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Handle null reduced actions with an absolute derivative floor

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This commit is contained in:
Emily Boudreaux
2026-09-17 09:45:56 -04:00
parent c393847c6f
commit 4ae2f3f134
3 changed files with 19 additions and 4 deletions
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6
experiments/check_numerical_strategies.py
View File

@@ -246,7 +246,8 @@ class Assessment:
continue
alpha, error, relative, floor = (number(row, key) for key in ("alpha", "difference_quotient_error", "relative_error", "residual_subtraction_roundoff_scale"))
valid.append((alpha, error, relative, floor))
self.check(f"reduced_fd_{alpha:g}_finite", all(nonnegative(x) for x in (error, relative, floor)))
self.check(f"reduced_fd_{alpha:g}_finite", all(nonnegative(x) for x in (error, floor)) and
(nonnegative(relative) or abs(action) <= roundoff(action)))
self.check(f"reduced_fd_{alpha:g}_completed_sides", all(nonnegative(number(row, key)) and number(row, key) <= tolerance for key in ("plus_gravity_norm", "minus_gravity_norm")))
if error > 20.0 * floor:
reliable.append((alpha, error))
@@ -254,7 +255,8 @@ class Assessment:
if not valid:
self.incomplete("reduced_central_difference_available", reason="No pair completed on both sides")
return
self.check("reduced_central_difference_accuracy", min(item[2] for item in valid) <= 1e-5,
self.check("reduced_central_difference_accuracy", any(
(nonnegative(item[2]) and item[2] <= 1e-5) or item[1] <= 20.0 * item[3] for item in valid),
minimum_relative_error=min(item[2] for item in valid), tolerance=1e-5)
reliable.sort(reverse=True)
orders = [math.log(b[1] / a[1]) / math.log(b[0] / a[0]) for a, b in zip(reliable, reliable[1:]) if a[0] != b[0]]

5
experiments/check_numerical_strategies_README.md
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@@ -33,8 +33,9 @@ can vanish.
Reduced probes must satisfy the freshly prepared gravity completion tolerance,
the lifted gravity tangent gate, and agreement of the Schur action with the
retained part of the full lifted action. Central differences must reach relative
error at most 1e-5 and show a resolved interval with order at least 1.5, or reach
the recorded residual-subtraction scale. A plateau above that scale is incomplete
error at most 1e-5 or an absolute error within the recorded residual-subtraction
scale. They must also show a resolved interval with order at least 1.5, or reach
that scale. Relative error is not meaningful for a null action. A plateau above that scale is incomplete
evidence rather than an automatic claim of a bad Jacobian: the retained-residual
amplification of the remaining gravity error has not been bounded. The recorded
roundoff scales are heuristics, not rigorous forward-error bounds.

12
experiments/test_check_numerical_strategies.py
View File

@@ -140,6 +140,18 @@ class NumericalStrategyChecks(unittest.TestCase):
report, code = assess(self.folder, required=("gravity",))
self.assertEqual(code, 2, report)
def test_null_reduced_action_uses_absolute_arithmetic_floor(self):
summary, _, _, _, differences = gravity_fixture(self.folder)
summary["reduced_action_norm"] = 0.0
summary["lifted_retained_action_difference"] = 0.0
for row in differences:
row["difference_quotient_error"] = row["residual_subtraction_roundoff_scale"] * .1
row["relative_error"] = float("inf")
write_metrics(self.folder, "numerical_strategy_summary.csv", summary)
write_rows(self.folder, "numerical_strategy_reduced_derivative.csv", differences)
report, code = assess(self.folder)
self.assertEqual(code, 0, report)
def test_unfinished_restoration_record_is_incomplete(self):
summary, _, _, _, _ = gravity_fixture(self.folder)
del summary["accepted_state_change"]