The thermoelectric literature encodes decades of hard-won design knowledge — which dopants raise the figure of merit ZT in which chemistries, which strategies suppress lattice thermal conductivity, and which material families fail and how — but that knowledge is locked in prose across tens of thousands of papers. We extract it at scale. From 10,158 open-access thermoelectric papers we build a structured knowledge graph (24,121 property measurements, 7,443 material modifications with typed dopant/strategy/effect fields, and 4,479 documented failure signals, at 0.97 extraction precision on a 300-paper audit), then mine it for four families of design rule: (1) dopant → ZT effects resolved by chemical system, (2) modification-strategy → property effects separating ZT enhancement from κ_lattice suppression, (3) synthesis-route → measured ZT associations, and (4) a failure-mode taxonomy — negative evidence that materials databases almost never capture. The mined rules recover canonical thermoelectric knowledge without being told it — La-doped SrTiO₃ [8], filled skutterudites (Co-Sb + Zr/Bi) [7], Se-substituted Bi₂Te₃, and band-convergence doping [6] all emerge from frequency alone — which both validates the extraction and turns the graph into a reusable design resource. Finally, we formalize the mined rules as scientific priors: provenance-backed, chemistry-specific evidence of known levers (modifications that repeatedly improved performance) and known pitfalls (documented failure modes), each carrying an evidence strength and an applicability scope. Encoded this way, the priors make candidate prioritization explainable — every recommendation can be justified in plain language from the literature evidence for its chemistry (e.g. "supported by 14 ZT-raising modifications across 49 papers, with no reported failure modes"), and the same evidence transfers to genuinely novel candidates through their chemical system. This converts a ranking pipeline into an explainable scientific-reasoning layer.