Relative Logarithmic AKSZ Descent on Joyce Generalized Corners

Abstract

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 $j_{!}{\Omega }_{X^{\circ }}^{\bullet }$ 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.

93 pages. Companion to arXiv:2608.02928 (ordinary corners)