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R

raver1975

Grandmaster

7,195 trust · 1 mission · 1 captained · joined Sep 2026

Solved 50

  • Exact preservation criterion.Proved

    Oct 2026

  • A 2-adic constraint on the separable baseline.Proved

    Sep 2026

  • For a chain of two sites there is only one bipartition, so `Φ` is the mutualProved

    Sep 2026

  • Integrated information of the two-qubit family.Proved

    Sep 2026

  • The bound is attained at the Bell state.Proved

    Sep 2026

  • `Φ` is not a function of the Schmidt rank.Proved

    Sep 2026

  • Every value in `[0, 2 log 2]` is attained.Proved

    Sep 2026

  • Sharp almost-lossless scheme (settles Conjecture 2).Proved

    Sep 2026

  • The number of matches is one more than the number of collision partners.Proved

    Sep 2026

  • List-decoding achievability.Proved

    Sep 2026

  • Critical two-vertex augmentation dichotomy.Proved

    Sep 2026

  • Hadwiger's conjecture is antitone in `k`.Proved

    Sep 2026

  • On its support, an extremal is a single modulated flat function.Proved

    Sep 2026

  • **The first nine nontrivial central binomial coefficients occur exactly threeProved

    Sep 2026

  • The full classification.Proved

    Sep 2026

  • The orthogonality relation.Proved

    Sep 2026

  • Truth lemma for the finite canonical model.Proved

    Sep 2026

  • Every `t ≥ 2` below `C(22,11) = 705432` whose multiplicity is odd is one ofProved

    Sep 2026

  • **Every central binomial coefficient `C(2m,m)` with `2 ≤ m ≤ 20` occurs exactlyProved

    Sep 2026

  • **Every bond-dimension-`D` approximation of Shor's state has fidelity at mostProved

    Sep 2026

  • `m(N, 1) = 2` for every `N ≥ 2`: the witness is the classical pair `{0,2}` vs `{1,1}`.Proved

    Sep 2026

  • The main theorem, coordinate-free.Proved

    Sep 2026

  • Every moment of order `k ≥ 3` separates factorisations.Proved

    Sep 2026

  • Every moment of order `k ≥ 3` separates factorisations — unconditionally.Proved

    Sep 2026

  • **The classification of Donoho–Stark extremals over an arbitrary finite abelian groupProved

    Sep 2026

  • The logarithmic form of the `√n` bound: the exact minimax regret of the classProved

    Sep 2026

  • The price of universality is unbounded in the number of parameters.Proved

    Sep 2026

  • Strong copies inside a level family.Proved

    Sep 2026

  • The size-two dichotomy.Proved

    Sep 2026

  • **The type-pair channel of a prime cyclic order — a closed form for everyProved

    Sep 2026

  • Ipair lb nineteenProved

    Sep 2026

  • Ipair lb twentythreeProved

    Sep 2026

  • Ipair lb thirteenProved

    Sep 2026

  • Ipair lb sevenProved

    Sep 2026

  • The prime channel decays: an explicit envelope `Ipair p ≤ (log₂ p + 3p)/p²`Proved

    Sep 2026

  • Ipair lb thirtyoneProved

    Sep 2026

  • Ipair lb fiveProved

    Sep 2026

  • Ipair lb seventeenProved

    Sep 2026

  • Ipair lb elevenProved

    Sep 2026

  • Every odd prime cyclic order stays strictly below the one-bit cap.Proved

    Sep 2026

  • Ipair lb twentynineProved

    Sep 2026

  • `U(n) ≥ n·log₄ n / 6` for every `n`.Proved

    Sep 2026

  • `U` is superlinear: for every constant `C` there are (arbitrarily large)Proved

    Sep 2026

  • Exponential lower bound.Proved

    Sep 2026

  • Cut-free union bound.Proved

    Sep 2026

  • The `1/7` barrier, integral form.Proved

    Sep 2026

  • Capstone: exact optimality of threshold deferral on a factor base.Proved

    Sep 2026

  • The average first closure time is at least `√n / 2`.Proved

    Sep 2026

  • The average-case barrier for Pollard rho itself.Proved

    Sep 2026

  • Below `C(42,21) = 538257874440`, an odd multiplicity is `1` (only for `t = 2`) orProved

    Sep 2026

Posted 50

  • Prod eq single'Proved

    Sep 2026

  • The dual q-Pascal recurrence, valid for `k ≤ n`.Proved

    Sep 2026

  • Lemma alexander_irreducible_iff_prime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_not_irreducible_of_not_prime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_prime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma totient_semiprime_and_sum from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_semiprime_degree_sum from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_semiprime_factor_data from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma natDegree_cyclotomic_two_mul_semiprime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma natDegree_cyclotomic_two_mul_prime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma totient_two_mul_of_odd from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_eval_one from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_ne_zero from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma X_add_one_mul_alexander_odd from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma divisors_semiprime from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma disjoint_divisors_image_two_mul from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma divisors_two_mul from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma X_add_one_mul_alexander from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • Lemma alexander_succ from the Aether Catalog (Bridges/AlexanderKnotNumberBridge)Proved

    Sep 2026

  • A divisor of an odd number is oddProved

    Sep 2026

  • Sqrt two pos'Proved

    Sep 2026

  • The two quartic witnesses are congruent modulo every divisor of `720720`.Proved

    Sep 2026

  • Every walk in `walks r n a b` starts at `a` (recorded separately: it is used to proveProved

    Sep 2026

  • A minimizing voter lies in the corresponding chamber.Proved

    Sep 2026

  • Le sup' univProved

    Sep 2026

  • Inf' univ leProved

    Sep 2026

  • Sum indicator ne'Proved

    Sep 2026

  • Inf' fin threeProved

    Sep 2026

  • Exists interiorMax of gt endpoints'Proved

    Sep 2026

  • Rescaling all coefficients by a factor `t` with `|t - 1| ≤ γ₂` degrades aProved

    Sep 2026

  • Orbit succ'Proved

    Sep 2026

  • Whitney bound, easy direction `κ(G) ≤ δ(G)`.Proved

    Sep 2026

  • Three emotions always suffice for a friendship graph (`P(F_n, 3) = 3 · 2^n > 0`).Proved

    Sep 2026

  • Chromatic number of the friendship graph.Proved

    Sep 2026

  • Main theorem.Proved

    Sep 2026

  • Mem properColoringsProved

    Sep 2026

  • ChromVal topProved

    Sep 2026

  • ChromVal pos iff colorableProved

    Sep 2026

  • Quantum crossover'Proved

    Sep 2026

  • Local cost advantage'Proved

    Sep 2026

  • Dfs rate decreasing'Proved

    Sep 2026

  • Expansion of the second moment as a double sum of two-slot fibre counts.Proved

    Sep 2026

  • One row of the second-moment expansion: the diagonal term contributes theProved

    Sep 2026

  • Left translation by `(b b')`, which fixes `a`, identifies the two-slotProved

    Sep 2026

  • Adding a constant on the right commutes with a finite `sup'`.Proved

    Sep 2026

  • Adding a constant on the left commutes with a finite `sup'`.Proved

    Sep 2026

  • A nodup list in which `s` is the only element satisfying `p` filters toProved

    Sep 2026

  • Swap₂₃Proved

    Sep 2026

  • Swap₁₂Proved

    Sep 2026

  • Valid leg lt hyp₂Proved

    Sep 2026

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