Funding for recreational cycle paths

The following question arose in Hamilton: Can recreational cycle paths attract funding (subsidy) from the NZTA?

NZTA (NZ Transport Agency) is the government land transport funding agency, they were  formerly LTNZ, and prior to that Transfund, just in case you know them by their old names.

So, can those recreational facilities be subsidised? Strictly speaking no, because government has strange rules. They fund recreational roads (e.g. SH1 to Cape Reinga, or SH94 to Milford Sound), but not recreational pathways. 

So when can pathways get subsidised? A few rules apply: