Topological descriptors of infrared spectra for the identification and monitoring of formulated polymer compounds

Formulated polymer compounds used in footwear soles are routinely identified from their infrared spectrum, but comparing spectra point by point presupposes that they are mutually aligned and share a common baseline. We build descriptors from the persistent homology of the spectrum. For a function sampled on a line the Vietoris–Rips construction of the literature collapses to an exact union-find computation of the degree-0 diagram of the superlevel-set filtration, in which every feature is one absorption band and its persistence is the topological prominence of that band. The classical persistence image is invariant under reparametrisation of the wavenumber axis and discards the band positions that carry the chemical information; we therefore introduce a position-aware variant over wavenumber and lifetime, the topological fingerprint image. On 39 industrial sole compounds it predicts the onset of thermal degradation – the quantity that bounds the moulding temperature – more accurately than the raw spectrum and than the standard chemometric pre-processing chains, and expressed as a processing decision with a distribution-free safety margin it returns a modest but certified gain in admissible moulding temperature over the polymer class alone. Controlled comparisons locate that advantage: it belongs to band prominence at a known wavenumber rather than to the topological construction, better understood as an exact, parameter-free route to the same quantity. No general robustness to acquisition artefacts is claimed, and we report the tasks that run the other way, among them identifying the material families, where conventional pre-processing is stronger.