For the author of scripts/degree6_independent_replication.py, or another party — not for us. Small, mechanical, and deliberately not done by the side being checked.
The gap
The P2 manuscript closes the historical complexity range twice:
- Result F (§6.5): degree ≤ 6 at height ≤ 3.
409,584 polynomials per interval. Has an independent second implementation, agreeing cell by cell across all 24 interval-by-degree cells (Table 9).
- Result F′ (§6.6): degree ≤ 6 at height ≤ 4.
2,351,328 polynomials per interval. Single implementation.
Result F′ is the one that carries the paper's closing sentence, because Ziff's A-lattice quintic has height 4 and height ≤ 3 does not in fact cover the record. So the replication currently covers the weaker of the two results.
Why we did not just do it ourselves
scripts/degree6_independent_replication.py already parameterizes almost everything by height — _enumerate_degree, class_size, _degree_polynomials and run_search all take a height argument, and only the artifact field at line ~274 hardcodes HEIGHT. Threading it is perhaps twenty minutes.
We did not do it because the replication's value is that it was written by another party against the frozen protocol and committed unchanged. An edit by us, to make it cover a class we chose later, would have to be disclosed as such — which costs more than it buys. It is worth asking its author for.
The task
- Thread
height through to the artifact field, so coefficient_height_max reports the argument rather than the module constant.
- Run all four intervals at height 4 and commit the artifacts.
- Extend
scripts/degree6_implementation_agreement.py to compare at height 4 as well, including the residual / mean-value check — that is the part that rules out the two implementations agreeing by both being trivially empty.
What to expect
Both should exclude on all four intervals, with the certified screen retaining zero candidates at every degree. Class sizes by degree, independently counted:
d=1: 23 d=2: 265 d=3: 2,639
d=4: 24,913 d=5: 229,703 d=6: 2,093,785 total 2,351,328
The closest member of the whole class sits 8.70e-9 from the nearest interval — a margin of 54 interval widths at its narrowest, against 5.8e2 at height 3. One extra unit of height cost an order of magnitude of approach resolution, which is itself worth confirming independently.
Cost: about 12 s per interval at height 3, so roughly 70 s per interval at height 4, ~5 minutes in all.
Watch the CI budget
The Python 3.9 job is the binding constraint on this suite (see docs/manuscripts/p2-algebraic-exclusion/README.md, "Decisions taken while drafting"). The existing replication test recensuses one interval — the narrowest, carrying Result A — and covers the other three through the agreement check. Do the same at height 4 rather than adding four rebuilds.
Done looks like
- Four
results/pslq-degree6-height4-replication-*/latest.json artifacts.
- The agreement artifact covering both heights, cells in agreement reported for each.
manuscript.md §6.6 "Replication." paragraph rewritten — it currently says the replication does not reach this class — and §7's second "Recommended, not done" bullet removed.- Any disagreement reported as a disagreement rather than reconciled.
For the author of
scripts/degree6_independent_replication.py, or another party — not for us. Small, mechanical, and deliberately not done by the side being checked.The gap
The P2 manuscript closes the historical complexity range twice:
409,584polynomials per interval. Has an independent second implementation, agreeing cell by cell across all 24 interval-by-degree cells (Table 9).2,351,328polynomials per interval. Single implementation.Result F′ is the one that carries the paper's closing sentence, because Ziff's A-lattice quintic has height 4 and height ≤ 3 does not in fact cover the record. So the replication currently covers the weaker of the two results.
Why we did not just do it ourselves
scripts/degree6_independent_replication.pyalready parameterizes almost everything by height —_enumerate_degree,class_size,_degree_polynomialsandrun_searchall take aheightargument, and only the artifact field at line ~274 hardcodesHEIGHT. Threading it is perhaps twenty minutes.We did not do it because the replication's value is that it was written by another party against the frozen protocol and committed unchanged. An edit by us, to make it cover a class we chose later, would have to be disclosed as such — which costs more than it buys. It is worth asking its author for.
The task
heightthrough to the artifact field, socoefficient_height_maxreports the argument rather than the module constant.scripts/degree6_implementation_agreement.pyto compare at height 4 as well, including the residual / mean-value check — that is the part that rules out the two implementations agreeing by both being trivially empty.What to expect
Both should exclude on all four intervals, with the certified screen retaining zero candidates at every degree. Class sizes by degree, independently counted:
The closest member of the whole class sits
8.70e-9from the nearest interval — a margin of 54 interval widths at its narrowest, against5.8e2at height 3. One extra unit of height cost an order of magnitude of approach resolution, which is itself worth confirming independently.Cost: about 12 s per interval at height 3, so roughly 70 s per interval at height 4, ~5 minutes in all.
Watch the CI budget
The Python 3.9 job is the binding constraint on this suite (see
docs/manuscripts/p2-algebraic-exclusion/README.md, "Decisions taken while drafting"). The existing replication test recensuses one interval — the narrowest, carrying Result A — and covers the other three through the agreement check. Do the same at height 4 rather than adding four rebuilds.Done looks like
results/pslq-degree6-height4-replication-*/latest.jsonartifacts.manuscript.md§6.6 "Replication." paragraph rewritten — it currently says the replication does not reach this class — and §7's second "Recommended, not done" bullet removed.