Universal Kernel

anchor

Also vantage

The report an observer stands on. Moving it along a letter is a re-anchoring.

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Plate W.1The kernel graph of one clock with the anchor, report 0, ringed in gold; a re-anchoring along the letter 01, the gold arrow, moves the vantage to report 1.

As mathematics

With the clock cc fixed, an anchor is a line ℓ\ell of PG(2,2)\mathrm{PG}(2,2) missing cc, one vertex of the complete quadrilateral K4K_4 formed by the four such lines. Its stabilizer in the clock’s group S4≅AGL(2,F2)S_4\cong\mathrm{AGL}(2,\F_2) is GL⁡(2,F2)≅S3\GL(2,\F_2)\cong S_3: choosing an anchor is choosing an origin of the affine plane AG(2,F2)\mathrm{AG}(2,\F_2) on the four reports, which matches each place with the displacement that reaches it.

As a line of the plane the anchor belongs to the object of the seven lines, with stabilizer S4bS_4^b. With the clock varying, the pairs (clock, anchor) are the antiflags of the Fano plane, the object of size 28 with stabilizer S3S_3.

Its name in another fieldBridge
a vertex of the kernel graph K4K_4built
an origin of the affine plane AG(2,F2)\mathrm{AG}(2,\F_2)built
with its clock, an antiflag of the Fano planebuilt
a frame of the lifta reading
Built from
reportletter
In the dictionary
the seven lines