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The Detectability Gap: Hidden Heterogeneity in Hallucination Detection Across Language Models
Pranav Darshan, Pranav A, Sravan Karthick T, Minal Moharir, Ivan P. Yamshchikov
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 90%
Last extracted: 9/30/2026, 6:38:27 AM
Summary
This paper investigates the 'detectability gap' in hallucination detection for language models, revealing that aggregate performance metrics conceal systematic heterogeneity. By partitioning hallucinations into 'Ghost' (high answer agreement across seeds) and 'Flickering' (low agreement) regimes, the study demonstrates that Ghost hallucinations are significantly harder to detect than Flickering ones. This asymmetry persists even when using decoupled evaluation signals like lexical/semantic dispersion and diffusion trajectory features, proving it is not merely an artifact of circularity in agreement-based detection. The prevalence of these regimes is model-dependent, with some models producing mostly stable errors and others variable ones.
Entities (13)
Relation Signals (8)
Ghost Hallucination → definedby → High Answer Agreement
confidence 99% · Ghost hallucinations therefore contain a dominant repeated answer
Flickering Hallucination → definedby → Low Answer Agreement
confidence 99% · Flickering hallucinations are more dispersed across seeds
Ghost Hallucination → haslowerdetectabilitythan → Flickering Hallucination
confidence 98% · Ghost AUC ranges from 0.34 to 0.55, while Flickering AUC ranges from 0.80 to 0.96. The detectability gap is consistently large.
Detectability Gap → persistsunder → Lexical Dispersion
confidence 96% · The lexical gap is +0.13 to +0.29... Both signals favor Flickering in every model and dataset combination
Detectability Gap → persistsunder → Semantic Dispersion
confidence 96% · The semantic gap is +0.08 to +0.26... Both signals favor Flickering in every model and dataset combination
LLaDA 8B → hashighprevalenceof → Ghost Hallucination
confidence 95% · The proportion of Ghost hallucinations ranges from 65 to 77% for LLaDA
Dream 7B → haslowprevalenceof → Ghost Hallucination
confidence 95% · Dream has only 16 to 30% Ghost hallucinations
Detectability Gap → persistsunder → Diffusion Trajectories
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Abstract
Abstract:Sampling based consistency is widely used for hallucination detection, yet aggregate performance can conceal systematic differences in which errors are detectable. This work studies that heterogeneity across four language models and three factual question answering datasets. Partitioning hallucinations by answer agreement reveals high agreement (Ghost) and low agreement (Flickering) regimes with an apparent detectability gap of $0.35$ to $0.46$ AUC. Because the statistics used to define the regimes and measure this gap are strongly coupled ($|\rho|\approx0.94$ to $1.00$), the raw result is treated as a property of agreement based detection rather than independent evidence. After freezing regime assignments, lexical and semantic response dispersion preserve the asymmetry, with bootstrap $95\%$ intervals excluding zero in all $12$ model and dataset settings. A stricter test using individual diffusion trajectories and no cross seed information preserves the asymmetry across all three LLaDA datasets ($p<0.005$) and directionally across all three Dream datasets, with one reaching significance. The hard regime varies substantially in prevalence across models ($16\%$ to $77\%$), and matched prompts frequently change regimes between models. These findings show that aggregate detection metrics conceal persistent, model dependent heterogeneity in language model failures and motivate regime conditioned evaluation.
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- Source: https://arxiv.org/abs/2609.35860v1
- Canonical: https://arxiv.org/abs/2609.35860v1
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GlobalSouthAI @ NeurIPS 2026: Rethinking AI for and from the Global South The Detectability Gap: Hidden Heterogeneity in Hallucination Detection Across Language Models Pranav Darshan Affiliation: Department of Computer Science and Engineering, R.V. College of Engineering, India Email: pranavdarshan.cs22@rvce.edu.in Pranav A Affiliation: Department of Computer Science and Engineering, R.V. College of Engineering, India Email: pranava.cs21@rvce.edu.in Sravan Karthick T Affiliation: Department of Computer Science and Engineering, R.V. College of Engineering, India Email: sravankt.cs20@rvce.edu.in Minal Moharir Affiliation: Department of Computer Science and Engineering, R.V. College of Engineering, India Email: minalmoharir@rvce.edu.in Ivan P. Yamshchikov Affiliation: CAIRO, Technical University of Applied Sciences Würzburg-Schweinfurt, Germany Email: ivan.yamshchikov@thws.de Abstract Sampling based consistency is widely used for hallucination detection, yet aggregate performance can conceal systematic differences in which errors are detectable. This work studies that heterogeneity across four language models and three factual question answering datasets. Partitioning hallucinations by answer agreement reveals high agreement (Ghost) and low agreement (Flickering) regimes with an apparent detectability gap of 0.350.35 to 0.460.46 AUC. Because the statistics used to define the regimes and measure this gap are strongly coupled (|ρ|≈0.94|ρ|≈ 0.94 to 1.001.00), the raw result is treated as a property of agreement based detection rather than independent evidence. After freezing regime assignments, lexical and semantic response dispersion preserve the asymmetry, with bootstrap 95%95\% intervals excluding zero in all 1212 model and dataset settings. A stricter test using individual diffusion trajectories and no cross seed information preserves the asymmetry across all three LLaDA datasets (p<0.005p<0.005) and directionally across all three Dream datasets, with one reaching significance. The hard regime varies substantially in prevalence across models (16%16\% to 77%77\%), and matched prompts frequently change regimes between models. These findings show that aggregate detection metrics conceal persistent, model dependent heterogeneity in language model failures and motivate regime conditioned evaluation. 1 Introduction Hallucination detectors often use stochastic consistency: sample a model several times and flag answers that fail to reproduce (Manakul et al., 2023; Wang et al., 2023; Farquhar et al., 2024; Zhang et al., 2023). A related line of work detects hallucinations from the denoising trace of diffusion language models directly (Chang et al., 2025; Hemmat et al., 2026; Qian et al., 2026). These works establish that consistency signals can miss confidently repeated errors and that diffusion trajectories carry detection relevant information; the present study is complementary; it shows that such errors form a distinct, model dependent behavioral population whose detectability is quantitatively lower for both a cross seed agreement signal and a within seed trajectory signal, and it measures how large that gap is and how it survives several independent operationalizations. Aggregate scores can conceal systematic differences in which errors are detectable. We examine whether stochastic generations reveal distinct hallucination populations, and whether their detectability differs when evaluation is separated from the information defining those populations. Our motivation is to support the development and deployment of trustworthy and reliable AI systems globally. Uneven infrastructure, skills, and governance capacity can amplify AI risks (UNDP, 2025). Where independent verification is difficult, confidently repeated errors may invite misplaced trust. The goal is to inform affordable, effective safeguards that flag hallucinations before users rely on them. Rather than assuming uniformly higher trust or lower AI literacy across these diverse communities, we study a technical obstacle: errors that evade otherwise useful detection signals. We evaluate four instruction tuned diffusion and autoregressive models on TriviaQA, HotpotQA, and PopQA. Generations differ only in sampling seed. Hallucinations are grouped into high agreement (Ghost) and low agreement (Flickering) regimes. The primary contributions are: 1. We expose persistent detectability differences between Ghost and Flickering hallucinations, motivating regime specific evaluation rather than aggregate scores alone. 2. We examine the circularity of raw agreement and test the asymmetry with two decoupled response level measures across all 1212 settings, then with individual diffusion trajectories without cross seed information. 3. We show that regime prevalence and the regime assigned to the same prompt depend on the model. 2 Experimental Setup Models and datasets. The study evaluates four instruction tuned language models: two masked diffusion models, LLaDA 8B (Nie et al., 2025) and Dream 7B (Ye et al., 2025), and two autoregressive models, Qwen2.5 7B (Team, 2025) and Llama 3.1 8B (Grattafiori et al., 2024). Evaluation is conducted on three open domain factual question answering datasets: TriviaQA (Joshi et al., 2017), HotpotQA (Yang et al., 2018), and PopQA (Mallen et al., 2023). For each prompt, K=3K=3 generations are sampled with different random seeds while all other decoding conditions are held fixed. The autoregressive models provide agreement level controls, while only the diffusion models are used for the trajectory analysis. Correctness and hallucination labels. A generation is considered correct when its answer contains a gold alias. A prompt is labeled as a hallucination (Y=1Y=1) when none of its sampled generations contains the gold answer. Alias matching is performed at the token level for the diffusion corpora and using a case insensitive substring match for the autoregressive corpora. Gold answers are used only for labeling and evaluation, never as input to a detection signal. Behavioral regimes. For each generation, a gold free answer span is extracted and compared across seeds using token level Jaccard similarity at threshold τ. Let A1,…,AKA_1,…,A_K denote the answer spans and let τC_τ denote the resulting single linkage clusters. The plurality fraction is defined as θ^K=1Kmaxc∈τ|c|. θ_K= 1K _c _τ|c|. (1) Among hallucinated prompts, two operational behavioral regimes are defined: Ghost:θ^K>12,Flickering:θ^K≤12.Ghost: θ_K> 12, : θ_K≤ 12. (2) Ghost hallucinations therefore contain a dominant repeated answer, whereas Flickering hallucinations are more dispersed across seeds. Table 1 illustrates the distinction. These are operational behavioral partitions and do not imply distinct latent mechanisms. Type Question Three sampled answers Gold Ghost What sport does Masahito Noto play? baseball / baseball / baseball football Flickering Who composed “The Mission”? various / James Horner / The Doors Ennio Morricone Table 1: Ghost hallucinations repeat incorrect answers; Flickering hallucinations produce different incorrect answers. No sampled answer contains the gold answer. Evaluation signals. For a signal s, detectability within regime R is measured by the AUC separating hallucinations in R from correct answers. The detectability gap is Δ(s)=AUCFlickering(s)−AUCGhost(s). (s)=AUC_Flickering(s)-AUC_Ghost(s). (3) The raw agreement analysis uses pairwise disagreement across sampled answers. Because this statistic is closely coupled to the plurality fraction that defines the regimes, it is treated as descriptive. The main analysis instead freezes the regime assignments and evaluates lexical and semantic response dispersion that do not reuse the regime defining computation. Bootstrap 95%95\% confidence intervals are computed at the prompt level using B=2000B=2000 resamples. A separate diffusion only analysis uses denoising trajectory features from individual seeds without information across seeds. 3 The Detectability Gap and Its Circularity Agreement based detectability. The raw disagreement signal 1−π^1- π separates hallucinations from correct answers much more effectively in the Flickering regime than in the Ghost regime. Across the evaluated model and dataset combinations, Ghost AUC ranges from 0.340.34 to 0.550.55, while Flickering AUC ranges from 0.800.80 to 0.960.96. The resulting detectability gap is consistently large, ranging from 0.350.35 to 0.460.46 AUC, with all bootstrap 95%95\% confidence intervals excluding zero. Thus, an aggregate agreement signal can appear effective while performing poorly on a substantial population of hallucinations. The role of circularity. The raw gap cannot be interpreted as independent evidence of heterogeneous detectability because the same answer agreement structure defines the regimes and constructs the disagreement signal. Ghost hallucinations are defined by large θ θ, while the evaluated signal is its agreement based complement, 1−π^1- π. Their correlation ranges from −0.94-0.94 to −1.00-1.00 across settings. The raw agreement result is therefore treated as descriptive. The stronger test freezes the Ghost and Flickering assignments and changes the evaluation signal so that it does not reuse answer span clustering, plurality, or the agreement threshold. 4 Detectability Heterogeneity Beyond Agreement The central test freezes the Ghost and Flickering assignments and replaces the agreement signal with measurements that do not reuse the regime defining computation. 000.10.10.20.20.30.30.40.4LLaDA TLLaDA HLLaDA PDream TDream HDream PQwen TQwen HQwen PLlama TLlama HLlama P00Decoupled gap Δ (Flickering minus Ghost AUC)Lexical dispersionSemantic dispersion Figure 1: Decoupled gap Δ , defined as Flickering AUC minus Ghost AUC. Bootstrap 95%95\% confidence intervals are shown for lexical and semantic dispersion. All twelve model and dataset settings have positive gaps. Decoupled evaluation. Two response level measures are considered. Lexical dispersion is the mean pairwise 1−1-Jaccard over content words in the whole responses. It does not use the answer span heuristic, cluster sizes, plurality fraction, or agreement threshold. Semantic dispersion is the mean pairwise cosine distance between all MiniLM L6 v2 embeddings of the whole responses (Reimers and Gurevych, 2019). Although both measures capture variation across stochastic generations, neither reuses the computation that defines the regimes. The lexical gap is +0.13+0.13 to +0.29+0.29 and the semantic gap is +0.08+0.08 to +0.26+0.26. Both signals favor Flickering in every model and dataset combination, and all bootstrap 95%95\% confidence intervals exclude zero. Figure 1 summarizes the result. The asymmetry is smaller than the raw agreement gap, but its direction does not change when the evaluation signal is changed. 5 Within Seed Evidence The response level analysis shows that the detectability gap survives measurements separated from the regime definition. Diffusion models provide a stricter test because each generation exposes a denoising trajectory. The trajectory signal therefore uses information from a single seed without access to the other sampled seeds. Trajectory only evaluation. The trajectory features capture when answer tokens become committed, confidence before commitment, and confidence change at commitment. No information about the other seeds, answer agreement, clustering, or plurality is provided to the detector. A leakage free out of fold logistic detector separates hallucinations from correct answers, after which predictions are evaluated separately for the frozen Ghost and Flickering groups. On LLaDA, the trajectory only gap is positive on all three datasets, with Δ=0.106 =0.106, 0.1230.123, and 0.0920.092 on TriviaQA, HotpotQA, and PopQA, respectively. All three permutation tests reach p<0.005p<0.005. Dream shows the same direction on all three datasets, with gaps of 0.0350.035, 0.0720.072, and 0.1630.163, although only PopQA reaches significance (p=0.003p=0.003). Complete results and confidence intervals are reported in Table 12. Importantly, Ghost AUC rises to 0.600.60 to 0.790.79 under trajectory information. Ghost hallucinations are therefore not inherently undetectable. They remain harder to detect than Flickering hallucinations even when information across seeds is removed from the signal. 6 Model Dependence of the Hard Regime The detectability asymmetry is consistent across models, but the composition of the hallucination population is not. The proportion of Ghost hallucinations ranges from 6565 to 77%77\% for LLaDA, 5959 to 77%77\% for Qwen, and 6262 to 67%67\% for Llama, while Dream has only 1616 to 30%30\% Ghost hallucinations. Thus, the model with the smallest hard regime still exhibits the same positive decoupled detectability gaps. The dependence on the model is also visible when the same prompts are evaluated by different models. Among 347347 prompts hallucinated by both LLaDA and Dream, 181181 move from Ghost under LLaDA to Flickering under Dream, whereas only 1717 make the reverse transition. A McNemar test gives p<10−35p<10^-35. Only 6767 Ghost cases remain Ghost under both models. These transitions show that, within this matched comparison, regime membership is not determined solely by the question. The generation model itself plays an important role in determining whether a hallucination is stable or variable across seeds. 7 Conclusion These results show that hallucination detectability is heterogeneous across behavioral regimes and that regime membership itself depends on the generation model. The raw agreement gap is strongly coupled to the regime definition, but the asymmetry persists under lexical and semantic response level measurements that do not reuse that computation. A stricter trajectory only analysis also preserves the asymmetry for LLaDA and shows the same direction across all three Dream datasets. For accessible safeguards in the Global South and other resource constrained settings, detection must address consistently wrong answers, not only variable ones. Regime specific evaluation and trajectory based warnings are steps toward this goal, rather than guarantees of safe use. Deployment affordability and performance on locally relevant languages and tasks remain to be evaluated. References Chang et al. (2025) S. Chang, J. Yu, W. Wang, Y. Chen, J. Yu, P. Torr, and J. Gu TraceDet: hallucination detection from the decoding trace of diffusion large language models. arXiv preprint arXiv:2510.01274. Cited by: §1. Farquhar et al. (2024) S. Farquhar, J. Kossen, L. Kuhn, and Y. Gal Detecting hallucinations in large language models using semantic entropy. Nature 630, p. 625–630. External Links: Document Cited by: Appendix E, §1. Grattafiori et al. (2024) A. Grattafiori, A. Dubey, A. Jauhri, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783. External Links: Link Cited by: §2. Hemmat et al. (2026) A. Hemmat, P. Torr, Y. Chen, and J. Yu TDGNet: hallucination detection in diffusion language models via temporal dynamic graphs. arXiv preprint arXiv:2602.08048. Cited by: §1. Joshi et al. (2017) M. Joshi, E. Choi, D. S. Weld, and L. Zettlemoyer TriviaQA: a large scale distantly supervised challenge dataset for reading comprehension. In Proceedings of the 55th Annual Meeting of the Association for Computational Linguistics (ACL), p. 1601–1611. External Links: Document Cited by: §2. Mallen et al. (2023) A. Mallen, A. Asai, V. Zhong, R. Das, D. Khashabi, and H. Hajishirzi When not to trust language models: investigating the effectiveness of parametric and non parametric memories. In Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (ACL), p. 9802–9822. External Links: Document Cited by: §2. Manakul et al. (2023) P. Manakul, A. Liusie, and M. J. F. Gales SelfCheckGPT: zero resource black box hallucination detection for generative large language models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP), External Links: Link Cited by: §1. Nie et al. (2025) S. Nie, F. Zhu, Z. You, X. Zhang, J. Ou, J. Hu, J. Zhou, Y. Lin, J. R. Wen, and C. Li Large language diffusion models. In Proceedings of the 42nd International Conference on Machine Learning (ICML), External Links: Link Cited by: §2. Qian et al. (2026) Y. Qian, Y. Tan, Y. Liu, W. Yu, and S. Pan DynHD: hallucination detection for diffusion large language models via denoising dynamics deviation learning. arXiv preprint arXiv:2603.16459. Cited by: §1. Reimers and Gurevych (2019) N. Reimers and I. Gurevych Sentence BERT: sentence embeddings using siamese BERT networks. In Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing (EMNLP), p. 3982–3992. External Links: Link Cited by: §4. Team (2025) Q. Team Qwen2.5 technical report. arXiv preprint arXiv:2412.15115. External Links: Link Cited by: §2. UNDP (2025) UNDP The next great divergence: why AI may widen inequality between countries. Technical report United Nations Development Programme. External Links: Link Cited by: §1. Wang et al. (2023) X. Wang, J. Wei, D. Schuurmans, Q. Le, E. Chi, S. Narang, A. Chowdhery, and D. Zhou Self consistency improves chain of thought reasoning in language models. In International Conference on Learning Representations (ICLR), External Links: Link Cited by: §1. Yang et al. (2018) Z. Yang, P. Qi, S. Zhang, Y. Bengio, W. W. Cohen, R. Salakhutdinov, and C. D. Manning HotpotQA: a dataset for diverse, explainable multi hop question answering. In Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing (EMNLP), p. 2369–2380. External Links: Document Cited by: §2. Ye et al. (2025) J. Ye, Z. Xie, L. Zheng, J. Gao, Z. Wu, X. Jiang, Z. Li, and L. Kong Dream 7b: diffusion large language models. arXiv preprint arXiv:2508.15487. Cited by: §2. Zhang et al. (2023) J. Zhang, Z. Li, K. Das, B. A. Malin, and S. Kumar SAC3: reliable hallucination detection in black box language models via semantic aware cross check consistency. In Findings of the Association for Computational Linguistics: EMNLP 2023, External Links: Link Cited by: §1. Appendix A Experimental Setup and Reproducibility The evaluation covers four instruction tuned models and three open domain factual question answering datasets. Table 2 gives the prompt counts used for each model and dataset. The main analysis uses K=3K=3 seeds per prompt, with all decoding parameters fixed while only the sampling seed varies. Model Corpus Triv. Hot. Pop. LLaDA scaled 1000 800 1050 Dream dream 200 200 200 Qwen2.5 7B AR 400 400 400 Llama 3.1 8B AR 800 800 800 Table 2: Prompt counts per model and dataset. Each prompt uses K=3K=3 seeds in the main analysis. Autoregressive generations use temperature 0.80.8, nucleus probability p=0.95p=0.95, and seeds 42,123,456\42,123,456\. Diffusion generations use the models’ standard denoising samplers over 128128 steps. The diffusion scripts do not expose a scalar sampling temperature, so no temperature is reported for LLaDA or Dream. The answer span is extracted with a gold free first sentence heuristic. The token level Jaccard threshold is τ=0.5τ=0.5 unless otherwise stated. A generation is correct when its answer contains a gold alias. A prompt is hallucinated when none of its sampled generations contains a gold alias. Gold information is used only for labels and scoring, never as an input feature. Learned detectors use five fold out of fold cross validation with standardization local to each fold and ten shuffles. Fixed scalar signals are evaluated directly on their prompt level scores. Bootstrap confidence intervals use B=2000B=2000 prompt level resamples. Permutation tests use B=2000B=2000 shuffles. The high depth LLaDA corpus contains 5050 prompts and 1818 seeds per dataset, for 150150 prompts in total. It is used only for robustness over seed depth. Appendix B Confidence and Aggregate Agreement Mean denoising confidence provides little separation between correct and wrong answers on LLaDA. Table 3 reports the complete confidence baseline. Conf. Conf. Conf. % high Dataset correct wrong ECE error AUC wrong TriviaQA 0.951 0.950 0.52 0.502 56.4 HotpotQA 0.955 0.959 0.72 0.502 76.7 PopQA 0.964 0.965 0.64 0.497 67.5 Table 3: LLaDA confidence baseline. Mean confidence is similar for correct and wrong answers, while confidence to error AUC remains near chance. Agreement across seeds is more informative. Hallucinated prompts disagree more than correct prompts on all three datasets, with Mann Whitney p<10−6p<10^-6. As a single scalar feature, disagreement gives AUC 0.610.61, 0.610.61, and 0.660.66 on TriviaQA, HotpotQA, and PopQA respectively (Table 4). Disag. Disag. First Dataset hall. correct AUC sent. AUC TriviaQA 0.41 0.24 0.61 0.71 HotpotQA 0.51 0.34 0.61 0.64 PopQA 0.59 0.34 0.66 0.73 Table 4: Aggregate agreement across seeds on LLaDA. The first sentence variant uses content word disagreement in the first sentence. Appendix C Full Agreement Results and Circularity Table 5 reports the complete raw agreement result for all twelve model and dataset settings. Model Dataset N hall.% Ghost% Ghost AUC Flick. AUC Gap [95% CI] LLaDA TriviaQA 1000 50.0 77.4 0.506 0.963 0.457[0.429,0.485]0.457\,[0.429,0.485] LLaDA HotpotQA 800 72.2 69.9 0.479 0.900 0.422[0.390,0.458]0.422\,[0.390,0.458] LLaDA PopQA 1050 61.9 65.1 0.521 0.917 0.396[0.365,0.425]0.396\,[0.365,0.425] Dream TriviaQA 200 49.5 30.3 0.511 0.881 0.370[0.302,0.441]0.370\,[0.302,0.441] Dream HotpotQA 200 75.5 28.5 0.340 0.796 0.455[0.388,0.519]0.455\,[0.388,0.519] Dream PopQA 200 61.0 16.4 0.443 0.795 0.352[0.279,0.425]0.352\,[0.279,0.425] Qwen TriviaQA 400 36.8 76.9 0.515 0.948 0.432[0.382,0.485]0.432\,[0.382,0.485] Qwen HotpotQA 400 63.2 59.7 0.478 0.899 0.421[0.375,0.468]0.421\,[0.375,0.468] Qwen PopQA 400 54.0 58.8 0.538 0.905 0.367[0.322,0.413]0.367\,[0.322,0.413] Llama TriviaQA 800 29.1 66.5 0.546 0.927 0.381[0.344,0.418]0.381\,[0.344,0.418] Llama HotpotQA 800 71.0 62.5 0.403 0.837 0.434[0.405,0.463]0.434\,[0.405,0.463] Llama PopQA 800 49.6 65.0 0.549 0.905 0.356[0.327,0.387]0.356\,[0.327,0.387] Table 5: Raw agreement gap under disagreement score 1−π^1- π. Bootstrap confidence intervals use B=2000B=2000 prompt level resamples. The raw Ghost AUC ranges from 0.340.34 to 0.550.55, while Flickering AUC ranges from 0.800.80 to 0.960.96. The raw gap ranges from 0.350.35 to 0.460.46 and every gap confidence interval excludes zero. The result is partly mechanical because the disagreement signal is closely related to the statistic used to define the regimes. Table 6 reports the correlation between plurality and disagreement. Model Dataset ρ(θ^,1−π^)ρ( θ,1- π) LLaDA TriviaQA −0.996-0.996 LLaDA HotpotQA −0.991-0.991 LLaDA PopQA −0.998-0.998 Dream TriviaQA −1.000-1.000 Dream HotpotQA −0.939-0.939 Dream PopQA −0.985-0.985 Qwen TriviaQA −0.998-0.998 Qwen HotpotQA −0.993-0.993 Qwen PopQA −0.998-0.998 Llama TriviaQA −0.995-0.995 Llama HotpotQA −0.990-0.990 Llama PopQA −0.997-0.997 Table 6: Mechanical coupling between plurality and disagreement. The raw agreement gap is therefore treated as descriptive rather than as independent evidence. Appendix D Decoupled Response Level Controls The Ghost and Flickering assignments are fixed using the plurality fraction. Two response level measurements are then evaluated without reusing the answer span, clustering procedure, plurality statistic, or Jaccard threshold. Lexical dispersion is the mean pairwise 11 minus Jaccard distance over content words in the full responses. Semantic dispersion is the mean pairwise cosine distance between normalized all MiniLM L6 v2 embeddings of the full responses. Raw agreement Lexical dispersion Semantic dispersion Model Dataset G F Δ G F Δ G F Δ LLaDA TriviaQA .506 .963 .457 .643 .770 .126 .690 .831 .142 LLaDA HotpotQA .479 .900 .422 .605 .824 .219 .642 .814 .172 LLaDA PopQA .521 .917 .396 .746 .880 .134 .809 .891 .083 Dream TriviaQA .511 .881 .370 .605 .835 .230 .618 .732 .115 Dream HotpotQA .340 .796 .455 .547 .789 .242 .534 .724 .190 Dream PopQA .443 .795 .352 .598 .849 .251 .669 .825 .156 Qwen TriviaQA .515 .948 .432 .614 .853 .238 .627 .888 .261 Qwen HotpotQA .478 .899 .421 .574 .760 .186 .612 .810 .198 Qwen PopQA .538 .905 .367 .635 .862 .228 .690 .833 .144 Llama TriviaQA .546 .927 .381 .593 .880 .287 .628 .813 .184 Llama HotpotQA .403 .837 .434 .461 .689 .228 .539 .627 .088 Llama PopQA .549 .905 .356 .628 .809 .181 .641 .760 .119 Table 7: Detectability gap for frozen Ghost and Flickering regimes. G and F denote Ghost and Flickering AUC. All twelve lexical and all twelve semantic confidence intervals exclude zero. The lexical gap is positive in all twelve settings, ranging from 0.130.13 to 0.290.29. The semantic gap is also positive in all twelve settings, ranging from 0.080.08 to 0.260.26. The asymmetry is smaller than the raw agreement gap, but remains positive after the mechanically coupled component is removed. Appendix E Entailment Based Regime Robustness The Ghost and Flickering partition uses a gold free answer span with token level Jaccard clustering, which is a lexical proxy for whether two samples express the same answer. A stricter and widely used criterion instead clusters samples by bidirectional entailment, so that two answers are grouped only when each entails the other [Farquhar et al., 2024]. This appendix recomputes the regimes under that criterion and checks whether the decoupled detectability gap survives. For each hallucinated prompt, the first sentence of every seed response is taken as the answer, and two seeds share a cluster when a natural language inference model assigns entailment in both directions. The model is the public nli-deberta-v3-base cross encoder, and clustering is single linkage. The plurality fraction and the Ghost cut at one half are unchanged. The decoupled lexical and semantic dispersion signals are then scored against the frozen entailment regimes exactly as in Appendix D; under the token level plurality partition these columns reproduce Table 7. Reassign. Ghost % Lexical Δ Semantic Δ Model Dataset % plur. ent. plur. ent. plur. ent. LLaDA TriviaQA 38.4 77.4 43.8 .126 .164 .142 .223 LLaDA HotpotQA 29.9 69.9 43.4 .219 .187 .172 .171 LLaDA PopQA 47.2 65.1 19.7 .134 .163 .083 .170 Dream TriviaQA 26.3 30.3 20.2 .230 .192 .115 .165 Dream HotpotQA 22.5 28.5 11.3 .242 .321 .190 .390 Dream PopQA 14.8 16.4 6.6 .251 .322 .156 .085 Qwen TriviaQA 42.2 76.9 41.5 .238 .166 .261 .158 Qwen HotpotQA 32.8 59.7 30.0 .186 .193 .198 .233 Qwen PopQA 40.7 58.8 22.7 .228 .246 .144 .204 Llama TriviaQA 45.1 66.5 41.2 .287 .242 .184 .288 Llama HotpotQA 47.4 62.5 37.0 .228 .212 .088 .276 Llama PopQA 39.3 65.0 56.4 .181 .243 .119 .230 Table 8: Regime robustness under bidirectional entailment clustering. Ghost % is the share of hallucinations assigned to Ghost under the token level plurality criterion (plur.) and the entailment criterion (ent.). Lexical and semantic Δ are the decoupled Flickering minus Ghost AUC gaps under each partition. The entailment criterion reassigns a large fraction of prompts and lowers Ghost prevalence, yet both decoupled gaps remain positive in all twelve settings. The entailment criterion is stricter than token clustering and reassigns 1515 to 47%47\% of hallucinated prompts, which lowers the Ghost prevalence in every setting (Table 8). Despite this large change in the partition, the decoupled lexical gap remains positive in all twelve settings and the semantic gap remains positive in all twelve settings. The cross model ordering of Ghost prevalence is preserved. The detectability asymmetry therefore does not depend on the token level equivalence rule, although the prevalence magnitude does. Appendix F Disjoint Generation Control The response level controls freeze the regimes and change the measurement, but the regime assignment and the dispersion score are computed from the same sampled responses. This appendix removes that shared dependence by assigning the regime from one set of generations and scoring detectability on a disjoint set. The high depth LLaDA corpus provides eighteen seeds per prompt, which supports this split. For each of fifty random partitions the eighteen seeds are divided into an assignment half and a scoring half of nine seeds each. The hallucination label and the Ghost or Flickering assignment use only the assignment half, while the lexical and semantic dispersion signals use only the scoring half. The two halves never share a generation. Table 9 reports the mean gap and the fraction of splits with a positive gap. Lexical Δ Semantic Δ Dataset mean % >0>0 mean % >0>0 TriviaQA 0.306 100 0.288 100 HotpotQA 0.135 100 0.078 100 PopQA 0.065 96 0.019 76 Table 9: Disjoint generation control on the high depth LLaDA corpus (5050 prompts, 1818 seeds), averaged over 5050 random nine by nine seed splits. Regime assignment uses one half of the seeds and the dispersion score uses the disjoint other half. Under this stricter separation the decoupled gap remains clearly positive on TriviaQA and HotpotQA, where both the lexical and semantic gaps are positive in every split. On PopQA the gap is weak: the lexical gap is small and the semantic gap is close to zero, positive in 76%76\% of splits. The asymmetry therefore persists when assignment and scoring use disjoint generations on two of the three datasets, while PopQA, which already has the smallest response level gap, is not robust to this separation at this sample size. Only the high depth LLaDA corpus supports this analysis, so it is not available for the other models. Taken together, the raw agreement gap (Table 5), the decoupled lexical and semantic dispersion gaps (Table 7), the entailment based recomputation of the regimes (Table 8), and the disjoint generation split (Table 9) are four independent operationalizations of answer agreement, spanning three different ways of deciding when two sampled answers count as the same response: token level span clustering, bidirectional entailment, and a split that never lets the same generation contribute to both the regime label and the detectability score. The gap is positive under every one of them, so it is not an artifact of any single choice of how Ghost and Flickering are defined. Appendix G Robustness Over Seed Depth The high depth LLaDA corpus contains 5050 prompts and 1818 seeds per dataset. The plurality estimate from three seeds averaged over many subsets tracks the eighteen seed estimate closely, with Spearman correlation approximately 0.9990.999 and mean absolute error approximately 0.0090.009. A single draw of three seeds is noisier, with mean absolute error approximately 0.140.14 (Table 10). Analysis Result Interpretation Three seed average vs. eighteen seeds ρ≈.999ρ≈.999 closely aligned Three seed average vs. eighteen seeds MAE ≈.009≈.009 low average error Single three seed draw vs. eighteen seeds MAE ≈.14≈.14 individual draws are noisy Regime agreement ≈79%≈ 79\% most labels remain stable HotpotQA gap, K=3K=3 to 1818 0.2440.244 to 0.2500.250 gap remains positive Table 10: Seed depth robustness on the high depth LLaDA corpus. Recomputing the Ghost and Flickering labels from eighteen seeds rather than three seeds agrees on approximately 79%79\% of hallucinated prompts. The raw agreement gap remains positive on all three datasets. On HotpotQA the gap changes from approximately 0.2440.244 at three seeds to 0.2500.250 at eighteen seeds. Holding the eighteen seed partition fixed and recomputing the signal from K∈3,6,9,12,18K∈\3,6,9,12,18\ subsets produces a roughly constant gap. This analysis does not establish that three seeds are universally sufficient. Appendix H Threshold Sensitivity The token level Jaccard threshold is swept over τ∈0.34,0.5,0.67,1.0τ∈\0.34,0.5,0.67,1.0\ while the Ghost cut remains fixed at θ^>12 θ> 12 (Table 11). Dataset τ=.34τ=.34 τ=.50τ=.50 τ=.67τ=.67 τ=1.0τ=1.0 TriviaQA .456 .457 .452 .452 HotpotQA .422 .422 .428 .428 PopQA .396 .396 .398 .398 Table 11: Raw agreement gap under alternative token level Jaccard thresholds on LLaDA. The raw gap changes by less than 0.0060.006 within each dataset. The lexical decoupled gap changes by at most approximately 0.050.05 per setting. Examples of the lexical gap ranges are [0.211,0.219][0.211,0.219] for LLaDA on HotpotQA, [0.265,0.287][0.265,0.287] for Llama on TriviaQA, and [0.207,0.228][0.207,0.228] for Qwen on PopQA. The qualitative conclusion does not depend on the selected threshold. Appendix I Strict Control Using Diffusion Trajectories The trajectory analysis provides a stronger independence check because it uses no information across seeds. For each answer token, the analysis records normalized commit timing, the fraction of low confidence before commit, maximum and mean confidence before commit, confidence at commit, a one step confidence jump, and a short confidence ramp. These quantities are summarized into a 2121 dimensional prompt level vector. Agreement, plurality, answer span clustering, and all other cross seed consistency features are excluded. Trajectory features are available for 8383 to 98%98\% of prompts depending on dataset. Prompts without a resolvable trajectory are excluded before cross validation. A single ℓ2 _2 logistic detector is trained using repeated five fold out of fold cross validation. The resulting scores are evaluated separately on frozen Ghost and Flickering groups. Model Dataset Ghost Flick. Δ [95% CI] p LLaDA TriviaQA .631 .737 .106[.033,.178].106\,[.033,.178] .003 LLaDA HotpotQA .598 .721 .123[.076,.170].123\,[.076,.170] <.001<.001 LLaDA PopQA .794 .886 .092[.060,.123].092\,[.060,.123] <.001<.001 Dream TriviaQA .602 .637 .035[−.081,.153].035\,[-.081,.153] .60 Dream HotpotQA .626 .699 .072[−.039,.185].072\,[-.039,.185] .18 Dream PopQA .645 .808 .163[.035,.291].163\,[.035,.291] .003 Table 12: Trajectory only control. The detector uses dynamics within a single seed and no information across seeds. On LLaDA the gap is positive on all three datasets, with confidence intervals excluding zero and permutation p<0.005p<0.005. On Dream the gap is positive on all three datasets but reaches significance only on PopQA. Ghost AUC is above chance under trajectory information, ranging from 0.600.60 to 0.790.79. The result therefore does not indicate that Ghost hallucinations are impossible to detect. It indicates that they remain harder to detect than Flickering hallucinations. Appendix J Model Dependent Regime Prevalence The proportion of hallucinations assigned to Ghost varies substantially across models (Table 13). Model Architecture Ghost share of hallucinations LLaDA diffusion 6565 to 7777 Dream diffusion 1616 to 3030 Qwen2.5 7B autoregressive 5959 to 7777 Llama 3.1 8B autoregressive 6262 to 6767 Table 13: Ghost prevalence across the three datasets. Ghost is the larger share of hallucinations in LLaDA, Qwen, and Llama, but a minority in Dream. These prevalence values are computed under the token level plurality criterion and are sensitive to how answer equivalence is judged. Recomputing the regimes with bidirectional entailment clustering of the sampled answers reassigns a fraction of hallucinated prompts and reduces the Ghost share, yet the cross model ordering is preserved and the decoupled lexical gap remains positive in all twelve settings (Appendix E). The prevalence magnitude should therefore be read as criterion dependent, whereas the detectability asymmetry itself is robust to this choice. Appendix K Matched Model Transition Analysis The 600600 Dream prompts form an exact subset of the LLaDA corpus, allowing prompt matched comparison. The full three state transition matrix, with LLaDA as rows and Dream as columns and states ordered as Correct, Ghost, Flickering, is [194916276718171782]. bmatrix194&9&16\\ 27&67&181\\ 7&17&82 bmatrix. Among the 347347 prompts hallucinated by both models, the two state matrix is [671811782]. bmatrix67&181\\ 17&82 bmatrix. Dream Ghost Dream Flickering LLaDA Ghost 67 181 LLaDA Flickering 17 82 Table 14: Matched regime transitions among the 347347 prompts hallucinated by both models. The regime changes on 57.1%57.1\% of jointly hallucinated prompts (Table 14). The Ghost to Flickering transition occurs on 181181 prompts, while the reverse transition occurs on 1717 prompts. McNemar’s test gives p≈8×10−36p≈ 8× 10^-36. Only 6767 prompts remain Ghost under both models. The correct or hallucination label agrees on 90.2%90.2\% of the 600600 matched prompts. Appendix L Behavioral Audit Each model’s three seeds are classified by dominant behavior among matched hallucinated prompts (Table 15). Behavior LLaDA Dream Repeat one answer 69.8% 19.1% Diversify 29.4% 63.7% Fragment not separately reported 15.1% Repeated abstention at most 2.2% at most 2.2% Table 15: Dominant behavior among matched hallucinated prompts. Within the Ghost to Flickering cell containing 181181 prompts, LLaDA repeats one wrong answer on 96.7%96.7\% of prompts. Among these, 33.7%33.7\% are verbatim repetitions and 63.0%63.0\% are paraphrased repetitions. Dream is diverse on 84.0%84.0\% of these prompts and fragmented on 14.9%14.9\%. Repeated abstention is the dominant behavior on at most 2.2%2.2\% of prompts for either model and occurs in only 1.1%1.1\% of Dream generations in this transition cell. The transition is therefore associated with diversification and fragmentation rather than refusal. Appendix M Qualitative Examples Table 16 gives one Ghost and one Flickering example for each model, together with a matched model transition. In every example, none of the three seeds contains the gold answer. Type Data Question Gold Seed answers θ θ Ghost, LLaDA PopQA What sport does Masahito Noto play? football baseball, baseball, and baseball 1.001.00 Flickering, LLaDA PopQA Who composed “The Mission”? Ennio Morricone various, James Horner, and The Doors 0.330.33 Ghost, Dream TriviaQA In which city are the Oscar statuettes made? Chicago Hollywood, Los Angeles, and Los Angeles 0.670.67 Flickering, Dream TriviaQA Which composer wrote “The Dam Busters March”? Eric Coates an English composer, John Moore, and Edward Elgar 0.330.33 Ghost, Qwen HotpotQA Language of the people whose principal town was Anhaica? Apalachee Timucua, Timucua, and Timucua 1.001.00 Flickering, Qwen PopQA Who was the composer of “Hello”? Masaharu Fukuyama Bruno Mars, “a covered pop song”, and “various songs” 0.330.33 Ghost, Llama PopQA Religion of St George’s Cathedral? Greek Orthodox “several cathedrals, cannot determine” three times 1.001.00 Flickering, Llama TriviaQA Fictional school in ‘Please Sir’? Fenn Street School no verification, Fenn St. Secondary Modern, and Fenn St. Elementary 0.330.33 Matched LLaDA Ghost to Dream Flickering LLaDA to Dream TriviaQA Final, unfinished novel by Charles Dickens? Edwin Drood LLaDA: Bleak House three times; Dream: “Tale of Our Time”, Bleak House, and Dombey n/a Table 16: Representative hallucinations across models. Ghost examples show repeated incorrect answers, while Flickering examples show divergent incorrect answers. The final row shows a matched prompt whose regime changes between models. The matched Dickens example provides a direct illustration of model dependent regime membership. LLaDA produces Bleak House on all three seeds, whereas Dream produces three different incorrect answers. The question is fixed while the generation model changes the stochastic structure of the error. Appendix N Leakage and Label Robustness Several audits test whether the reported results can be explained by information leakage or implementation artifacts. All learned detector evaluations use five fold cross validation with preprocessing local to each training fold. No prompt is scored by a model trained on that prompt. Overwriting every denoising step after a checkpoint with noise and recomputing the features gives a maximum absolute feature difference of 0.00.0 at all 3131 checkpoints. This verifies construction from the causal prefix. No online or offline feature reads a gold field. Permuting the labels collapses detection to chance. Gaussian random features remain within 0.060.06 of chance AUC. Duplicate checks pass, and corrupting the gold field leaves features unchanged with maximum difference 0.00.0. Across these tests there is no evidence of the tested leakage or implementation artifacts. N.1 Semantic Reassessment The entire subset of incorrect Ghosts is reassessed to bound the effect of exact match grading. The reassessment covers 387387, 404404, and 423423 prompts for TriviaQA, HotpotQA, and PopQA respectively. A consensus answer is relabeled correct only when it passes an embedding retrieval filter using BGE large with cosine similarity at least 0.750.75 and bidirectional DeBERTa entailment with both directions at least 0.50.5. The reassessment is automated rather than based on blinded human annotation. TriviaQA HotpotQA PopQA Ghosts initially incorrect 387 404 423 Verified correct 4 2 0 Relabeled percentage 1.0 0.5 0.0 Ghost percentage, original to relabeled 77.477.4 to 77.277.2 69.969.9 to 69.869.8 65.165.1 to 65.165.1 Agreement AUC, original to relabeled .609.609 to .611.611 .606.606 to .604.604 .659.659 to .659.659 Raw Ghost AUC, original to relabeled .506.506 to .507.507 .479.479 to .475.475 .521.521 to .521.521 Detector recall, original to relabeled .584.584 to .580.580 .626.626 to .627.627 .844.844 to .844.844 Table 17: Semantic reassessment of the Ghost population. Every quantity depending on Ghost moves by less than 0.0050.005. Only 44, 22, and 00 Ghosts are verified correct (Table 17). A generous lexical upper bound gives 1111, 77, and 11 possible relabelings. Every quantity that depends on Ghost moves by less than 0.0050.005. The reassessment therefore indicates that exact match grading explains only a small fraction of the evaluated high agreement errors. Appendix O Supporting Online Detector The full behavioral detector is included as supporting evidence. It uses 3636 causal features evaluated at 3131 checkpoints. The four feature blocks are prefix information with 55 features, consistency information with 1212 features, diffusion commit dynamics with 99 features, and question priors with 1010 features. The detector uses five fold out of fold evaluation and ℓ2 _2 logistic regression with C=0.2C=0.2. The operating threshold is selected to control the cumulative false positive rate at no more than 30%30\%. AUC within group Recall at FPR 30 Dataset Ghost Flick. Ghost Flick. TriviaQA 0.71 0.97 58 92 HotpotQA 0.69 0.95 63 85 PopQA 0.88 0.97 84 94 Table 18: Full online detector on the scaled LLaDA corpus. At cumulative FPR no greater than 30%30\%, the detector achieves TPR of 66%66\%, 69%69\%, and 88%88\% on TriviaQA, HotpotQA, and PopQA (Table 18). Median detection occurs at steps 2828, 2424, and 88 of 128128. Recall remains higher for Flickering than Ghost on every dataset. These results motivate warnings before generation is complete, potentially allowing a system to request verification before users rely on an answer. This is a candidate safeguard for resource constrained deployments, including in the Global South, not a demonstrated low-cost solution. A small logistic classifier does not establish low end-to-end cost: multiple generations, feature extraction, latency, and false alarms must also be evaluated. The reported 30%30\% false positive ceiling further requires validation against local needs and the consequences of unnecessary warnings. Appendix P Additional Diagnostic Analyses The following analyses are retained in compressed form because they provide supporting evidence without carrying the central claim. P.1 Per Step Agreement Recomputing answer agreement at every denoising step gives little improvement over final answer agreement on TriviaQA and HotpotQA, with AUC changing from 0.610.61 to 0.610.61 on both datasets. PopQA changes from 0.660.66 to 0.790.79 (Table 19). Feature set Triv. Hot. Pop. Final answer agreement 0.61 0.61 0.66 Per step answer agreement 0.61 0.61 0.79 Plus text overlap 0.70 0.67 0.80 Full consistency block 0.70 0.70 0.81 Full detector 0.73 0.75 0.90 Table 19: Per step agreement compared with final answer agreement on LLaDA. The analysis establishes that temporal resolution of agreement alone does not eliminate the detectability asymmetry. It does not establish that transient early disagreement across seeds is absent because convergence timing across seeds is not directly measured. P.2 Transfer Across Corpora Training the online detector on two datasets and evaluating it on the held out third gives mean transfer AUC of 0.7480.748, compared with 0.7930.793 in domain. The signal therefore transfers partly across datasets. P.3 Candidate Mechanism Probe A correlational test of subject popularity as an explanation for Ghost membership on PopQA gives AUC 0.410.41. This result is below chance and does not support popularity as an explanation for the hard regime. Stability under stochastic perturbation, early commitment, and collapse onto a popularity prior remain hypotheses rather than demonstrated mechanisms. The present analyses do not establish a causal explanation for why some hallucinations remain highly consistent. Appendix Q Claim and Evidence Summary Table 20 summarizes the evidence hierarchy. Claim Evidence Establishes Dependence status Caveat Raw agreement gap Four models and three datasets Descriptive agreement based asymmetry Mechanically coupled Not independent evidence Lexical asymmetry persists Positive gap in all twelve settings Asymmetry survives a decoupled lexical measurement No exact computational reuse Still a dispersion measure Semantic asymmetry persists Positive gap in all twelve settings Asymmetry survives a decoupled semantic measurement No shared lexical computation Still a dispersion measure Trajectory asymmetry LLaDA significant on all three datasets; Dream positive on all three Within seed dynamics contain additional information No information across seeds Limited to diffusion models Prevalence varies Ghost share from 16%16\% to 77%77\% Error population composition depends on model Descriptive Four models only Regime membership varies 181181 versus 1717 matched transitions Prompt identity alone does not determine regime Descriptive matched result One matched model pair Seed depth robustness Three to eighteen seeds Gap remains positive at greater seed depth Robustness evidence LLaDA only Table 20: Summary of the central evidence. The trajectory analysis is the only analysis in which the evaluated signal uses no information across seeds. Appendix R Statistical Procedures Agreement and correctness contrasts use two sided Mann Whitney tests. The reported values are approximately 5×10−125× 10^-12 for TriviaQA, 3×10−73× 10^-7 for HotpotQA, and 1×10−201× 10^-20 for PopQA. Learned detectors use five folds with predictions held out from training and averaged over shuffles. Bootstrap confidence intervals use B=2000B=2000 prompt level resamples. Each bootstrap resample redraws prompts and recomputes both subgroup AUCs, so the gap intervals are paired. Permutation tests use B=2000B=2000 shuffles of Ghost and Flickering assignments among hallucinated prompts while detector scores remain fixed. The finite sample convention is p=b+1B+1.p= b+1B+1. (4) The smallest reportable value is approximately 5×10−45× 10^-4, which is reported as p<0.001p<0.001 when appropriate. The analyses beyond the primary decoupled result are exploratory robustness analyses and are not corrected for multiple comparisons. Appendix S Aggregate AUC Decomposition When the hallucination population is a mixture of Ghost and Flickering regimes evaluated against the same correct population, aggregate AUC is a prevalence weighted combination of the two regime specific AUCs. Let πG _G denote the Ghost prevalence among hallucinations. Then AUCagg _agg =Pr(Sh>Sc)+12Pr(Sh=Sc) = (S_h>S_c)+ 12 (S_h=S_c) (5) =∑r∈G,FPr(Rh=r∣Yh=1)AUCr = _r∈\G,F\ (R_h=r Y_h=1)\,AUC_r =πGAUCG+(1−πG)AUCF. = _GAUC_G+(1- _G)AUC_F. Here ShS_h and ScS_c denote detector scores for hallucinated and correct examples, while RhR_h denotes the regime of a hallucinated example. Aggregate performance therefore depends jointly on regime prevalence and detectability conditioned on regime. Because Ghost prevalence varies substantially across models, aggregate AUC can change as the composition of the hallucination population changes, even when regime conditioned detector behavior is similar. Appendix T Scope and Limitations The experiments cover four models, one size range, one sampling configuration per model, and K=3K=3 seeds in the main analysis. The high depth robustness study contains 150150 LLaDA prompts and does not provide a matched seed depth study for autoregressive models. Correctness is determined by gold alias containment. The diffusion corpora use token level matching, while the autoregressive corpora use a case insensitive substring match. These procedures can misjudge paraphrases and formatting variants. The assignment of hallucinations to the Ghost and Flickering regimes depends on how answer equivalence is judged. The reported partition uses a gold free answer span with token level clustering, which can group answers that share surface tokens without sharing meaning. Recomputing the regimes with bidirectional entailment clustering reassigns a fraction of hallucinated prompts and lowers the Ghost prevalence, so prevalence magnitudes are criterion dependent. The decoupled detectability gap remains positive in every setting under this alternative criterion (Appendix E), so the central asymmetry does not depend on the specific equivalence rule. The semantic reassessment is automated and reduces the measured effect of possible exact match errors, but it does not constitute human adjudication. The trajectory analysis applies only to diffusion models. Evidence is strong for LLaDA and directional but less precise for Dream. The Ghost and Flickering taxonomy is an operational behavioral partition. It identifies a reproducible distinction in the evaluated settings but does not establish that every hallucination in other architectures or domains belongs to the same two regimes. The Global South framing is a deployment motivation, not a regional impact finding. We do not measure users’ trust, AI literacy, or comparative exposure to hallucination harms, nor do these benchmarks establish performance across local languages and knowledge contexts. Future evaluation should involve communities in defining relevant tasks and acceptable error rates, and measure end-to-end compute, latency, and cost before claiming affordable protection.