Here are some of KEY research components we used as our ingredient advisory board.
Below is the summary of the studies, with references.
Calcium-containing, sodium bicarbonate- based toothpaste formulations were shown by electron microscopy to smooth tooth enamel WITHOUT introducing new scratches. In contrast, commercial whitening toothpaste removed similar scratches but also created NEW ONES. 
Calcium-containing dentifrices were shown by electron microscopy and hardness measurements to put MINERAL onto the surface of enamel and to HARDEN IT. Conventional fluoride toothpaste did not. 
After 15 test cycles, using serial treatments with calcium- containing, bicarbonate toothpaste, surface roughness was REDUCED by more than 50% and peak height was reduced by two thirds. 
Secondary caries remain a problem limiting the longevity of those who have composite fillings. Calcium Phospate (NACP) had the highest enamel remineralization and it was significantly HIGHER than fluoride-releasing control group. It remineralized 4-FOLD that of a the fluoride-releasing control. 
Dental caries is a chronic infectious disease that results in the destruction of tooth tissue. It is caused by complex interaction of oral microorganisms in dental plaque, diet and a broad array of host factors that needs to be present for tooth decay to occur.
For interproximal plaque, the essential oil mouth rinse produced statistically significance reductions in total recoverable streptococci counts S. mutans counts of 69.9 % and 75.4%. [3a]
Exposure to a half-strength essential oil mouth rinse produced statistically significant reductions on all of the strains tested with percent reductions ranging from 85,74 % for S. gordonii to 99.77% for S. sobrinus when compared to the control study. [3b] The authors concluded that their study provided evidence that the essential oil mouthwash tested, significantly reduced the level of S. mutans, and demonstrated in situ bactericidal activity.
High abrasive pasts results in the greatest wear. Medium-abrasive pastes (1.76 um +/- .85um) and acidic fluoride gels (2.46 +/- .72 um) showed greater wear than with a low- abrasive paste (.84 +/- .38 um). Spot lesions should be brushed with oral hygiene products of low abrasivity.  Celtic Sea Salt is between 0.035 – 0.5 microns (um).
Both fluoride and the desensitizing agents alone reduced erosion, but no additive effect was found. Combinations of fluoride and KNO3 did not reduce erosion. Desensitizing substances in toothpastes, alone or in combination, can reduce erosion, but is not valid for all formulas. 
Dental products containing calcium carbonate work to provide effective relief of sensitive teeth. 
Samples of whole human enamel was analyzed by spark source mass spectrometer. HIGH strontium concentrations levels in teeth of low caries (cavity) individuals and LOW strontium concentrations were found in those who were high caries individuals. Strontium STIMULATES CALCIUM DEPOSITION IN BONES AND TEETH. Giving rats strontium in their diet increases the buildup of dentin in their teeth.
French Celtic Sea Salt has naturally occurring levels of strontium. It is 1.8% minerals and trace elements.
Out of 35 inorganic elements, strontium was the only element found to be present in significantly lower amount in carious teeth. 
Bleaching gels cause enamel erosion. Hydrogen peroxide caused the most significant enamel erosion. Hydrogen peroxide even with additives like calcium gluconate or fluoride still causes enamel erosion. Basically, it’s a bad idea to whiten your teeth with bleaching gels. 
Sensitivity is thought to be due to the hydrogen peroxide molecules passing through the enamel and dentin into the pulp and causing pulpal inflammation 
SLS can remove the pellicle and a smear layer present on dentin. 
Toothpaste formulations without SLS could be favorable in preventing erosion.