Hermitian – Layer Alignments

One of the frequent commenters at Dr Conspiracy’s blog is Hermitian. He has provided us with the following useful information that shows how the layers align at 8×8 blocks on a 300×300 DPI grid.

I have completed my analysis of the size and position of the nine object rectangles that comprise the composite image of the WH LFCOLB PDF image. My efforts have focused on the central question – Were the nine rectangles placed by man or machine? The overwhelming answer is that the placement was done by man. No file-size optimization software would have made the same placement decisions as are found in the WH LFCOLB PDF image.

[NBC: Actually, it is hard to understand why a forger would so carefully align the boundaries, while an algorithm is trivially simple]

For my analysis, I chose an x,y coordinate system with origin at the upper left corner of the background layer. This point was therefore also the rulers origin. Consequently the x-axis is horizontal and x increases from left to right. The y-axis is vertical and y increases from top to bottom. This x,y coordinate convention is consistent with the most popular graphics programs that are currently provided by current sources. These include Adobe Photoshop CS6, Adobe Illustrator CS6, Adobe Acrobat XI Pro, and Inkscape. All of these programs set the rulers origin in the upper left corner of the screen and the (x,y) coordinates of each rectangle are measured from the origin to the upper-left corner of the rectangle.

This approach assumes that a modern digital graphics program and a Macintosh computer were used to create each of the nine images that comprise the WH LFCOLB composite PDF image.

Results were obtained for two different pixel resolutions — 300 PPI X 300 PPI and 150 PPI X 150 PPI. These were respectively the resolutions of the background layer and the eight non-background layers in the WH LFCOLB composite image. Three grids were analysed. These are 300 PPI X 300 PPI in blocks of 8 X 8, 300 PPI X 300 PPI in blocks of 16 X 16, and 150 PPI X 150 PPI in blocks of 8 X 8.

Each of the nine rectangles satisfy the 8 MOD 0 condition for the top and right edges for the 300 PPI X 300 PPI resolution. The left and bottom edges touch at least one pixel of at least one character of text contained within each layer. The right edge of the mostly text layer also touches pixels.

Those edges of rectangles that satisfy the 16 MOD 0 condition for the 300 PPI X 300 PPI resolution also satisfy the 8 MOD 0 condition for the 150 PPI X 150 PPI. The modulo condition is satisfied whenever the quotient is an integer.

Layers 2, 3, 5 and 6 satisfy all three conditions for both the top and right edge of each rectangle. The exact positions of Layers 4, 8, and 9 are not critical. The “Non” in “None” layer satisfies the first condition but not the other two for the top and right edges. However, this object is constrained in both coordinate directions. Oddly, the left edge of layer 6 satisfies all three modulo conditions. Layers 1, 4, 7, 8 and 9 do not satisfy the second and third modulo condition for the right edge. However layer 1 (of these five layers) is constrained by the right edge of the page. Layers 4, 8, and 9 are not constrained in the x direction. And, as previously stated the “Non” layer is constrained in both x and y directions and therefore does not satisfy the second and third modulo condition for either the top or right edge.

Finally the top edge of each of the nine layers satisfies all three conditions with the exception of the “Non” layer. Also the quotients are the same for the last two modulo conditions. The quotients for the last to conditions are exactly half of the quotients of the first condition.

The results that follow are preliminary and are still being checked. If anyone finds a numerical error please post it and I will post a corrected page.

Resolution = 300 PPI X 300 PPI / 8 X 8 Blocks
Top and Right Sides Obey 8 MOD 0
Left and Bottom Sides Align with Grid Lines (and also Touch Pixels)

                                      
N   (x,y)         (w,h)     (x+w,y)    ((x+w)/8,y/8)
1 (   0,   0)  (2552,3304) (2552,   0) (319,  0)	Background
2 ( 373, 880)  (1819,1454) (2192, 880) (274,110)	Mostly Text
3 (1270,2848)  ( 778, 199) (2048,2848) (256,356)	Onaka Signature
4 ( 710,2928)  ( 274,  42) ( 984,2928) (123,366)	Onaka Date
5 (1836,2160)  ( 228, 123) (2064,2160) (258,270)	Reg. Gen. Date
6 ( 432,2240)  ( 216,  47) ( 648,2240) ( 81,280)	Loc. Reg. Date
7 (1458,1960)  (  70,  34) (1528,1960) (191,245)	Non
8 ( 735,2528)  ( 217, 243) ( 952,2528) (119,316)	Bottom Speckle
9 (1050,  32)  ( 142, 132) (1192,  32) (149,  4)	Top Speckle

Resolution = 300 PPI X 300 PPI / 16 X 16 Blocks
Integer Quotients satisfy 16 MOD 0

N    (x,y)       (w,h)     (x+w,y)     ((x+w)/16,y/16)
1 (   0,   0) (2552,3304) (2552,   0)  (159.5,  0  )    Background
2 ( 373, 880) (1819,1454) (2192, 880)  (137  , 55  )    Mostly Text
3 (1270,2848) ( 778, 199) (2048,2848)  (128  ,178  )    Onaka Signature
4 ( 710,2928) ( 274,  42) ( 984,2928)  ( 61.5,183  )    Onaka Date
5 (1836,2160) ( 228, 123) (2064,2160)  (129 , 135  )    Reg. Gen. Date
6 ( 432,2240) ( 216,  47) ( 648,2240)  ( 40.5,140  )    Loc. Reg. Date
7 (1458,1960) (  70,  34) (1528,1960)  ( 95.5,122.5)    Non
8 ( 735,2528) ( 217, 243) ( 952,2528)  ( 59.5,158  )    Bottom Speckle
9 (1050,  32) ( 142, 132) (1192,  32)  ( 74.5,  2  )    Top Speckle

Resolution = 150 PPI X 150 PPI / 8 X 8 Blocks
Integer Quotients satisfy 8 MOD 0

N     (x,y)        (w,h)     (x+w,y)   ((x+w)/8,y/8)
1     (0,0)     (1276,1652) (1276,0)    (159.5,0)       Background
2 (186.5,440)  (909.5,727)  (1096,440)  (137  ,55)      Mostly Text
3   (635,1424)   (389,99.5) (1024,1424) (128  ,178)     Onaka Signature
4   (355,1464)   (137,21)    (492,1464)  (61.5,183)     Onaka Date
5   (918,1080)   (114,61.5) (1032,1080) (129  ,135)     Reg. Gen. Date
6   (216,1120)   (108,23.5)  (324,1120)  (40.5,140)     Loc. Reg. Date
7   (729,980)     (35,17)    (764,980)   (95.5,122.5)   Non
8 (367.5,1264) (108.5,121.5) (476,1264)  (59.5,158)     Bottom Speckle
9   (525,16)      (71,66)    (596,16)    (74.5,2)       Top Speckle

5 thoughts on “Hermitian – Layer Alignments

  1. Let me appologize for my “you don’t have the guts to post this comment”. Obviously you do possess the requisite intestinal fortutide and ditto you are obviously after the truth. Thanks for the improvements to my poor formatting — especially the data.

    Hermi

  2. No problem. You comment had entered the pending box and I noticed your recent comment so I checked and decided to post it as a posting rather than as a comment.

  3. I love the fiction in your exposition.
    Let’s make sure we all understand the fact that birth on soil, subject to jurisdiction is what makes a personal natural born.

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