Absolutely fascinating, coder1987!  Quite an effort!

I will confess that the use of the word “exact” in the quote you cite was injudicious.  It is “exact” only to within the tolerances associated with the methodology of using a ruler and a protractor on a gas station map.  Which was the methodology that was probably used by the Zodiac at the time, and was most definitely used by me when I did this analysis.  I cannot truthfully assert that Arthur Leigh Allen’s house in Vallejo was the “exact” location that was being indicated – only that the house is within a reasonable tolerance of the spot indicated by the cypher.

Was he pointing to the house?  Or to the triangle that you found?  Or to something else in the vicinity?  We will likely never know.

(Assuming, of course, that our shared solution is correct.  I’m not 100% convinced that the whole cypher isn’t simply gibberish.)

@dmw 

Thanks DMW, I was glad to see that you came back to respond.  There is a way to know if he was pointing to this triangle, that is falsifiable.  That would be the ground penetrating radar test, which is fast, cheap, and non-invasive.  Given that this triangle happens to be found near his first crime scene in Vallejo, it is worth a quick check by authorities to see if he buried anything here. 

If there is nothing there, it can be quickly ruled out in minutes, with minimal effort. 

If there is something there, that is physical evidence in one of the most infamous cold cases of all time, and must be retrieved by authorities for proper analysis. It would also validate this proposed solution at the same time.

As over 2 million alternatives were tested, this is the mathematical needle in the haystack.

I shared the work with the authorities, and so if they do find evidence there, we can safely say the cipher is solved.  

Also, did you write any software to arrive at this solution?  You followed all of the Zodiac clues as I did, but when I tested all plausible candidates programmatically, my lat/lon’s land by LHR, not on a house.  I used the Haversine formula for my projection from Mt. Diablo.

It is worth noting that Oliv92 also arrived at the same plaintext, and also tested millions of candidates, but did not share their code, and was missing the ranking method (proximity to crime scene), and subjectively selected IN THREE AND THREE EIGHTHS RADIANS TEN as their second favorite candidate solution.  It seems they presented it two years after you did, but with a more well defined methodology.

I was surprised to see that neither of you received many comments from others, because I believe you were both on the right track, but not quite there for different reasons, as neither one found this triangle by LHR.  Oliv92 could have, but they didn’t check the satellite imagery it seems.  They had the right lat/lon’s, but needed a ranking algorithm to identify a unique solution from their candidates.

It’s true that the radar finding something in the triangle would prove your case, but if it didn’t find anything, that wouldn’t disprove it.  Zodiac may have been pointing at the triangle, without actually physically placing anything there.

I used no computer programs.  If you look at my write-up, I’m pretty step-by-step about what I did.  Remember, I worked backwards – I wasn’t trying to find “the” solution, just a possible solution.  So I chose a location – Arthur Leigh Allen’s house – placed it on the map, calculated the appropriate distance and angle, and then checked to see if there was a way to encode that in the cypher.  When you measure three and three eights inches and 10 “radians” directly, and then look to see if those numbers could be encoded, the solution is pretty obvious.

I have to confess that I don’t find the triangle to be as compelling a piece of evidence as you do.  But that’s an entirely subjective opinion and I could be totally wrong.

@dmw 

“I have to confess that I don’t find the triangle to be as compelling a piece of evidence as you do.  But that’s an entirely subjective opinion and I could be totally wrong.”

I respect all opinions, however the triangle on the ground does match the morphology of the triangle in the ciphertext, when overlaid.  They both even have a very slight tilt to the east, maybe 5 degrees or less.  Do you think this is coincidental, or natural in origin?

If it is a coincidence, I’d be curious to ask a statistician what the odds of that happening are. 

I tried to find if any other equilateral triangle shaped crop marks of this size or larger have ever been found on Earth, and I could not.  Crop marks such as this are catalogued and studied specifically because they are indicative of human excavation, but they have to be found before they can be studied and physically examined on site.

There have been other triangle (non equilateral) crop marks found in the past, typically proven to be the foundations for old Roman forts that were razed.  They were designed in the triangular shape for a practical purpose, to fit in the surrounding environmental context of where they were constructed.

The triangular morphology for crop marks is incredibly rare to find via satellite imagery, because nature does not produce them.

Posted by: @dmw

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It’s true that the radar finding something in the triangle would prove your case, but if it didn’t find anything, that wouldn’t disprove it.

This is, of course, a crucially important observation, and one that must apply to all such offerings. We cannot have any current knowledge as to whether or not an actual bomb mechanism was dug into a hillside anywhere. We were, however, charged to search for one in either case.

The Zodiac’s primary aim, through his letters, appears to have been mostly to taunt. Getting LE tied up in searching for such a mechanism would have met his needs at all levels, and nothing about this as an aim would require anything to be actually in situ. Consequently, for our exclusion criteria we need to steer away from any thought as of “is there anything there?” and go with the more immediately and easily verifiable “could there have been anything there?” Does our location fit with the assignment given?

Interesting then, @DMW, your interpretation that your proposed solution points to the home of a primary suspect could, in fact, be seen as matching some aspects of what we are given.

By the time of the Melvin Belli letter (20 Dec. 1969) The Zodiac was still expressing some difficulty getting the bomb together:

“At the moment the children are safe from the bomb because it is so massive to dig in & the triger mech requires much work to get it adjusted just right.”

Only in the absence of being able to “hold back” at this time might he actually reach his limit of self control and “set the bomb up.”

On the 20 Apr. 1970 it again appears that, if he is actually working on anything at all, it very likely is still in his basement at home.

“I have killed ten people to date. It would have been a lot more except that my bus bomb was a dud. I was swamped out by the rain we had a while back.”

@DMW. From your paper:

When we consider the angle markings around the blue circle on the map, though, we run into a discrepancy. These markings imply that, in the Zodiac’s system, a full circle has 12 divisions. These divisions are NOT equal to radians.

The map thus shows us an angular measurement that does not equal the measurement mentioned in the post script. At this point it is unclear – does the Zodiac mean to use radians as his angular measure? Does he mean to use a number from 0 to 12? It is also possible that he is using the 0 to 12 system but calling each division in this system a radian, even though this is not technically correct, simply because there is no other word for such a division.

On this point, and in support of the proposed solution in your paper (and, indeed, other similarly approached proposals), I think we can fairly reason as follows.

If we take an honest stand back and look with fresh eyes at the postscript we can be at least certain that the Zodiac was not referencing any angular measure in units of trigonometrical Radians. As it was given to us, we had:

“PS. The Mt. Diablo Code concerns Radians & # inches along the radians.”

There is simply no logical interpretation equating to marking off a distance “along” an angle, let alone along the units of any angle. We measure distances along a line. The compass rose on the map makes it clear that we are looking for a distance directly out from Mount Diablo along some specified radius of a circle, the measured length of which will be “# inches.” There is nothing more involved here than to merely recognise that the Zodiac conflated “radians” with “radii” at some fundamental level.

That said, given that the actual word “RADIANS” appears in your proposed solution, which otherwise makes use of the division into twelfths, we would have to assume a couple of other points, including that this error was already present when The Zodiac gave us the code initially; and it might explain why he felt he had to give us a further postscript since he may have realised his mistake by then, when it was too late to go back to correct it.

A further observation then arises from the fact that we have ‘RADIANS’ in the plural, even though at this stage were only interested in one specific ‘RADIAN’ (radius).

Again, its The Zodiac himself who uses the plural, and I would suggest the reason for this is likely that he envisaged his division of the compass rose as effectively creating a wheel with 12 spokes (plural). Going around from the indicated magnetic north in a clockwise direction he was then merely counting spokes (plural) until he got to ten. All the spokes, thus visualised, would be cut at “# inches” equally, and thus we have “# inches along [all] the radians” (spokes), and not just the tenth.

As to the last assertion from your quote above, however, it is only proper to point out that there are indeed “other word[s] for such a division” of a full circle into twefths. “HOUR” would be one, as indeed “TWELFTHS”. We could also specify the angle without introducing anything essentially out of place if we proposed “#OCLOCK.” And there’s at one other named twelfth division that gains at least some interest through being contextually topical.

@shaqmeister I tested your theory about OCLOCK or HOURS being in the plain text.

Before adding these two words:

Total candidates: 2,044,224
Passed length (=32): 154,572
Passed homophonic locks: 61
Passed map bounds: 54
Rejection rate: 99.9974%
Survivors: 54

PRIMARY SOLUTION: INTHREEANDTHREEEIGHTHSRADIANSTEN
3.375 in x 6.4 mi/in = 21.6 mi at 10:00
(38.109952, -122.185349)
Nearest: blue_rock_springs (1.15 mi)

After adding these words:

Total candidates: 3,066,336
Passed length (=32): 234,540
Passed homophonic locks: 62
Passed map bounds: 55
Rejection rate: 99.9982%
Survivors: 55

PRIMARY SOLUTION: INTHREEANDTHREEEIGHTHSRADIANSTEN
3.375 in x 6.4 mi/in = 21.6 mi at 10:00
(38.109952, -122.185349)
Nearest: blue_rock_springs (1.15 mi)

It did not change the result, and only yielded a single valid survivor of the constraint filtering, which is ranked 51 out of 55.

Posted by: @coder1987

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@shaqmeister I tested your theory about OCLOCK or HOURS being in the plain text.

Thanks for running that, @coder1987. Are you able to give details of what exactly you are applying as your ranking criteria?

@shaqmeister Sure, although it has already been mentioned on here and in the paper.

The ranking algorithm is simple, rank by proximity to known Zodiac crime scenes.  This is an objective ranking based on physical, objective reality, and is the most logical ranking algorithm for this cipher, unless you can find a better one.

This is expressed as a single line of code, which is publicly available.

survivors.sort(key=lambda x: x[“nearest_dist_mi”]), where nearest_scene_dist is the Haversine distance between  the projected coordinate and the nearest crime scene to that point.

If Oliv92 had ranked his survivors in this manner, he would have arrived at the same solution as I did, rather than presenting multiple possible solutions.

Posted by: @shaqmeister

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Posted by: @coder1987

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@shaqmeister I tested your theory about OCLOCK or HOURS being in the plain text.

Thanks for running that, @coder1987. Are you able to give details of what exactly you are applying as your ranking criteria?

Okay. So, to answer my own question through review of the code-generated z32_results.json, it would appear that your ranking is attained solely upon proximity to one or other of three prior victim sites? Would that be correct?

Posted by: @coder1987

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The ranking algorithm is simple, rank by proximity to known Zodiac crime scenes.  This is an objective ranking based on physical, objective reality, and is the most logical ranking algorithm for this cipher, unless you can find a better one.

For myself, if I were to consider ranking at all, I would be looking at proximity to known school bus routes at the time as my primary criterion.

@shaqmeister It would be four victim sites, not three.

Lake Herman Road, Blue Rock Springs, Lake Berryessa, and the Paul Stine crime scene (Washington and Cherry).

Let me know if you have a better ranking algorithm that yields a better solution, that is why I shared it.  Others are welcome to try, they might find something more interesting than the triangle by LHR.

Due to the ranking algorithm, Zodiac cherry picks IN THREE AND THREE EIGHTHS RADIANS TEN, since it is derived from the locations of his documented criminal activity.  Reality, rather than an opinion.

Again, ground penetrating radar is the necessary final step to determine validity.  That would be the scientific approach, at least.

It would indeed be four. Thanks for the correction, coder.

As well as shying away from ranking at such an early stage of analysis, I would also wish to widen out the implicit assumptions, as in your case, that require that the expected coordinate pair completes the cipher. I have always been committed to the point which I believe I saw DMW bring up again recently, that as means towards our solution we have only the cipher and the map. To this end, then, I cannot merely sweep away the fact that the map can never, of itself, provide a precise location without something further, and thus I would be looking at allowing all candidates to be possibly open ended initially, in the hope that something additional appears there.

@shaqmeister Close but still missing an important detail.  We did not only have the cipher and the map.  We also had the post script hint regarding “The Mount Diablo Code”.  Regarding the map, there are more important details about it, such as the scale and drawing his symbol on Mt. Diablo with the numerical values.  Even the scale played an important role, as if I had used a different scale in my calculations, everything would be wrong.  It would land in the incorrect location.

Some interpret his branding symbol as a targeting scope, but in his post script hint for the Mt. Diablo Code, it can also be interpreted as a unit circle in a polar coordinate system.  Subjective but valid.

The “something further” you mentioned would be recovering the potentially buried forensic evidence within the visible, decades old landmark.  And so I find myself again pointing to ground penetrating radar for that part, where we go beyond the cipher and into the real world.

Also, the decoded coordinates will plot on the provided map, it is within the boundaries.  We can see the south side of LHR, which is where this lands.

Posted by: @coder1987

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Some interpret his branding symbol as a targeting scope, but in his post script hint for the Mt. Diablo Code, it can also be interpreted as a unit circle in a polar coordinate system.  Subjective but valid.

What has always struck me as frustratingly odd is that no-one – and I mean absolutely no-one – appears to have opened their mind to the fact that the symbol is, in fact, nothing other than a symbolisation of “the (celestial) Zodiac.” This is exactly how it is used on Zodiac watches and countless other products over the years branded as “Zodiac.” Minimistically, it conveys the cross-lines of the solstices/equinoxes and the circle of the signs, of which the latter (in the heavens) is divided into 12 and could reasonably be counted out from 0 at the top.