{
  "all_gates_pass": true,
  "claims": [
    "Under finite drift energy assumptions, the intra-generation KL divergence between the generated distribution and the training target is bounded above by (1/2)\u03b5\u0302\u1d62\u00b2, the learned-path score error energy (Proposition 3.1).",
    "A matching lower bound on the chi-squared divergence, \u03c7\u00b2(p\u0302^(i+1) \u2225 q\u1d62) \u2265 (1/4)\u03b7\u1d62\u03b5\u00b2\u22c6,\u1d62 \u2212 C\u00b7\u03b5\u2074\u22c6,\u1d62, holds for small score errors (\u03b5\u00b2\u22c6,\u1d62 \u2264 1), where \u03b7\u1d62 \u2208 [0,1] is the observability coefficient (Proposition 3.3, Definition 3.2).",
    "Combining the upper and lower bounds yields a two-sided equivalence \u03c7\u00b2(p\u0302^(i+1) \u2225 q\u1d62) \u224d \u03b5\u00b2\u22c6,\u1d62 in the perturbative regime (Theorem 3.4).",
    "When the score-error series \u2211\u1d62 \u03b5\u00b2\u22c6,\u1d62 diverges, the accumulated divergence across generations cannot vanish and has a non-zero floor limsup D\u1d62 \u2265 \u03b1\u03b7\u0304\u03b5\u0304 / [16(1+(1-\u03b1)\u00b2)] (Proposition 4.1).",
    "When \u2211\u1d62 \u03b5\u00b2\u22c6,\u1d62 converges, accumulated divergence across generations satisfies D_{N+1} + C_bias \u224d \u03a3\u1d62(1-\u03b1)^{2(N-i)}\u03b5\u00b2\u22c6,\u1d62 + (1-\u03b1)^{2(N+1-i\u2080)}D_{i\u2080}, decaying geometrically at rate (1-\u03b1)\u00b2 per generation, where \u03b1 is the fraction of fresh data mixed in each round (Theorem 4.2).",
    "The \u03b1-dependent tradeoff between drift and stability is empirically confirmed on a 10D Gaussian mixture and on Fashion-MNIST/CIFAR-10, with low \u03b1 producing collapse-driven drift and high \u03b1 maintaining stability (Figure 1)."
  ],
  "diagnostics": {
    "constant_error": 0.02,
    "harmonic_partial_sum_6000": 0.18553627488260488,
    "summable_error_total_240": 0.1312620854944664
  },
  "gates": {
    "all_six_claims_mapped": true,
    "all_source_hashes_match": true,
    "claim1_gaussian_path_identity_exact": true,
    "claim1_kl_upper_all_20_panels": true,
    "claim2_eta_unit_interval": true,
    "claim2_lower_leading_term_all_observable_panels": true,
    "claim2_unobservable_control_has_energy": true,
    "claim3_small_error_ratio_near_observability": true,
    "claim3_two_sided_ratio_finite_positive": true,
    "claim4_constant_floor_panels_pass": true,
    "claim4_harmonic_nonfloor_control": true,
    "claim4_literal_conflation_detected": true,
    "claim5_convolution_identity": true,
    "claim5_fresh_data_shortens_memory": true,
    "claim5_geometric_rates_exact": true,
    "claim5_no_fresh_data_destructive_control": true,
    "claim5_summable_error_series": true,
    "claim6_all_three_source_datasets_pinned": true,
    "claim6_three_alpha_levels_pinned": true
  },
  "paper": {
    "arxiv_id": "2602.16601v1",
    "openreview_id": "QYA0Q28ssf",
    "title": "Quantifying Error Propagation and Model Collapse in Diffusion Models"
  },
  "scope": {
    "claim4": "Literal live claim conflates Proposition 4.1(i)'s non-summability premise with part (ii)'s additional uniform error-floor premise; the displayed positive floor is not supported by divergence of the series alone.",
    "experiments": "10D GMM, Fashion-MNIST, and CIFAR-10 conclusions are pinned source evidence; image divergence uses the source's learned-feature Gaussian proxy and is not an independent rerun.",
    "gaussian_audit": "Exact Gaussian endpoint/path identities and deterministic memory recurrences test the formulas but do not replace the paper's stochastic-process proofs."
  }
}