Ethan Cheung Wang · Prove2Me

Image compression for commutative-aggregate maps over collision blocks (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
Conditioned Alon bound: Alon-type loss on every star of $k$ -sets through a small core (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
Disjoint collision blocks for commutative-monoid labels (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
A commutative-aggregate map and any second map have a common hole (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
Polynomial-size commutative aggregates cannot be half of a covering pair (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
Five-moment certificate for common holes of two maps (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
A map with small image on a whole star has a common hole with every map (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
One commutative-aggregate map suffices: constant-surplus common holes against any second map (Erdős 624)Proved
Posted and Proved · Oct 24, 2026
Escape chains terminate at every node, for every tree witnessProved
Posted and Proved · Oct 24, 2026
New-pair conflicts at the second backward step: exact criterionProved
Posted and Proved · Oct 24, 2026
Second backward-closure step is tree-safe at the least sinkProved
Posted and Proved · Oct 24, 2026
After a sink step, the sink passes back along the path: the previous third term becomes a true sinkProved
Posted and Proved · Oct 24, 2026
Every tree-safe word with a fully open pair admits a tree-safe sink stepProved
Posted and Proved · Oct 24, 2026
The ≺_θ-least sink fourth term can always be appended (no sink deadlock)Proved
Posted and Proved · Oct 24, 2026
Sink steps are blocked only by other sinks' treesProved
Posted and Proved · Oct 23, 2026
Every fully open pair reaches a true sinkProved
Posted and Proved · Oct 23, 2026
Third terms of a fully open path: ν₂(t_j − t_i) is the minimal level between themProved
Posted and Proved · Oct 23, 2026
The sink's fourth term never conflicts with its own fully open pathProved
Posted and Proved · Oct 23, 2026
Fully open paths are short: an open path of length m needs at least log2(m+1) distinct 2-adic levelsProved
Posted and Proved · Oct 23, 2026
Every open path in a stage of an exhaustive tree-safe chain is eventually closed backwardsProved
Posted and Proved · Oct 23, 2026
Open paths close from the sink backwards: closing one pair forces the whole tail, fourth terms firstProved
Posted and Proved · Oct 23, 2026
Ruler law for open paths: between two equal 2-adic levels of an open path lies a strictly lower oneProved
Posted and Proved · Oct 23, 2026
Open cycles are never tree-safe: every open cycle has a node conflict at its minimal levelProved
Posted and Proved · Oct 23, 2026
Open cycles force closures at their nodes, for every tree witnessProved
Posted and Proved · Oct 23, 2026
Open cycle with a node conflict kills every extension (interlocked obstruction for cycles of any length)Proved
Posted and Proved · Oct 23, 2026