DQIS — Addendum I: Temporal Stratification of Tail Dependence Risk

DQIS — Addendum I: Temporal Stratification of Tail Dependence Risk (v20, current cleaned version — June/July 2026). Supplementary analysis to the DQIS Consolidated Framework v36 (concept DOI 10.5281/zenodo.19855263). This addendum addresses the tail-dependence concern raised in the consolidated framework — the risk that supposedly independent surveillance channels co-fail under stress, collapsing the multiplicative security of the quorum. It shows the concern decomposes into two mechanistically distinct problems with different temporal signatures, and reports the direct measurements that now bound them. Channel architecture (read first). The channel layer has been redesigned and measured (Consolidated v36 front block; Objections O38/O39). The current panel is six channels in two categories — five "presence" channels (mHSP70 · PS · CSFT · T-δ CIN via cGAS-STING · T-α metabolic) plus one "absence" channel (NK/missing-self). The original five biophysical channels are fully superseded: T-δ is now a Chromosomal Instability sensor (cGAS-STING pathway, Beernaert & Parkes 2023), T-γ* (bioelectric) is dropped, and T-β/T-ε are retained only as non-core AND-gate/vote candidates. Legacy five-channel material survives only as pointers to the Superseded Ledger. (1) Evolutionary Tail Dependence (ETD): requires sustained selective pressure over many cell generations. At the DQIS early-interception window (10¹–10⁴ cells, ~10–50 generations) the cumulative probability that an ETD mechanism emerges is small — ~0.03% at 10² cells, rising to ~15% only at the marginal 10⁴-cell edge of the design envelope, and reaching certainty only at the clinical threshold (~10⁹ cells) where DQIS no longer operates. The framework is explicitly designed to act inside the window where ETD is negligible. (2) Environmental Tail Dependence (EnTD): arises from shared microenvironmental stressors (hypoxia, acidosis) without mutation; present from the earliest stages, spatially bounded, and the appropriate target for Clayton-copula modelling. The previously reported T-α/T-δ lower tail dependence (LTD ≈ 0.25) is no longer treated as a within-tumour measurement: it reflected a hypothesised ACLY→acetyl-CoA→HAT metabolic-epigenetic coupling (O33), and the T-δ CIN redesign makes T-δ mechanistically orthogonal to metabolism, so the coupling does not apply to the current panel. Direct within-tumour Kendall τ-b on real data is ≈ 0.02–0.10 for inter-channel pairs (τ < 0.20 across histotypes), i.e. practical independence. Direct empirical measurements. Clayton-copula θ fitted (May 2026) on four public single-cell datasets. GBM (GSE131928, Neftel 2019, 7,911 IDHwt cells): θ = 0.199 [0.173–0.221] — NOT cold, reclassified as hot (indistinguishable from melanoma θ ≈ 0.218). PDAC (GSE155698, Steele 2020, 11,448 EPCAM+ cells): θ = 1.214 [1.195–1.235] — confirmed cold, resolved by the population-level IPS module. Normal pancreas (GSE84133, Baron 2016, 5,432 cells): θ = 1.107 — intrinsically cold before any cancer (PDX1/HNF1B/PTF1A co-regulation, not KRAS-induced), which is why θ alone cannot discriminate PDAC and motivates a penetrance signal. Melanoma (GSE72056, Tirosh 2016) θ ≈ 0.17–0.218 serves as the validation control. Penetrance discovery: the IPS signal is 15.5× in invasive PDAC versus normal pancreas (P(false alarm) = 0.0003), 10.1× in IPMN precancerous lesions. A second, more recent round of measurements (June 2026) tested the tail-dependence premise directly on real immune escape — the empirical core of this addendum: within-tumour inter-channel independence was measured (Kendall τ-b < 0.20, N_eff 3.3–4.1 of 5) across melanoma, GBM and PDAC (cross-validated on GSE115978), and co-resistance under selection was stress-tested twice — on two Merkel-cell-carcinoma relapses via MHC-I loss (Paulson 2018, GSE117988/GSE118056), where independence held under selection, and on a genetically-defined CD19+/CD19− B-ALL escape (GSE153697), where the channels did not co-fall (N_eff ≈ 4.65/6). No new θ fitting was performed after May 2026; the June work is the co-evasion stress-test, not a re-measurement of θ. Contents. The addendum provides: the ETD/EnTD decomposition and the early-window boundary (ETD < 5% for M < 10⁴ cells, G < 50 generations); the Clayton-copula tail-dependence formalism and the direct θ-measurement protocol (§10) with the empirical results (§10-bis); the Penetrance Discovery and the T-ζ/IPS dual-mode module for biophysically-cold tumours (§11–12); TASE 2.0 — the channel-internal Tissue-Aware Stemness Exclusion, re-anchored to T-α after T-γ* was dropped (the original T-γ*-bound TASE is in the ledger; §13 is now a stub); the Pulsed Activation Architecture specification (§3b); and the T-δ CIN redesign with its impact on the tail-dependence calculus (§16), including the Adaptive Quorum integration (§16.5). The Adaptive Quorum k=1/N + Gate_G shifts security from statistical rarity to biological specificity: with Gate_G active the escape probability becomes P_escape ≈ (p_i)^N × F × p_G, with the Ki-67 proliferation gate (p_G ≈ 0.01) orthogonal to all sensing channels via the CDK4/6-Rb-E2F pathway; the required Gate_G validation experiments (O29, Ki-67 nanobody, Phase 2+) are specified. The historical "Channel Paradox" (adding a correlated channel capping security below Phase 0, the ~13× artefact) is retired: it was an artefact of the never-measured θ_ME = 0.40 value; on the measured panel (ρ ≈ 0.08) it does not arise and is retained only as the rationale for the θ < 0.20 independence gate. Not a peer-reviewed publication — a prior-art deposit released under CC BY 4.0. Read alongside the DQIS Consolidated Framework v36 and the Register of Scientific Objections v35. Contact: [email protected] documents (current versions): DQIS Consolidated Framework v36; Register of Scientific Objections v35. Contact: [email protected] documents: - DQIS Consolidated Framework (main document): https://zenodo.org/records/21128521- Register of Scientific Objections v35.0: https://zenodo.org/records/21128725