**Standing Buddha Mathura-school in Gupta-age**

**excavated in Jamalpur (mathura-A5/ 5th India)**

**Vertical Connection**

This sculpture of standing-buddha is one of important formative relic of
Mahayana art in India Gupta-age.

Anyone can not doubts the excellent embodiment at this sculpture,

the specific form with deep meditative expression that was made up by accurate
skills.

However, it should understand that there is a more primal vision to enable
that's fine expression.

It is being the intensive philosophy at Mahayana.

The complete digestion of the matrix system to govern practical figures
is being,

Consequently a figure of human corresponding the matrix perfectly must
be the figure of buddha.

This concept on formative art accords just with fundamental concept of
integral Mahayana.

First, the figure of the sculpture overlapping with the matrix status of

connecting vertically 4-units of "3step reducing join", is shown below.

This status was caught as first view of the vertical connection in an early phase of this investigation.

There are 2-sets of concentric circles at above and below.

When the upper set of them is overlapped congruously with the actual concentric
zone in the halo,

the consistency with the integral fabric of the sculpture and the matrix appears.

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The matrix status connecting vertically 4-units of "3step-reducing-join"

Explanation of the total matrix system. here

explanation about this status of matrix

As the comprehensive development in this investigation,

It had became sure that the matrix status of this sculpture is more high
status expanded into the advanced radial connection.

It is explained that the matrix status shifted from the construction of the upper figure to a radial connection type.

As rational description, this advanced status must be explained like next.

The matrix status connecting vertically with 2-units of "the radial unit connecting with 8-units of [3-step reducing join]".

The figure overlapping with the sculpture and the matrix status is showed below.

The grasp of the total condition that the sculpture is absorbing tonality
of the matrix, It occurs from overlooking.

It is actual to gaze specific elemental areas that the aspect of the matrix
governs exactly the sculpture, after overlooking.

A protrusion on the top of head is fitted very exactly into the cross region
of the matrix.

The new design of protrusions of gupta-mathura-school was urged by the method to homologize

that is different from type of ealy-mathira-school.

It is clear that the hooping form of vesture around buddha's neck is governed
from

intersecting circles and ponts of the matrix that is high density at this
area.

The left hand and the dropping marge of vesture makes up the movement like
vertical swing waves.

It is sure that the design is effected from the aspect of the matrix.

the status from the hem of vesture until toes,

it is showing the sufficient correspondence with the under concentrics
circle area of the matrix.

This choice is superb as the adaptation interpreted the matrix.

And there is perfect correspondence.

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The matrix status of [2-vertical-connection] of [8-radial-connected-unit] of [3step-reducing-join]

explanation about this status of matrix

**Halo Construction
**

The prescription for relation to correspond to the matrix that the mathura-school in gupta-age decided,

is different from the idea found at important relics of early mathura-school as the precedent science.

The halo construction of gupta sculptures is a direct transfiguration tracing complicate aspects

crossing circles in concentric zone of the matrix.

In the early phase of this investigation,

the prescript adopting the matrix for sculptures that gupta-mathira-school decided,

was deduced an independent new choice from the method the precedent school in Mathra.

However, developing to other regions,

It became sure that the direct transfiguration from the set of concentric circles of the matrix into the physical concentric zone

of sculptures is the standard method used extensively in Eurasia, already released prime examples show,

Tibetan vajrayana-mandalas, Celtic disks, Ancient mirrors in China and Japan.

In this aspect, It is showing that the method of early-mathura-school is isolating from the large historical stream.

But, probably the method of early-mathira-school was succeeded by into masters

in schools of Mahayana buddhism pictures until Asuka-age in Japan at least.

This investigation has taken sufficient examinations about the survey.

Closeup figures of the halo are below.

The realized sculpture's concentric zone is steadily absorbing the robust effective construction

consist of complicate crossing circles of the matrix.

At an approach of learning the relation of the halo and the matrix,

as this integrated appearance is realized by practices of very delicate and complicate figuration,

getting first enough image of the total reration of the halo and the matrix,

then the practice to check should break into inscribed details in the high resolution jpg photo.

There are needful coupled practices in order to grasp the mechanical application,

to closeup confirmations to several key-details transfering in the halo,

and to imagine the coordination of them,

If those practices is not done, it is difficult to understand aptly for the status.

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In order to check the correspondence of "3-step concentric circles and discriminative

intersecting points in the matrix" and "formative design in the halo",

the way to overlap the divided half construction of the matrix avails.

It is able to practice at high resolution jpg below.

Smaller concentric circle of the matrix looks like containing a little deviation to fine correspondence with the actual circle of the halo.

However, it should allow for the chance that this smaller concentric circle of the matrix is homologized to

the less-visible circle that is the loose ridge curving into few depth, describing lotus petals.

Statuses of other elements seems to be enough correspondences,

admitting the reality that any sculpture is made up by human actual works against materials, it should say there is just high ability.

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The prescript to the actual concentric zone of the halo is not only to adapt concentric circles and

discriminative intersecting points of the matrix.

There are circles appearing only in the sculpted halo, never corresponding to concentric circles and intersecting points in the matrix.

Those three circles are ordered afresh as "materialization of circumscribed circles" of

"radial sets of circles appearing characteristically in certain areas of the matrix".

Figures to explain for situations of those three actual circles of the halo,

overlapping the matrix that emphasizes each certain radial sets of circles, are putting in below.

It is positive to be enough correspondences.

This emphasized radial set of circles of the matrix is touches in the inner edge of the halo's mounded narrow ring.

The outer edge of the ring is overlapping with second concentric circle of the matrix.

Different from other two,

Intersecting points are coming just on tops of circles of this radial set to touch with the certain circle of the halo.

It is due to the dimension of the matrix.

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This emphasized radial set of circles of the matrix touches to the inner edge of another mounded narrow ring, as well.

The outer edge of the ring is defined by the discriminative intersecting points on axes.

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The appearance that one of halo's circle is intend to be circumscribed to this emphasized radial circle set of the matrix is certain.

Despite this, there is a measure of deviation between the halo and the matrix,

at upper right area of inner edge of the mounded narrow ring.

However, this little deviation from the demand status to correspond the matrix and the halo,

it seems to be in ambit that is limited unavoidable deviation, now human hands works.

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It is the main forecast about the way of halo that the design is realized as fitting into 16-radial matrix.

When quantity of element-matrix of radial connecting are augmented,

discriminative sets of radial circles appearing at specific areas build up visualization like circles.

It is clear that the halo takes in all concentric circles, with astounding accuracy.

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16-radial matrix (3step-reducing units)

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investigation by Yagihashi Tsukasa (jabrec-art-music)@2011feb-2

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