Recursive temporal attention spanner

Integrate this at the attention-logit and mask stage of a causal Transformer. For a sequence of n tokens, create two copies S and T of the token indices. Set the biclique edge label to the token's causal time difference or to a discretized event timestamp; set the diagonal S-T label to 1 as in the paper. Build a sparse edge set recursively. At a subproblem containing m source indices and m target indices, choose a block size f(m), initially f(m)=max(1,ceil(m*exp(-sqrt(log(max(m,3)))))). Add a linear-size routing skeleton using a greedy temporal 3-hop cover: repeatedly add the candidate edge that covers the largest number of currently uncovered ordered pairs (s,t) having a nondecreasing-label path of at most three edges, then stop after 2m edges or when all pairs are covered. For every candidate path, explicitly check label order. Recursively process the selected block twice and the complement once, as prescribed by the recurrence. Convert retained S-T edges to an n-by-n boolean attention mask, and use it in every layer or cycle masks across three consecutive layers so information can traverse certified paths. The paper supplies the target recurrence and the 3-hop invariant; the greedy cover and f schedule are engineering approximations and should be measured against exact dense-pair coverage. First run on WikiText-103 or synthetic timestamped sequences with n in {256,512,1024}, comparing dense causal attention, local attention, and random sparse attention at equal hidden size. Measure retained-edge count, GPU memory, wall-clock attention FLOPs, perplexity, and the fraction of source-target pairs whose minimum temporal hop distance increases by more than 3x. Success is a 2x or larger attention-memory reduction with less than 1% perplexity degradation and empirical 3-hop coverage above 99%.