Verifiable AI infrastructure is being constructed on foundations that age unevenly. The dominant substrate for production-scale verifiable inference—trusted execution environments on Intel, AMD, and NVIDIA silicon—roots its attestation in classical elliptic-curve signatures whose private keys are fused into chips at manufacture. Those roots cannot be rotated in software; migrating them requires a hardware refresh cycle measured in years. A sufficiently large fault-tolerant quantum computer running Shor’s algorithm would render the signing keys of every deployed generation recoverable, turning archival attestation reports into retroactively forgeable artifacts. For ephemeral verification this is a manageable migration problem; for evidence that must outlive the hardware that produced it—regulatory records, model provenance, adjudicatory evidence, scientific reproducibility—the foundation is structurally fragile. We contrast this with mathematics-rooted verifiable computation: STARK-family proof systems whose soundness rests on a public, hash-dominated mathematical assumption stack and whose trust ages gracefully under the best known quantum attacks. This is a vision paper. We do not claim that STARK-based verification is production-ready for frontier-scale inference; it is not. We do claim that the aging behavior of a trust substrate is a first-class engineering property, that current investment patterns implicitly privilege substrates whose trust decays, and that the asymmetry of consequences argues for a deliberate hybrid trajectory. We contribute a trust-aging taxonomy, a retroactive-forgery threat model, a capability-vs-durability comparison, and a three-layer path forward: hybrid architectures, STARK-friendly ML research, and cryptographic agility in AI evidence regimes.