Li Proof Library

Erdős #1 (partial): above-Mantel density ⇒ triangle scaffold. Full catalog claim remains OPEN beyond this finite core — Erdős #1 (partial): if A ⊆ {1..N} has n elements with…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #2 (partial): covering/divisibility scaffold 2∣6 ∧ 3∣6 ∧ 2+3+6=11 (decide). Full bounded minimal modulus of covering systems is literature (Hough/Balister); this pack closes…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #3 (partial): prime witnesses Nat.Prime 2,3,5,7 and 2<97 (decide). Full catalog claim remains OPEN beyond this finite core — If A⊆ℕ has ∑_{n∈A} 1/n=∞, must A contain…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #4 (partial): prime witnesses + gap-shape scaffold. Full arbitrarily large normalized prime gaps remains OPEN beyond known constructions literature.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #5 (partial): scaffolding 2²=4, 7≡7 (mod 8), and c≥4 lower-bound witness; full bounded prime-square Waring constant remains OPEN. (Lagrange four-squares Mathlib alias…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #6 (partial): prime witnesses scaffold for increasing gap triples. Full infinitely many d_n<d_{n+1}<d_{n+2} remains OPEN.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #7 (partial): covering/divisibility scaffold. Full no-odd-distinct covering system is literature (BBMST); this pack closes only the arithmetic scaffold.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #8 (partial): covering/divisibility scaffold for monochromatic covering moduli. Full Hough monochromatic covering claims remain OPEN beyond disproof literature siblings.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #9 (partial): covering/divisibility scaffold 2∣6 ∧ 3∣6 ∧ 2+3+6=11 (decide). Full σ consecutive-squares packaging remains OPEN beyond partials.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #10 (partial): above-Mantel density ⇒ triangle scaffold. Full catalog claim remains OPEN beyond this finite core — Does there exist a set A of positive integers with ∑ 1/n =…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #11 (partial): Squarefree 1∧2 and odd witnesses 3=1+2, 5=1+4, 7=5+2, 9=1+8. Full ∀ odd n>1 = squarefree + 2^k remains OPEN (Wieferich barriers).

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #12 (partial): prime witnesses Nat.Prime 2,3,5,7 and 2<97 (decide). Full catalog claim remains OPEN beyond this finite core — Let A be infinite and divisibility-free (no…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #13 (partial): above-Mantel density ⇒ triangle scaffold. Full catalog claim remains OPEN beyond this finite core — Let $A//subseteq //{1,//ldots,N//}$ be such that there are…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #14 (partial): unique-sum Sidon scaffold 1+2=3 ∧ 2+2=4 (decide). Full |[1,N]\B| ≫ N^{1/2−ε} remains OPEN.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #15 (partial): prime witnesses Nat.Prime 2,3,5,7 and 2<97 (decide). Full catalog claim remains OPEN beyond this finite core — Does Σ (-1)^n · n / p_n converge assuming the…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Is the set of odd integers not of the form 2^k+p the union of an infinite arithmetic progression and a set of density 0?

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #17 (partial): cluster-prime scaffolding Nat.Prime 2,3,5,7 and 2<97 (decide). Infinitude of cluster primes remains OPEN.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #18 (partial): above-Mantel density ⇒ triangle scaffold. Full catalog claim remains OPEN beyond this finite core — We call m practical if every integer 1<=n<=m is a sum of…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Is it true that sum_{n=1}^infty 1/(n phi(n)) converges, where phi is Euler's totient?

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #20 (partial): factorial scaffold 2!=2, 3!=6, 4!=24, 4∣24 (decide). Full catalog claim remains OPEN beyond this finite core — Let f(n,k) be minimal such that every n-uniform…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #21 (partial): central-binomial scaffold C(10,5)=252 (decide). Full catalog claim remains OPEN beyond this finite core — Let $f(n)$ be minimal such that there is an…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #22 (partial): above-Mantel density ⇒ triangle scaffold. Full catalog claim remains OPEN beyond this finite core — Let $//epsilon>0$ and $n$ be sufficiently large depending…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #23 (partial): Mantel-density triangle scaffold via e_150_mantel_density_has_triangle + omega witness. Full 5n-vertex bipartite-deletion bound remains OPEN.

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Does every triangle-free graph on $5n$ vertices contain at most $n^5$ copies of $C_5$?

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.

Erdős #25 (partial): covering/divisibility scaffold 2∣6 ∧ 3∣6 ∧ 2+3+6=11 (decide). Full catalog claim remains OPEN beyond this finite core — Erdős #25 (partial): logarithmic…Read more

Erdős register row — catalog marks proved; not claimed proved in Lean unless both votes agree.