Exact Consecutive-Pattern Popularity in the Class Avoiding 123, 231 and 312

We determine exact totals of consecutive patterns in the class Av_n(123,231,312). For n >= 3, N_n(321) = E_(n+1) - 2 E_n, and N_n(132) = N_n(213) = ((n-2)n E_(n-1) - E_(n+1) + 2 E_n)/2. With the normalization N_n(p)/(n|A_n|), the limits are pop(321) = 4/pi^2 and pop(132) = pop(213) = 1/2 - 2/pi^2. This is a limited mathematical preprint concerning one consecutive-avoidance class, not a general solution for arbitrary permutation patterns. The total nE_(n-1), Euler numbers, OEIS A000708 and its EGF, and the circular-difference integral-operator framework are known prior work. References identify Hassler-Kirgizov Class 12 / Table 1 / equation (1.1), Ehrenborg-Kitaev-Perry Theorem 7.5, the known Kitaev-Mansour count, and Zhao (2014)'s different classical nonconsecutive setting. Independent AI mathematical audit: Claude Sonnet 5.5 v0.2 MODEL / PROOF / COMPUTATION PASS; v0.3 differential audit PASS. Claude's own REFERENCES assessment is PARTIAL: Claude did not inspect HK v2, EKP Section 7 or Zhao (2014), and did not execute Windows. ChatGPT's primary-source checks are separately attributed. Windows PowerShell v0.4.1 reproduction: PASS in the owner's supplied console record, not execution by Claude or the publication assistant. The full supplied report and console output are included in the ZIP. Novelty: INCONCLUSIVE. Human peer review: NOT PERFORMED / Not human peer-reviewed. Copyright (C) 2026 Ryutaro Yonezu. All rights reserved, including code and supplementary material. The v0.4 mathematical text, proofs, code and original audit archives are preserved byte-for-byte. Windows v0.4.1 only normalizes three path conversions in memory and is not a new mathematical version. Historical HOLD and Windows-untested records are frozen archival statements; the owner explicitly authorized this v1.0 public release. GitHub repository: https://github.com/yonezaemon1-hub/no54-class12-consecutive-pattern-popularityGitHub Release v1.0: https://github.com/yonezaemon1-hub/no54-class12-consecutive-pattern-popularity/releases/tag/v1.0