TAM-Chain: Multi-Scale Thyroid Cytology Classification via Absorbing Markov Chains and Shannon Entropy Uncertainty Quantification for False-Negative Suppression and Domain-Shift Adaptation TAM-Chain, a multi-scale thyroid cytology classification framework combining Absorbing Markov Chain theory with Shannon Entropy-based uncertainty quantification, achieved a Macro F1 score of 0.9741 and an absolute False-Negative Rate of 0.00% on an internal test set of 235 cases, according to an arXiv paper (arXiv:2609.28590v1). On an independent external validation set of 1015 cases with severe domain shift, TAM-Chain maintained a Macro F1 of 0.7026 by adaptively adjusting its expected stopping step and triggering specialist referrals, outperforming single-magnification baselines. The framework models multi-magnification (10x, 20x, 40x) feature extraction as an absorbing stochastic process to support optimal stopping and human-in-the-loop referral for false-negative suppression. arXiv:2609.28590v1 Announce Type: new Abstract: Background & Problem: Thyroid Fine-Needle Aspiration Biopsy FNAB cytology based on the Bethesda System plays a pivotal role in early thyroid cancer detection; however, deep learning approaches face substantial challenges regarding high false-negative rates and overconfidence under clinical domain shift. Methods: In this study, we propose TAM-Chain, a multi-scale 10x, 20x, 40x thyroid cytology classification framework leveraging Absorbing Markov Chain theory combined with Shannon Entropy-based Uncertainty Quantification. The framework dynamically models multi-magnification feature extraction as an absorbing stochastic process, enabling optimal stopping criteria and a human-in-the-loop referral mechanism to strictly suppress critical diagnostic errors. Results: Extensive evaluation on an internal test set N = 235 demonstrates a Macro F1 score of 0.9741 with an absolute False-Negative Rate FNR of 0.00%. On an independent external validation set N = 1015 presenting severe domain shift, TAM-Chain maintains superior stability and classification performance Macro F1 = 0.7026 by adaptively adjusting the expected stopping step and triggering specialist referrals, significantly outperforming single-magnification baselines. Conclusion: The TAM-Chain framework proves to be a highly effective, safe, and adaptable solution for digital pathology workflows, successfully harmonizing automated diagnostic efficiency with stringent biological safety.