constitution · epochs · watch · epoch 4

c_5d4f3299fa6dd70fc6

tommy-mor · sha1:0e81b5e1958ca486bffe87c800cc68e389c9a810

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Solve Rank Centrality exactly instead of capping power iteration.

`compute_scores_from_edges` ran power iteration for at most 10 000 sweeps and
returned whatever vector it had reached, with no signal when the cap bound. On
a preference chain the spectral gap is Theta(1/n^2), so the cap binds past
n ~= 1500 -- and worse, the L1 *step* tolerance is an absolute test, so on a
1024-node chain with mixed ratios it declared success after 4325 sweeps while
leaving 486 of 1024 items at the wrong rank. A 1024-node star fails outright:
it needs 14 154 sweeps.

New `stationary` module owns every candidate solver -- power, Aitken-accelerated
power, Gauss-Seidel/SOR, preconditioned BiCGSTAB, dense LU, dense GTH, and a
sparse GTH state reduction with minimum-degree elimination -- behind one `solve`
that splits disconnected components, tries the sparse direct path first (trees
and chains reduce in O(n) with zero fill), and falls back to Gauss-Seidel then
power iteration on the dense graphs elimination cannot help with. Every answer
carries its own recomputed residual and a `converged` flag; nothing comes back
claiming success it did not earn.

Scores are also produced in log space. A chain of n items each preferred 2:1
spans 2^(n-1), which leaves the f64 range at n ~= 1075, so `pi` genuinely cannot
order a long chain no matter how it is computed. `Solution::log_pi` stays exact
there and is what `ranked_items_subset` now sorts on.

Edges are sorted before aggregation, so the result no longer depends on
`HashMap` iteration order. The legacy builder produced a different bit pattern
on 7 of 7 rebuilds of the same graph; the sort costs ~10% of chain construction.

Adds `benches/stationary_solvers.rs` (~80s) and `examples/solver_probe.rs`
(~30s), which reports time, residual, and rank displacement against closed-form
answers per topology. No new dependencies.

Co-authored-by: Cursor <cursoragent@cursor.com>

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