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Chemical systems are interpreted through the species they contain and thereactions they may undergo, i.e., their chemical reaction network (CRN). Inspite of their central importance to chemistry, the structure of CRNs continuesto be challenging to deduce from data. Although there exist structural lawsrelating species, reactions, conserved quantities and cycles, there has beenlimited attention to their measurable consequences. One such is the dimensionof the chemical data: the number of independent reactions, i.e. the number ofmeasured variables minus the number of constraints. In this paper we attempt torelate the experimentally observed dimension to the structure of the CRN. Inparticular, we investigate the effects of species that are concealed andreactions that are irreversible. For instance, irreversible reactions can haveproportional rates. The resulting reduction in degrees of freedom can becaptured by the \emph{co-production law} $\Upsilon = \ell_\bullet +\wedge_\bullet$ relating co-production relations $\Upsilon$ to emergentnon-integer conservation laws $\ell_\bullet$ and broken cycles$\wedge_\bullet$. This law resolves a recent conundrum posed by amachine-discovered candidate for a non-integer conservation law. We also obtainlaws that allow us to deduce network structure in cases where some speciescannot be discerned or distinguished by a given analytical technique. Thisenables us to relate portions of spectral data to portions of CRN structure,for instance isosbestic points relate to local conservation laws. We anticipatethat the reconstruction of CRN structure will thereby simplify and increasinglyresemble the type of logical puzzles encountered in molecular structuredetermination via spectroscopy.

On data and dimension in chemistry I -- irreversibility, concealment and emergent conservation laws