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| 1 | # Graded connectors, run 2 — combine levels by evidence strength. Pre-registration |
| 2 | |
| 3 | 2026-10-18. Written and committed **before any code change or run**. Follows run 1 (`RESULTS.md`, `5d99c5c`), |
| 4 | where "the finest level that passes the gate wins" failed: sparse word-level evidence overrode stronger |
| 5 | class-level evidence. |
| 6 | |
| 7 | ## The one change |
| 8 | |
| 9 | New link scorer **BEST-G**: for a token pair, consider every level (W, G, S1, S2) whose pair passes the gate |
| 10 | (PMI > 0, G > 10.83); use the PMI of the level with the **largest G statistic** (the most significant |
| 11 | evidence). No edge if no level passes. Everything else (corpus, hierarchy, gate, Eisner parse, span types, |
| 12 | budgets, seeds, tiers) is exactly as in `PREREG.md`. |
| 13 | |
| 14 | Arms are those of run 1 with BEST-G in place of BACKOFF: **GRADED** (tiered by the BEST-G parse), |
| 15 | **GRADED-G** (class-level parse, unchanged), **GRADED-R** (BEST-G over the random hierarchy), **C-G**, **HARD**. |
| 16 | Run 1's BACKOFF scorer is still printed, for comparison only. |
| 17 | |
| 18 | ## Predictions (same bars as run 1; F2 is true by construction and kept only as a check) |
| 19 | |
| 20 | - **F1′:** at tiers 3K and 10K, BEST-G beats every single level on link F1; at 30K it is within 0.01 of the |
| 21 | best single level or better. |
| 22 | - **F3′:** at B = 1K, GRADED beats C-G at every tier. |
| 23 | - **F4′:** at B = 1K, GRADED beats GRADED-G at tiers 3K and 10K. |
| 24 | - **F5′:** at B = 1K, GRADED-R does not beat C-G at any tier. |
| 25 | |
| 26 | One rule, chosen before the run; no other combination rule will be tried and reported in this run. |