decrease Conjecture

TANAKA Akio
1 Dimension conjecture of word
23/09/2013 23:04
Word has dimension. New addition of meaning to word makes dimension of word decrease.
Basis
Pull back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

2 SAITO Shuji, SATO Kanetomo
24/09/2013 10:14S
SAITO Shuji, SATO Kanetomo. Algebraic Cycle and Etal Cohomology. 2012.

3 Pull-back map of higher Chow group
23/09/2013 16:11
Pull-back map of higher Chow group is bijection.
Conjecture on language
When word has additional meaning, dimension of word is decreased by dimension of additional meaning.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

4 Y. Nesterenko, A. Suslin
23/09/2013 15:30
Y. Nesterenko, A. Suslin.
Homology of the general linear group over a local ring, and Milnor’s K-theory. Math. 1990.

5 Higher Chow ring
23/09/2013 15:21
Double graded Abel group becomes double graded ring by defined intersection product.
Its product become commutative at one degree and become noncommutative at the another degree.

6 W.Fulton
23/09/2013 11:01
W. Fulton. Intersection Theory, 2nd ed. 1988.
Refer to the next.
Dimension Conjecture at Synthesis of Meaning. 9 September 2013. hillseverzoho.

7 V. Vodoedsky
22/09/2013 20:09V.
V. Vodoedsky
On motivic cohomology with Z/2-coefficients. Math.98. 2003.
On motivic cohomology with Z/l-coefficients. Ann. of Math.

8 Map that norm residue map induces
22/09/2013 20:03
When k is field and n is commutative integer, map that norm residue map induces is bijection.

                                                               Tokyo
                                                        1 May 2014
  Sekinan Research Field of Language

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This note in unfinished.
Tokyo
17 June 2018
SRFL Lab

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