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# Internal Helper: Rapidly tally pairs in a given block matrix
tally_block_pairs <- function(block_mat, item_traits, item_keys) {
pairs_list <- list()
b_size <- ncol(block_mat)
# Extract all pairs from the blocks
for (i in 1:(b_size - 1)) {
for (k in (i + 1):b_size) {
tA <- item_traits[block_mat[, i]]
tB <- item_traits[block_mat[, k]]
kA <- item_keys[block_mat[, i]]
kB <- item_keys[block_mat[, k]]
# Alphabetize traits so A-C is treated the same as C-A
t1 <- pmin(tA, tB)
t2 <- pmax(tA, tB)
# Determine keying match
match_type <- ifelse(kA == kB, "equal", "mixed")
# Create canonical IDs for hashing
pairs_list[[length(pairs_list) + 1]] <- paste(t1, t2, match_type, sep = "_")
}
}
# Return table of counts
return(table(unlist(pairs_list)))
}
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