AI 中文总结
本文研究Joyce广义角流形上AKSZ-BV-BFV理论的相对对数源复形，提出与分辨率无关的表示及Stokes迹系统，验证有限转移准则，但一般存在性仍开放。
AI 中文摘要
我们研究了面向广义角的Joyce流形上AKSZ-BV-BFV理论的与分辨率无关的相对对数源复形。在几何假设(G1)-(G3)下，所允许的光滑幺半分解的Dupont-Panzer-Pym总相对对数复形表示$j_!Ω_{X^\circ}^\bullet$，并携带相同的紧支撑导出迹。该比较刻意未过滤：它通过共同内部识别总相对上闭链类，但不识别个别分辨面、分离的BFV后裔、非线性映射空间或绝对正则化积分。对于内禀$b$-源${}^{b}T[1]X$，我们制定了恢复严格面状结构所需的额外Stokes和转移数据。Joyce面范畴上的乘法正则化Stokes迹系统给出了预辛内禀BV-BFV恒等式和关联下降。有限数据(G4)是线性细分/聚合转移准则；(G5)是经典阿贝尔BF理论的独立循环级场准则。两者均非一般存在性定理，此处也未构造一般严格乘法内禀迹。我们证明了余维二环所需的区间收缩，并通过其两个对角分辨的公共星细化分析了正实锥形。在显式有限乘积-Whitney对数类上，例外平方在正规面全化后满足(G4)，转移微分恰为带符号的内禀关联微分。其有限代数BF对偶给出循环对数-胞腔影子，但非完整连续内禀$b$-de Rham数据(G5)。一般非线性连续前推、内禀乘法迹的存在性以及圈级对数图积分仍待解决。
英文摘要
We study resolution-independent relative logarithmic source complexes for AKSZ-BV-BFV theory on face-oriented Joyce manifolds with generalized corners. Under the geometric hypotheses (G1)-(G3), the Dupont-Panzer-Pym total relative logarithmic complexes of admitted smooth monoidal resolutions represent $j_!Ω_{X^\circ}^\bullet$ and carry the same compactly supported derived trace. The comparison is deliberately unfiltered: it identifies total relative cocycle classes through the common interior, but not individual resolved faces, separate BFV descendants, nonlinear mapping spaces, or absolute regularized integrals. For the intrinsic $b$-source ${}^{b}T[1]X$ we formulate the additional Stokes and transfer data needed to recover strict facewise structures. A multiplicative regularized Stokes trace system on Joyce's face category gives the presymplectic intrinsic BV-BFV identity and incidence descent. The finite datum (G4) is a linear subdivision/aggregation transfer criterion; (G5) is a separate cyclic field-level criterion for classical abelian BF theory. Neither is a general existence theorem, and no general strict multiplicative intrinsic trace is constructed here. We prove the interval contractions needed for codimension-two collars and analyze the positive real conifold through the common star refinement of its two diagonal resolutions. On an explicit finite product-Whitney logarithmic class the exceptional square satisfies (G4) after normal-face totalization, and the transferred differential is exactly the signed intrinsic incidence differential. Its finite algebraic BF dual gives a cyclic logarithmic-cellular shadow, but not the full continuum intrinsic $b$-de Rham datum (G5). General nonlinear continuum pushforward, existence of the intrinsic multiplicative trace, and loop-level logarithmic graph integrals remain open.
Comments93 pages. Companion to arXiv:2608.02928 (ordinary corners)
