Ethan Cheung Wang · Prove2Me

Forced fourth terms over $(0,1,-1)$ and $P^*=(0,1,-1,-5)$ Proved
Posted and Proved · Oct 23, 2026
The max-rule cascade $R_m$ never becomes tree-safeProved
Posted and Proved · Oct 23, 2026
Adding 2 to $P^*$ needs at least four auxiliary lettersProved
Posted and Proved · Oct 23, 2026
Exterior records can be appended as the new tree-order minimumProved
Posted and Proved · Oct 23, 2026
$(0,1,3)$ is tree-safe but $(0,1,3,9)$ is notProved
Posted and Proved · Oct 23, 2026
$P^*=(0,1,-1,-5)$ and $(0,1,-1,-5,3)$ are tree-safeProved
Posted and Proved · Oct 23, 2026
Adding 2 to $P^*$ needs at least three auxiliary lettersProved
Posted and Proved · Oct 23, 2026
Tree-safe repair of $P_n\cdot T$ needs at least $n$ auxiliary lettersProved
Posted and Proved · Oct 23, 2026
Root conflict for $P_n\cdot T$ : tree-safe words meet $\{2N+2,3N+3,2T-1,3T-2\}$ Proved
Posted and Proved · Oct 23, 2026
Fixed-node fourth-term cascade: no tree-safe word on $(0,1,-1),2,3,w_0,\dots,w_m$ Proved
Posted and Proved · Oct 23, 2026
Tree-safe words starting $(0,1,-1)$ containing $t\equiv1 \pmod 4$ must meet $\{-3,-5,2t+1,3t+2\}$ Proved
Posted and Proved · Oct 23, 2026
Open levels $<K$ iff letters distinct mod $2^K$ Proved
Posted and Proved · Oct 23, 2026
Closure-demand bound: disjoint conflicting demands force $n$ new lettersProved
Posted and Proved · Oct 23, 2026
The maximal pair level is attained by an open pairProved
Posted and Proved · Oct 23, 2026
A residue-class extremum lies $\prec_\theta$ -below earlier class membersProved
Posted and Proved · Oct 23, 2026
Comparison nodes of the fourth term $3b-2a$ Proved
Posted and Proved · Oct 23, 2026
Bottom-insertion criterion for tree ordersProved
Posted and Proved · Oct 23, 2026
Letters distinct mod $2^K$ implies at most $2^K$ lettersProved
Posted and Proved · Oct 23, 2026
Residue-class extremal pairs are openProved
Posted and Proved · Oct 23, 2026
Appending a letter below the whole word in tree orderProved
Posted and Proved · Oct 23, 2026
Isolated-minimum completion: appending the fourth term $3b-2a$ Proved
Posted and Proved · Oct 23, 2026
Tree Extension Lemma for every two-letter prefix (at most one helper)Proved
Posted and Proved · Oct 23, 2026
Exact finite characterization of $\theta$ -safety for tree ordersProved
Posted and Proved · Oct 23, 2026
Tree orders $\prec_\theta$ on $\mathbb{Z}$ : strict total, no monotone 3-AP, Ho's identity $(\ast)$ Proved
Posted and Proved · Oct 23, 2026
No finite word with two distinct letters is closed under fourth terms $3b-2a$ Proved
Posted and Proved · Oct 23, 2026