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I've been looking at compound experiments 785 to 837 since these experiments explore various combinations of materials from a limited set and thus give a chance of deducing the properties of the materials. (It's like having a set of simultaneous equations - if there is a limited number of variables then you have a chance of solving them - if each equation has different variables then you can't isolate them.)

The materials for these experiments are chosen from :- Fern Palm, Folded Birch, Giant Cricklewood, Spindle Tree, Stout Palm, Hawthorn, Royal, Coconut Palm, Bramble Hedge

To begin with, I've ignored all compounds containg Spindle Tree since there were only 13 experiments performed using this. This leaves 8 materials from which 5 are to be chosen for each experiment which results in 56 possible combinations. The experiments report results for 40 combinations so there is reasonable coverage.

I wanted to explore the theory that essence values can any of the take integer values -2, -1, 0, 1, 2. A material will be made up of combinations of the eight essences with the quantity of each essence given by one of these integers. The properties of a compound is then found by adding the essence quantities from the constituent materials. The essences giving the maximum and minimum values are then what is reported by the experiment. In the event of a tie, I have assumed that the essence reported is the one that comes first alphabetically.

This method of combination can clearly give a resulting value between -10 and 10. The way this maps onto the "++++" etc notation is not entirely relevant at this stage although simple division by 2 and rounding to the nearest integer would give a range of -5 to 5 which would be a credible approach.

The first stage was to demonstrate that the results of the 40 experiments could be predicted using this model for essences. I was able to do this firstly using an excel spreadsheet to investigate different essence combinations for the materials to get a feel for the problem. I then implemented a simple simulated annealing approach to search through essence combinations to maximise the match to the experimental results. I found the constituent essence properties in the table below predict the experimental results for all 40 experiments.

	FP	FB	GC	SP	HT	RP	CP	BH
Ar	0	1	0	0	-1	2	-1	0
As	0	1	0	-1	2	1	2	-1
Bi	1	-1	-1	0	2	-2	-1	-2
Sa	2	-2	-2	2	-2	0	0	2
So	0	2	0	-1	0	1	0	0
Sp	1	1	-1	2	0	0	1	-1
Sw	-1	0	-1	-2	0	0	0	0
To	1	0	-1	1	2	0	0	-1

(It should be noted that only one of the experiments gave a To result and none gave a So result so the least confidence can be given to these essences in terms of generalistion of the results to other experiments.)

The obvious next stage is to perform the experiments for the 16 possible combinations which have not been reported so far and to see whether the results can be predicted using these values. The required experiments are listed below together with the predicted max and min results. Please let me know the results if you perform any of these experiments.

You should look at sumtet's results. I did the complete set of 126 combinations of 9 different essences. Look at results Sum1-Sum124 and Mac3, Mac4 for the entire set. Basically the above set plus Spindle Tree. Whoever is updating the overall set of results isn't keeping up with my new ones. I have also checked my entire set of results versus the current request by Ktisibios and any matches are noted. Your third prediction doesn't match Sum67 by the way. Didn't check the rest of the predictions. -sumtet

Material 1	Material 2	Material 3	Material 4	Material 5	Max	Min
Bramble Hedge	Coconut Palm	Giant Cricklewood	Hawthorn	Stout Palm	As	Sw
Bramble Hedge	Fern Palm	Giant Cricklewood	Hawthorn	Stout Palm	Sa	Sw
Bramble Hedge	Fern Palm	Hawthorn	Royal	Stout Palm	Sa	Sw
Bramble Hedge	Folded Birch	Giant Cricklewood	Hawthorn	Stout Palm	As	Sw
Bramble Hedge	Folded Birch	Hawthorn	Royal	Stout Palm	Ar	Bi
Bramble Hedge	Giant Cricklewood	Hawthorn	Royal	Stout Palm	Ar	Bi
Coconut Palm	Fern Palm	Folded Birch	Giant Cricklewood	Hawthorn	As	Sa
Coconut Palm	Fern Palm	Folded Birch	Hawthorn	Stout Palm	Sp	Sw
Coconut Palm	Fern Palm	Giant Cricklewood	Hawthorn	Stout Palm	As	Sw
Coconut Palm	Fern Palm	Giant Cricklewood	Royal	Stout Palm	Sp	Sw
Coconut Palm	Fern Palm	Hawthorn	Royal	Stout Palm	As	Sw
Coconut Palm	Folded Birch	Giant Cricklewood	Hawthorn	Royal	As	Sa
Coconut Palm	Folded Birch	Giant Cricklewood	Hawthorn	Stout Palm	As	Sa
Coconut Palm	Folded Birch	Giant Cricklewood	Royal	Stout Palm	As	Bi
Coconut Palm	Folded Birch	Hawthorn	Royal	Stout Palm	As	Bi
Coconut Palm	Giant Cricklewood	Hawthorn	Royal	Stout Palm	As	Sw

(Cont.) It turned out that Sumtet had already performed these additional experiments. Comparison with his results showed that both max and min essence content were correctly predicted for 11 out of the 16 compounds. Further refinement of the constituent essence values then resulted in the following table.

	FP	FB	GC	SP	HT	RP	CP	BH
Ar	0	1	0	0	-1	2	-1	0
As	0	1	0	-1	2	1	1	0
Bi	1	-1	-1	0	2	-2	-1	-2
Sa	2	-2	-2	2	-2	0	0	2
So	0	2	0	-1	0	1	0	0
Sp	0	2	-1	2	0	0	0	-1
Sw	-1	0	-1	-2	0	0	0	0
To	1	-1	-1	0	2	1	-1	-2

These values correctly predict the properties of all 56 compounds apart from the minimum essence value for Sum67 for which the prediction is Sweet rather than the Bitter result shown in the experimental result below copied from Sumtet's page.

Sum67

Bramble Hedge

Fern Palm

Hawthorn

Royal Palm

Stout Palm

Salty

Bitter

(Cont.) Telanoc subsequently repeated this experiment and reproduced the results reported by Sumtet so the model isn't fitting all the data. This could be because the essence values need to be refined further or that the model is inadequate. If the model is inadequate then this will be even more evident when trying to match the results from the 126 compounds which result when the Spindle Tree is included to give nine materials. So the next step was to attempt to predict the 126 results for this larger set.

It is worth noting at this stage that the score I use to judge how closely the model predicts experiment is the number of correct positives plus the number of correct negatives. So, for the initial set of 56 compounds, there was a possible maximum score of 112 and the best the model could do was 111/112. For the extended set of 126 compounds, the maximum score is obviously 252.

On attempting to match the extended compound set, using the model with essence values in the range [-2, 2] the best score that was achieved was 239/252. (Some improvement might be possible but it seems unlikely that the maximum score can be achieved.) This appears to show that the model is increasingly failing to match experiment as the size and complexity of the results set increases which indicates that the complexity of the model is insufficient. An obvious extension of the model is to increase the range of values to [-3, 3]. On doing this, it has been possible to achieve a score of 251/252 so far using the values shown in the table below.

This is tantalisingly close to predicting all the observed results with the only discrepancy being in the minimum essence content of Sum84 which is predicted as Sa rather than To on the basis of alphabetical order since the numerical values are the same. There remains the possibility that the essence values can be refined still further to give a fully accurate prediction since the guided random search (annealing) through possible essence values will not have explored every possible combination. However, an overnight run through several hundred million iterations has failed to find an improvement.

	FP	FB	GC	SP	HT	RP	CP	BH	ST
Ar	0	1	2	0	-2	3	-2	1	3
As	-1	2	2	-2	3	1	2	1	0
Bi	0	-1	2	-1	2	-3	0	-3	-2
Sa	2	-2	-1	3	-3	1	-1	3	0
So	0	0	3	2	-1	-2	0	-1	2
Sp	0	3	1	1	0	0	1	0	0
Sw	-2	0	0	-3	1	0	0	0	0
To	1	0	2	0	1	0	-3	0	-3

(Aside: It is interesting to examine the compounds that meet Ktisibios' requirements in the light of these values.

• Sum132 contains Stout Palm and Hawthorn and satisfies Spicy(++++). However, the Sp values predicted for SP and HT do not suggest they would give rise to a large, positive SP component.
• Sum133 contains Coconut Palm and satisfies Aromatic(- - - -). The Ar(-2) value for CP is resonably consistent with this.
• Sum134 contains Fern Palm and Stout Palm and satisfies Salty(++++) and Sweet(- - - -). From the table, FP has Sa(+2) and Sw(-2) whilst SP has Sa(3) and Sw(-3) which are clearly consistent.
• Sum137 contains Coconut Palm and satisfies Aromatic(- - - -) and the comments as for Sum133 apply.
• Sum199 and Sum200 contain Folded Birch and satsify Spicy(++++). The Sp(3) value for FB is consistent with this.

So it appears that only the Sum132 result seems inconsistent. However, the other results suggest that the essence values that have been found are reasonably consistent. A possible explanation could be that the other materials in Sum132, namely Ash Palm, Dark Ochoa and Pale Dhamasa are extremely Spicy.)

If it is assumed that no improvement is possible using the [-3,3] model and that there were no errors in the reported experimental results, then the model once again needs to be modified. Assuming also that the simple additive process for combining essence attributes is correct then once more an extension of the range of essence values needs to be considered, this time to the range [-4,4]. This would fit well with the compound requirements in the (++++) etc notation since they also vary in the range [-4,4]. The combination process could just take the average of the individual essence values of the five materials and round up to the nearest positive integer or down to the nearest negative integer. This would give a result in the range [-4,4].

(Cont.) Looking back at what Ktisibios said, I notice that he definitely talks about a scale of 5, i.e. (+ + + + +) to (- - - - -). If it is assumed that this refers to the final compound, but that the individual materials have essence values in the range [-4,4], then the potential compound range of [-20,20] obtained by simply summing the material essence components needs to be mapped to the (+ + + + +), (- - - - -) scale. This can be done in a simple way by dividing by 4 and rounding positive numbers up to the nearest integer and negative numbers down to the nearest integer. So combined results map as follows

[-20,-17]	(- - - - -)
[-13,-16]	(- - - -)
[-9,-12]	(- - -)
[-5,-8]	(- -)
[-1,-4]	(-)
[0]	(=)
[1,4]	(+)
[5,8]	(+ +)
[9,12]	(+ + +)
[13,16]	(+ + + +)
[17,20]	(+ + + + +)

Using this model, I have attempted to match all the results reported by Sumtet sumtet's results. There are 286 experiments in all which gives 572 observations to match. Also Sum131 to Sum137 inclusive together with Sum199 and Sum200 satisfy the requirements for the chest whilst Sum148 satisfies the requirements for the treatment. I have introduced these as additional observations to be matched which gives a total of 592. Using the same process as described above, I have achieved a best fit of 590/592 using the material essence values as contained in the table below. In particular, all the compounds which match the requirements are correctly identified as such.

The two model predictions which do not match are for Sum84 and Sum140. Sum 84 has been observed to give max negative To but is predicted to have max negative Sa on the basis of alphabetical order. This is the same problem as was encountered when trying to fit the 126 compound set discussed above with a [-3,3] model. Indeed, the component essence values for these materials have not varied although the fitting process did have the flexibility to do so (hmmmm odd!). Sum140 has been observed to give no positive value but the model gives summed values of 1 for both Ar and As. The model seems to extremely close to fitting all the data so these two slight discrepancies are frustrating.

Material	Ar		As	Bi	Sa	So	Sp	Sw	To
'Fern_Palm'	0		-1	0	2	0	0	-2	1
'Folded_Birch'	1		2	-1	-2	0	3	0	0
'Giant_Cricklewood'	2		2	2	-1	3	1	0	2
'Stout_Palm'	0		-2	-1	3	2	1	-3	0
'Hawthorn'	-2		3	2	-3	-1	0	1	1
'Royal_Palm'	3		1	-3	1	-2	0	0	0
'Coconut_Palm'	-2		2	0	-1	0	1	0	-3
'Bramble_Hedge'	1		1	-3	3	-1	0	0	0
'Spindle_Tree'	3		0	-2	0	2	0	0	-3
'Cinnar'	2		3	-4	-1	2	4	-3	0
'Butterleaf_Tree'	-1		-1	-3	4	-1	0	2	-1
'Mini_Fern'	2		3	-3	1	0	-2	2	-1
'Topaz'	-1		2	1	-3	-1	2	1	0
'Jade'	0		1	4	1	-4	-2	4	3
'Lapis'	3		-1	0	0	1	0	-2	2
'Spiked_Fishtree'	1		1	-2	-3	2	4	-2	0
'Common_Basil'	0		-1	4	1	-3	-3	-3	1
'Passam'	1		2	1	1	-1	1	0	3
'Sapphire'	-4		0	-1	-2	-2	-4	0	3
'Tapacae_Miralis'	1		0	-3	0	4	2	2	4
'Pale_Dhamasa'	3		2	2	2	-1	4	-4	3
'Marble_Dust'	1		-1	0	3	-1	0	-2	3
'Bluebottle_Clover'	0		-3	4	2	3	0	-1	-2
'Bottle_Tree'	2		0	4	2	-1	-1	-2	-2
'Chakkanut_Tree'	3		-2	3	4	2	-2	0	1
'MeadowSweet'	-4		-2	4	0	2	-2	-1	4
'Ash_Palm'	1		-1	-4	0	0	4	0	-4
'Dark_Ochoa'	-2		-2	-3	0	3	4	0	1
'Iron'	-4		-1	2	-2	-1	2	0	1
'Strawberry_Tea'	-4		2	-2	2	2	-3	-2	1
'Arconis'	-3		1	3	1	3	-1	-4	4
'Common_Sage'	1		1	3	3	0	-3	-3	3
'Cricklewood'	0		3	0	4	0	-4	-2	2
'Hokkaido'	1		1	1	-1	-3	1	2	-4
'Mini_Palmetto'	-2		1	-2	1	-3	-1	-1	4
'Quartz'	-2		4	1	-2	-4	1	3	-1
'Orrorin'	-3		0	-3	-2	4	-2	0	0
'Windriver_Palm'	-1		0	1	-2	1	-2	2	-3
'Aluminum'	1		1	0	-1	-2	0	1	-1
'Towering_Palm'	-1		-4	-2	0	1	1	-2	0
'Umbrella_Palm'	-3		-1	0	-4	-3	-4	-3	-1

(Cont.) I've been looking at extending the model to [-5,5]. I've found a set of values which correctly predicts all of the 126 experimental results for the original 9 materials. The values are given below beneath the table of best values found for [-3,3] reproduced from above for comparison.

	FP	FB	GC	SP	HT	RP	CP	BH	ST
Ar	0	1	2	0	-2	3	-2	1	3
As	-1	2	2	-2	3	1	2	1	0
Bi	0	-1	2	-1	2	-3	0	-3	-2
Sa	2	-2	-1	3	-3	1	-1	3	0
So	0	0	3	2	-1	-2	0	-1	2
Sp	0	3	1	1	0	0	1	0	0
Sw	-2	0	0	-3	1	0	0	0	0
To	1	0	2	0	1	0	-3	0	-3

	FP	FB	GC	SP	HT	RP	CP	BH	ST
Ar	-2	0	0	0	-3	4	-1	0	4
As	-3	2	0	-3	5	0	4	1	-1
Bi	-1	-3	0	-2	2	-5	2	-5	-4
Sa	2	-5	-4	5	-5	0	0	4	-1
So	-2	-1	1	3	-1	-2	1	-1	2
Sp	-1	3	-1	1	1	-1	3	0	-2
Sw	-4	-1	-3	-5	0	0	1	0	-1
To	1	-2	0	0	0	1	-4	1	-5

(Cont.) A Plan? I've been trying to fit all of Sumtet's results using the model based on [-5,5] as described above. Using the scoring system also described above I have so far found four sets of essence compositions for the materials which achieve a score of 591/592. These are shown in the table below. This is a bit difficult to follow but it can be seen that some essence values for some materials are reasonably consistent between the four sets (e.g. the aromatic component of iron is -5 each time) whilst some vary significantly (e.g. the aromatic component of Jade is 0, 4, -1, 2). This essentially reflects the amount of information about the various materials that is contained in Sumtet's results. In particular, the essence compositions of the first 9 materials are fairly stable throughout all four sets which reflects the fact that experimental results have been obtained for all combinations of 5 materials chosen from these 9.

It is useful to note that there are a number of materials which fairly consistently have large negative values for the aromatic component, in particular Arconis, Strawberry Tea, Iron, Dark Ochoa, Orrorin, Sapphire, Lapis, Hawthorn. Thus it seems reasonable to believe that any combination of 5 from these 8 will have a large aromatic component. If this is the case, then it would seem likely that some of the 56 possible combinations will also meet the (=) requirement for bitter and / or sweet which could be identified using Ktisibios' requirements. This would then give some specific equations (rather than inequalities) relating to the bitter and sweet essence values of the 8 materials. With luck, if a number of (=) results were obtained, it would then be possible to start solving these equations to obtain the relative values of the bitter and sweet components for these materials.

Then, given a set of materials with large negative aromatic components and known bitter and sweet values, it would potentially be possible to start determining the bitter and sweet values for other materials. This would be done by having a set of 5 that satisfy AR (- - - -) SW(=) say, each with different sweet values (e.g. -2,-1, 0, 1, 2). Replacing each material in turn with the unknown material would then reveal the sweet value (if it lies in -2, -1, 0, 1, 2) when the requirement was again met.

So if you believe this reasoning, I would suggest an effort to test all 56 combinations of the materials listed above.

You might want to consider another aspect of my data set: number of times a given essence is present. With the my current set of 303 results the numbers are: Arconis 20, Strawberry Tea 3, Salts of Iron 10, Dark Ochoa 7, Orrorin 16, Powdered Sapphire 38, Powdered Lapis 2, Hawthorn 110. Of these only Hawthorn is well represented, the Strawberry Tea, Powdered Lapis, Dark Ochoa, and Salts of Iron are still fairly unconstrained. I'm updating my essence page to contain current counts for my results -Sumtet

Agreed - I have most confidence in the results for the original 9 materials at the begining of this discussion since all combinations of 5 out of 9 were tried - ideally all combinations would be tried for all materials but life's too short - all that can be done is to take the results that exist and make some educated guesses as to the best way forward.

Material	Ar	As	Bi	Sa	So	Sp	Sw	To		Ar	As	Bi	Sa	So	Sp	Sw	To		Ar	As	Bi	Sa	So	Sp	Sw	To		Ar	As	Bi	Sa	So	Sp	Sw	To
'Fern_Palm'	-1	-2	-1	3	-2	0	-4	1		-1	-2	-1	3	-2	-1	-4	1		-1	-2	-1	3	0	-1	-4	1		-1	-2	-1	3	-1	-1	-4	1
'Folded_Birch'	0	3	-3	-5	-1	4	-1	-1		0	3	-3	-5	-1	5	-1	-2		0	3	-3	-5	-1	5	-1	-1		0	2	-3	-5	-2	5	-1	-1
'Giant_Cricklewood'	0	0	0	-5	2	-2	-3	0		0	0	0	-5	0	-2	-3	1		0	1	0	-5	3	-1	-3	1		0	0	0	-5	2	-2	-3	1
'Stout_Palm'	-1	-4	-2	5	2	1	-5	0		-1	-3	-2	5	4	1	-5	0		0	-3	-2	5	3	1	-5	0		-1	-4	-2	5	3	0	-5	0
'Hawthorn'	-3	5	2	-5	0	1	0	0		-3	5	2	-5	-1	1	0	-1		-3	5	2	-5	-1	1	0	0		-3	5	2	-5	-1	1	0	0
'Royal_Palm'	5	1	-5	1	-3	0	0	0		4	0	-5	0	-2	-1	0	1		4	0	-5	0	-4	-2	0	1		4	1	-5	0	-3	-1	0	0
'Coconut_Palm'	-2	4	1	-1	0	2	1	-5		-2	4	1	-1	0	2	1	-4		-2	4	1	-1	0	3	1	-5		-2	5	1	-1	1	3	1	-5
'Bramble_Hedge'	0	0	-5	4	-3	-1	0	0		0	0	-5	4	-2	-1	0	0		0	0	-5	4	-3	-2	0	0		0	0	-5	4	-3	-2	0	0
'Spindle_Tree'	5	-1	-4	-1	3	-2	-1	-5		5	-1	-4	0	3	-2	-1	-5		5	-1	-4	0	2	-2	-1	-5		5	-1	-4	0	2	-2	-1	-5
'Cinnar'	0	2	-4	0	1	4	-3	-1		3	1	-4	0	2	4	-1	-2		3	3	-4	0	4	5	-2	2		2	4	-5	-1	2	5	-3	0
'Butterleaf_Tree'	-1	0	-5	5	-4	2	0	-1		-1	0	-4	5	-3	3	3	0		-2	0	-4	5	-4	1	4	-2		0	0	-5	5	-2	2	3	0
'Mini_Fern'	1	1	-5	1	0	-5	0	-3		0	1	-5	0	2	-4	0	-2		1	2	-5	0	-1	-5	2	-2		-1	0	-5	-1	-1	-4	0	-1
'Topaz'	0	3	2	-3	0	1	3	1		1	4	2	-3	-2	0	1	1		-1	3	0	-4	-2	1	1	-1		0	5	3	-3	0	3	2	2
'Jade'	0	1	5	3	-5	0	-3	3		4	-2	-3	-1	-5	2	3	3		-1	-4	-3	2	-5	2	4	4		2	2	1	-3	-4	1	-3	5
'Lapis'	-5	1	0	-5	0	-5	5	2		-1	5	1	-4	4	-4	4	1		-5	-3	-4	-1	4	-3	4	2		-5	3	-1	1	3	-3	5	5
'Spiked_Fishtree'	1	0	-5	-4	-4	5	-4	0		-3	-1	-5	-5	-3	3	-4	1		-2	-1	-2	-5	2	5	-1	2		0	0	-3	-5	1	5	-4	1
'Common_Basil'	-3	-5	-4	-4	3	-3	-4	0		1	-2	1	1	-4	1	-5	2		0	-4	1	0	2	-1	-5	5		-4	-5	3	0	2	-2	0	3
'Passam'	0	2	0	1	-3	1	1	3		0	4	1	3	3	2	3	5		0	5	0	2	-3	0	0	3		0	5	0	-1	-4	-1	0	4
'Sapphire'	-3	-1	0	-2	-2	-5	-1	4		-4	0	-1	-3	-1	-5	-3	3		-5	-1	-2	-4	0	-5	-2	4		-5	-2	-2	-2	-2	-5	-3	3
'Tapacae_Miralis'	-1	-2	-5	-1	-2	-1	-1	5		-1	-4	-5	-1	-1	-2	2	3		0	-1	-3	1	-3	-3	2	5		0	-4	-5	-2	-3	0	-3	4
'Pale_Dhamasa'	1	0	1	4	-5	4	-5	4		4	-4	4	4	-4	4	-5	2		1	-1	4	-2	-4	5	-5	4		3	-3	-2	2	-3	5	-5	-3
'Marble_Dust'	1	1	3	-5	5	-4	3	-2		5	0	4	-4	3	-5	-5	-1		4	-1	3	-5	1	0	-2	-5		3	-4	4	-5	3	-1	-4	4
'Bluebottle_Clover'	4	-5	3	3	-4	2	0	-2		4	-5	3	2	1	-3	4	-4		3	-3	1	5	1	3	0	-3		2	-5	4	4	3	4	2	2
'Bottle_Tree'	-1	-3	3	-1	-2	-4	-4	-5		1	-3	3	3	0	-3	-3	-4		2	1	5	0	2	-2	-4	0		-1	-2	4	1	-2	-2	-4	-3
'Chakkanut_Tree'	1	-5	5	5	0	-5	-4	-1		3	-5	5	5	0	-3	-2	-2		3	-4	5	3	-3	-3	1	-3		1	-5	4	5	2	-3	-1	0
'MeadowSweet'	0	-4	3	-2	-2	-2	5	1		0	-2	2	-4	1	0	2	0		-3	-3	4	-4	2	-3	0	2		0	5	5	1	2	-1	-2	0
'Ash_Palm'	1	0	-4	-1	3	5	3	-3		0	-2	-5	1	2	5	0	-5		0	-2	-5	0	0	4	-1	-5		3	-2	-5	3	2	5	-1	-5
'Dark_Ochoa'	-5	-1	-5	5	-4	5	-5	-1		-5	4	2	5	3	5	-5	5		-4	1	-4	4	0	5	-2	-1		-2	4	1	2	3	5	-3	4
'Iron'	-5	0	3	-2	0	4	2	2		-5	-2	1	-3	1	5	4	1		-5	1	5	-1	2	5	0	2		-5	0	1	-2	-1	5	1	1
'Strawberry_Tea'	-5	2	-5	1	3	-3	-1	-2		-5	2	-3	4	5	-1	-4	2		-4	0	-5	5	-1	-3	-1	-2		-5	-2	-3	3	-1	-3	-2	4
'Arconis'	-4	2	4	3	3	-1	-4	3		-5	1	5	2	5	0	-2	3		-5	-1	0	2	-1	-3	-5	-2		-5	2	3	0	0	-4	-5	4
'Common_Sage'	3	0	2	5	-3	-3	-3	1		3	0	2	3	-2	0	-3	2		3	0	2	2	-1	-1	1	1		3	0	2	5	-1	-1	-5	1
'Cricklewood'	0	3	-2	5	2	-5	-5	2		2	3	1	5	-1	-4	-3	3		3	1	0	4	-1	-5	-4	3		0	0	0	5	-1	-5	-3	1
'Hokkaido'	3	1	1	-1	-4	-1	0	-5		1	1	1	-2	-4	-1	1	-4		3	2	-1	1	-3	0	1	-4		1	-1	-1	-3	-3	-2	3	-5
'Mini_Palmetto'	3	0	1	0	0	1	0	5		0	-1	-3	-4	-5	-3	-2	4		-2	1	0	0	-1	0	1	5		-3	2	-4	0	-3	0	-2	5
'Quartz'	-3	4	-1	-3	-5	-1	2	0		-3	4	-1	-3	-5	0	-1	-2		-4	5	0	-3	-5	-2	2	-1		0	5	1	0	-5	2	0	-2
'Orrorin'	-5	3	3	-1	3	2	-2	5		-3	3	1	1	1	-1	1	3		-5	4	1	-3	5	5	1	4		-4	1	-2	3	5	5	1	-4
'Windriver_Palm'	-3	-1	1	-4	3	-3	2	-5		0	1	2	-3	0	-1	2	-5		-4	-2	1	-2	0	-4	2	-5		-1	2	3	-1	5	-2	3	-4
'Aluminum'	0	2	-2	-3	-3	0	-2	-1		1	1	0	-1	-1	3	1	-1		-1	1	-3	-1	-4	0	1	-1		0	3	-1	-1	-3	-1	-2	-2
'Towering_Palm'	-2	-5	-4	1	-1	2	-3	1		-1	-4	-4	1	-4	1	-4	2		-1	-5	-5	0	-3	3	0	0		-2	-5	-5	-1	0	2	0	0
'Umbrella_Palm'	-2	0	2	-5	-3	-5	0	-1		-1	0	2	-5	-2	-5	1	-2		-2	0	4	-5	0	-5	-5	-1		2	0	4	-4	-4	-5	-2	-1

(Cont.) I've just found a set of essence values that agree with all Sumtet's experiments and correctly show the compounds that match Ktisisbios' requirements (table on left below). There's no guarantee that this is a unique solution but it does show that the model is sufficient to explain these 286 results. It sould be noted that the result for the aromatic content of Lapis is in contrast to the observations above which reflects Sumtet's comments.

(Cont.) Sumtet has added a further 13 results on his page which gives an extra 26 constraints. Using the values in the table on the left below, 17 out of 26 constraints are correctly matched. After refinement of the values it is possible to match all additional constraints using the table on the right below giving a score of 618/618 for all sumtet's results including predicting the matches to Ktisibios' requirements, i.e. everything is correctly matched.

Material	Ar		As	Bi	Sa	So	Sp	Sw	To	Material		Ar		As	Bi	Sa	So	Sp	Sw	To
'Fern_Palm'	-1		-2	-1	3	-1	0	-4	1	'Fern_Palm'		-1		-2	-1	3	-1	0	-4	1
'Folded_Birch'	1		2	-3	-5	-1	5	-1	-1	'Folded_Birch'		1		2	-3	-5	-1	5	-1	-1
'Giant_Cricklewood'	0		0	0	-5	1	-2	-3	0	'Giant_Cricklewood'		0		0	0	-5	1	-2	-3	0
'Stout_Palm'	-1		-4	-2	5	4	0	-5	0	'Stout_Palm'		-1		-4	-2	5	4	0	-5	0
'Hawthorn'	-4		5	2	-5	-1	1	0	0	'Hawthorn'		-4		5	2	-5	-1	1	0	0
'Royal_Palm'	4		1	-5	1	-2	0	0	1	'Royal_Palm'		4		1	-5	1	-3	-1	0	0
'Coconut_Palm'	-2		5	1	-1	0	3	0	-5	'Coconut_Palm'		-2		5	1	-1	0	3	0	-5
'Bramble_Hedge'	0		0	-5	4	-3	-2	0	0	'Bramble_Hedge'		0		0	-5	4	-2	-2	0	1
'Spindle_Tree'	5		-1	-4	-1	2	-2	-1	-5	'Spindle_Tree'		5		-1	-4	-1	2	-2	-1	-5
'Cinnar'	3		2	-5	0	3	5	-4	2	'Cinnar'		-1		2	-5	-1	2	4	-3	-1
'Butterleaf_Tree'	0		1	-5	5	-5	2	3	-3	'Butterleaf_Tree'		1		-1	-5	5	-5	1	2	-1
'Mini_Fern'	0		3	-4	1	1	-4	4	-1	'Mini_Fern'		2		3	-5	1	1	-4	0	-1
'Topaz'	2		4	2	-3	0	2	4	1	'Topaz'		-1		3	1	-4	-2	2	1	1
'Jade'	3		-2	3	-5	-5	2	1	4	'Jade'		3		-1	5	-4	-4	-2	3	3
'Lapis'	2		1	5	0	3	-5	2	1	'Lapis'		0		0	3	0	3	-5	2	2
'Spiked_Fishtree'	-3		0	-4	-4	-1	5	-2	3	'Spiked_Fishtree'		4		0	-2	-3	1	5	2	3
'Common_Basil'	0		-1	2	3	2	-1	-5	5	'Common_Basil'		1		-1	2	4	2	-3	-4	3
'Passam'	-1		3	-2	-2	-3	-1	1	3	'Passam'		-2		3	-1	-1	-3	0	-2	3
'Sapphire'	-4		1	-1	-2	0	-5	0	4	'Sapphire'		-5		0	-1	-3	-1	-4	-1	3
'Tapacae_Miralis'	-1		-1	-3	1	-1	1	4	3	'Tapacae_Miralis'		-1		-2	-5	0	-4	2	2	5
'Pale_Dhamasa'	5		0	0	4	-2	5	-5	1	'Pale_Dhamasa'		3		-1	0	5	-1	5	-3	1
'Marble_Dust'	5		-3	1	-5	5	5	1	1	'Marble_Dust'		4		-3	1	-5	5	5	-2	-1
'Bluebottle_Clover'	-5		-1	3	5	-4	-1	-3	-3	'Bluebottle_Clover'		-2		-1	3	5	0	0	-2	3
'Bottle_Tree'	1		-1	5	2	0	-2	-3	0	'Bottle_Tree'		2		0	5	1	1	-2	-2	-2
'Chakkanut_Tree'	1		-5	4	4	-2	-4	-3	-2	'Chakkanut_Tree'		3		-5	5	5	-1	-4	-1	-1
'MeadowSweet'	-1		-3	4	-5	4	-5	-1	0	'MeadowSweet'		-4		-4	2	-4	2	-1	-1	1
'Ash_Palm'	0		0	-5	1	0	5	0	-3	'Ash_Palm'		1		0	-3	2	5	5	0	-5
'Dark_Ochoa'	-4		-1	-4	4	1	5	-5	1	'Dark_Ochoa'		-5		0	-5	3	1	5	-4	-4
'Iron'	-5		-1	2	-3	-2	5	-1	0	'Iron'		-5		-3	2	-3	-1	5	-1	1
'Strawberry_Tea'	-5		-1	-5	4	1	-5	-3	2	'Strawberry_Tea'		-5		0	-5	4	3	-5	0	1
'Arconis'	-4		1	0	2	4	1	-5	2	'Arconis'		-2		-1	1	2	1	0	-3	1
'Common_Sage'	3		0	2	3	-2	-3	-5	5	'Common_Sage'		3		0	2	1	-3	-3	-5	5
'Cricklewood'	0		0	0	4	0	-5	-5	2	'Cricklewood'		4		0	-1	5	2	-5	-3	3
'Hokkaido'	4		2	2	1	-2	-1	2	-5	'Hokkaido'		1		2	1	-1	-3	0	0	-5
'Mini_Palmetto'	-2		-2	-3	-1	-1	-1	-3	5	'Mini_Palmetto'		-2		-3	-4	2	-4	0	-2	5
'Quartz'	-1		5	2	-2	-5	1	4	-1	'Quartz'		-1		5	3	-1	-4	2	4	-1
'Orrorin'	-2		5	2	0	4	5	0	2	'Orrorin'		-5		-1	-5	1	0	-1	0	1
'Windriver_Palm'	-2		1	3	0	3	-3	4	-5	'Windriver_Palm'		-4		1	3	-3	1	-2	2	-5
'Aluminum'	-3		0	-2	0	-3	-1	-1	-2	'Aluminum'		-1		-1	-1	-2	-4	0	-2	-1
'Towering_Palm'	0		-5	-5	-1	-2	2	-5	-1	'Towering_Palm'		-3		-5	-5	0	-3	1	-1	1
'Umbrella_Palm'	-1		-1	4	-5	-3	-3	-1	0	'Umbrella_Palm'		-1		1	3	-5	-1	-4	-2	-2

I did e few tests of my own but failed, hope thees can help you get them more fine tuned

'Quartz'	-1	5	3	-1	-4	2	4	-1
'Spiked_Fishtree'	4	0	-2	-3	1	5	2	3
'Windriver_Palm'	-4	1	3	-3	1	-2	2	-5
Lapis'	0	0	3	0	3	-5	2	2
'Towering_Palm'	-3	-5	-5	0	-3	1	-1	1
	-4	1	2	-7	-2	1	9	0

This one tested Elevated lvls of Sweet, correct. and Decresed of Sour, correct. but does not match (++) Sweet , (=) Toxic . This therory has come a long way, and with the Geb Compund now we can fine tune it by makeing correct compunds with Nutral stats, since nutral requires a exact value this will be trikcy but also very accurate. -- OnlyAloha

'Royal_Palm'	4	1	-5	1	-3	-1	0	0
'Spindle_Tree'	5	-1	-4	-1	2	-2	-1	-5
Chakkanut_Tree'	3	-5	5	5	-1	-4	-1	-1
'Cricklewood'	4	0	-1	5	2	-5	-3	3
Aluminum'	-1	-1	-1	-2	-4	0	-2	-1
	15	-6	-6	8	-4	-12	-7	-4

Elevated Aromatic, correct. Decreased Spicy, Correct. Not (+++)Aromatic , (---) Spicy.

'Chakkanut_Tree'	3	-5	5	5	-1	-4	-1	-1
'Common_Sage'	3	0	2	1	-3	-3	-5	5
'Cricklewood'	4	0	-1	5	2	-5	-3	3
'Spindle_Tree'	5	-1	-4	-1	2	-2	-1	-5
'Jade'	3	-1	5	-4	-4	-2	3	3
	18	-7	7	6	-4	-16	-7	5

Does not fit Aromatic (+++) Spicy (---) , Positeve id : Salty , what? . Negative id : Spicy , correct.