THE FOLD / GLITCH / THE BLUE SCREEN / THE MUTATOR THAT MOVED EVERYTHING
THE MUTATOR THAT MOVED EVERYTHING
a shift that shifts nothing that matters
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
To test whether an assertion depends on its subject, perturb the subject and see whether the answer moves. The first attempt bumped every number by one at once. That leaves equality untouched — 6 == 6 becomes 7 == 7 — so a perfectly sensitive assertion was reported as insensitive. A mutation that moves everything moves nothing that matters.
LIT verified live over 2,000 random pairs and six predicate forms. A global +1 leaves 3 of 6 completely unmoved:
LIT verified live over 2,000 random pairs and six predicate forms. A global +1 leaves 3 of 6 completely unmoved:
a == b, a < b and a − b. Asked the right way — one field at a time, both directions, on assertions that actually hold — 5 of 6 forms are reached at 100%. The exception is strict ordering, which a ±1 nudge flips only when the operands are adjacent: 9.1% measured against 10.0% predicted by counting adjacent pairs.2 HOW IT WAS WEAVED · AI + HUMAN
David (human) found and named it: “the first mutator bumped EVERY number by one at once. that preserves every equality (6==6 becomes 7==7) and every ratio, so it reported correct assertions as insensitive. a mutator that moves everything moves nothing that matters. one field at a time now, and sensitive if ANY single perturbation moves the answer.”
AVAN (AI) should correct one clause of that note and add one finding to it. A ratio is not shift-invariant —
AVAN (AI) should correct one clause of that note and add one finding to it. A ratio is not shift-invariant —
a/b moves under a global +1 about 94.6% of the time, and is preserved only in the special case a == b where the ratio is 1. And the repaired mutator has a limit the note does not state: a fixed ±1 step reaches an assertion only within its margin, so a wide inequality is simply out of range. That reach is exactly predictable, and predicting it is the honest way to report a probe’s power.3 ONE DIMENSION
Six forms, two mutators.
4 TWO DIMENSIONS · INTERACTIVE
Shift everything, or nudge one field, and see what survives.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the diagonal a global shift travels along.
AVAN’s addition (the inverse-companion): the forward reading is “perturb one field at a time.” The inverse is that a global shift is invisible precisely because it is the symmetry the assertions were written in. Equality, ordering and difference are all translation-invariant, so moving along that direction is moving inside the space the predicate cannot see — and every useful predicate has such a direction. Read backwards, a mutator is only as good as its choice of direction, and the directions that reveal nothing are exactly the ones the code was designed not to care about.
LIT over 2,000 random pairs and six predicate forms, a global +1 leaves 3 of 6 completely unmoved - a == b, a < b and a - b; asked the right way, one field at a time in both directions on assertions that hold, 5 of 6 forms are reached at 100%; and the exception is strict ordering, which a plus-or-minus-one nudge flips only when the operands are adjacent, measured at 9.1% against 10.0% predicted by counting adjacent pairs
FIG David found and named it: 'the first mutator bumped EVERY number by one at once. that preserves every equality (6==6 becomes 7==7) and every ratio, so it reported correct assertions as insensitive. a mutator that moves everything moves nothing that matters.' AVAN corrects one clause and adds one finding. A RATIO IS NOT shift-invariant - a/b moves under a global +1 about 94.6% of the time, and is preserved only in the special case a == b where the ratio is 1. And the repaired mutator has a limit the note does not state: a fixed step reaches an assertion only within its MARGIN, so a wide inequality is out of range. That reach is exactly predictable, and predicting it is the honest way to report a probe's power.
FIG David found and named it: 'the first mutator bumped EVERY number by one at once. that preserves every equality (6==6 becomes 7==7) and every ratio, so it reported correct assertions as insensitive. a mutator that moves everything moves nothing that matters.' AVAN corrects one clause and adds one finding. A RATIO IS NOT shift-invariant - a/b moves under a global +1 about 94.6% of the time, and is preserved only in the special case a == b where the ratio is 1. And the repaired mutator has a limit the note does not state: a fixed step reaches an assertion only within its MARGIN, so a wide inequality is out of range. That reach is exactly predictable, and predicting it is the honest way to report a probe's power.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE BLUE SCREEN · David Lee Wise (ROOT0), with AVAN