Reference code for an enumeration pipeline: given a 2-connected simple graph and a closed surface type (orientable or non-orientable), it constructs partial 2-cell embedding states arc by arc, prunes branches that cannot extend to the target surface, and outputs deduplicated representatives of cellular embeddings on that surface and of general embeddings after upgrade. Intermediate embeddings may use simpler surfaces below the target in the same preorder as in the manuscript. This deposit accompanies the author's master's (graduate) thesis. Institutional rules on pre-defense public release are still unclear; until those rules are settled and the thesis defense has taken place, this record may be kept non-public or restricted rather than openly visible on Zenodo. Pair with the companion manuscript deposit when both are published.