Statement
Does TECT-Brazovskii natively support asymptotic-safe Newton constant with $G_{\rm eff}(k_* \sim 0.4,M_{\rm Pl})/G_{\rm obs} < 1/26$? — PARTIAL CLOSE 2026-05-26 (1-loop INTERIM NEGATIVE; exact-RG follow-up queued)
Pillar: P11
Tier: T2
Details
[PARTIAL CLOSE 2026-05-26 by Math409-AddH-AddA-AddA; corrected 2026-05-26 UTC per operator adversarial review] Explicit 1-loop calculation of TECT-Brazovskii running Newton constant. Shell-mode loop integral $I^{\rm Brz}{\rm shell-total} = (q/8)(\gamma/r_R)^{3/2}$ with Brazovskii enhancement factor $1/r_R^{3/2}{\rm TECT} \approx 3.67$ at canonical $r_R = 0.42$. Result: $\omega{\rm TECT}^{\rm 1-loop} = 4.42$ (central), uncertainty band $[1.5, 13.3]$ (factor 3 scheme-dependence). At $k_ = 0.41,M_{\rm Pl}$: $G_{\rm eff}/G_{\rm obs} = 0.572 \gg 0.0385$ required (shortfall factor 15, structural — well outside scheme-dependence band; NOT a "marginal" fail). Required $\omega$ for closure = 148 (33x larger than 1-loop, beyond typical higher-order extrapolation). Effective Schwarzschild check (POSTMORTEM §8.7) with $G_{\rm eff}$: $r_{\rm tex}/r_{\rm Sch}^{\rm eff} = 0.067 < 1$ — texture STILL inside Schwarzschild even with full B2 1-loop credit. Verdict (PARTIAL): B2 1-loop STRONG NEGATIVE INDICATOR. Pillar 11.A status canonicalised as T2 INTERIM NEGATIVE, exact-RG pending (PROVISIONAL qualifier NOT formally lifted — premature per operator audit). Definitive closure pending Math409-AddH-AddA-AddA-AddA exact-RG Wetterich (target 2026-12-31); most-likely outcome (70-80%) confirms 1-loop verdict → Pillar 11.A T1 OPEN terminal → TECT dominant DM defaults to Pillar 11.B (now LIKELY PRIMARY PATH). 8/8 self-test asserts PASS per CLAUDE.md §6.3.8 + POSTMORTEM §8.7.
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Source of truth
Docs/status/OPEN-QUESTIONS.md Active section, Q-2026-05-26-Math409-AddH-AddA-AddA-TECT-RunningG-Calculation row (raw).
Issue body is auto-synced from canonical source. Manual edits to the body will be overwritten on next sync. Discussion in comments is welcome and preserved.
Statement
Does TECT-Brazovskii natively support asymptotic-safe Newton constant with$G_{\rm eff}(k_* \sim 0.4,M_{\rm Pl})/G_{\rm obs} < 1/26$ ? — PARTIAL CLOSE 2026-05-26 (1-loop INTERIM NEGATIVE; exact-RG follow-up queued)
Pillar: P11
Tier: T2
Details
[PARTIAL CLOSE 2026-05-26 by Math409-AddH-AddA-AddA; corrected 2026-05-26 UTC per operator adversarial review] Explicit 1-loop calculation of TECT-Brazovskii running Newton constant. Shell-mode loop integral $I^{\rm Brz}{\rm shell-total} = (q/8)(\gamma/r_R)^{3/2}$ with Brazovskii enhancement factor $1/r_R^{3/2}{\rm TECT} \approx 3.67$ at canonical $r_R = 0.42$. Result: $\omega{\rm TECT}^{\rm 1-loop} = 4.42$ (central), uncertainty band $[1.5, 13.3]$ (factor 3 scheme-dependence). At $k_ = 0.41,M_{\rm Pl}$:$G_{\rm eff}/G_{\rm obs} = 0.572 \gg 0.0385$ required (shortfall factor 15, structural — well outside scheme-dependence band; NOT a "marginal" fail). Required $\omega$ for closure = 148 (33x larger than 1-loop, beyond typical higher-order extrapolation). Effective Schwarzschild check (POSTMORTEM §8.7) with $G_{\rm eff}$ : $r_{\rm tex}/r_{\rm Sch}^{\rm eff} = 0.067 < 1$ — texture STILL inside Schwarzschild even with full B2 1-loop credit. Verdict (PARTIAL): B2 1-loop STRONG NEGATIVE INDICATOR. Pillar 11.A status canonicalised as T2 INTERIM NEGATIVE, exact-RG pending (PROVISIONAL qualifier NOT formally lifted — premature per operator audit). Definitive closure pending Math409-AddH-AddA-AddA-AddA exact-RG Wetterich (target 2026-12-31); most-likely outcome (70-80%) confirms 1-loop verdict → Pillar 11.A T1 OPEN terminal → TECT dominant DM defaults to Pillar 11.B (now LIKELY PRIMARY PATH). 8/8 self-test asserts PASS per CLAUDE.md §6.3.8 + POSTMORTEM §8.7.
[Original Active text follows for archival]:
Source of truth
Docs/status/OPEN-QUESTIONS.mdActive section, Q-2026-05-26-Math409-AddH-AddA-AddA-TECT-RunningG-Calculation row (raw).Issue body is auto-synced from canonical source. Manual edits to the body will be overwritten on next sync. Discussion in comments is welcome and preserved.