An Empirical Study of Daopological Measures (Revised v2) Measure–Entropy Analysis of 10,455 Structural Units —with a Case Study of Detecting and Fixing an Implementation Bias

This paper is a revised version of An Empirical Study of Daopological Measures: Measure–Entropy Analysis of 10,455 Structural Units. In v1, we reported a “strong positive correlation between measure and entropy” as a novel empirical finding that contradicted the theoretical prediction of independent four-quadrant distribution. Subsequent code audit and independent replication revealed that this phenomenon was not a theoretical prediction failure, but an implementation bias: v1 had simplified the migration confidence c(x, y) to a binary indicator (“shared kernel family → 1, else → 0”), which made the structural measure µstructure and thetransferability entropy Htransfer mathematically function-dependent (r = 1.000). The four quadrants therefore collapsed into two. This paper reports the corrected results. By redefining c(x, y) as a weighted average of the Jaccard similarity over role sets and the Jaccard similarity over relation-type sets, all four quadrants expand, and the two-axis correlation drops to r = 0.8052. Corrected core results: (1) 10,455 structural units, 8,462 unique signatures, 37 academic domains; (2) Daopological entropy HD = 8.2947, with entropy ratio HD/ log |K| = 0.9172, still well above the 0.8 health threshold; (3) four-quadrant distribution: rich 4,777 / concentrated 451 / dispersed 451 / poor 4,776, with all four quadrants non-zero; (4) 198 cross-domain kernels spanning ≥ 3 domains, the largest spanning 16 disciplines; (5) only 14 fully isolated nodes (0.13%). We formally retract three claims from v1: (a) “2.93 billion structural nodes” (not reproducible by any of four natural algorithms); (b) “HD = 0.9705” (denomina tor polluted by surface-level signatures); (c) “strong positive correlation is a new theoretical finding” (actually an implementation artifact). The correction process itself constitutes a methodological contribution: in LLM-based knowledge-extraction pipelines, “apparently contradictory results” should first be assumed to be implementation-layer issues rather than theoretical discoveries; structured auditing (run code first, draw conclusions second) should become standard practice.