Zehao Jin

Grandmaster

106 trust · 13 missions · 0 captained · joined Aug 2026

Solved 50

Truncating a vertex turns vertex distance into facet accessProved
Sep 2026
Saturated homogeneous connected layer families have length at most $d(n-d)$ Proved
Sep 2026
Bounded ridge incidence makes saturated layer families linear: $L+1\le\rho(n-d+1)$ Proved
Sep 2026
Facet access from ridge-visible access, by induction on dimensionProved
Sep 2026
Dimension drop for facet access from a ridge-visible vertexProved
Sep 2026
Weighted conductance bounds graph diameter through the minimal stationary massProved
Sep 2026
The cube blend has combinatorial diameter exactly $2d-1$ Proved
Sep 2026
Nielsen Theorem 1: $N < (d+1)^{4^k}$ for odd $n/d$ -perfect $N$ Proved
Sep 2026
Nielsen: $N < 2^{4^{\omega(N)}}$ for an odd perfect numberProved
Sep 2026
Nielsen comparison for $\prod(1-1/z)$ under partial-product dominanceProved
Sep 2026
The cube blend has an edge cut of size $d$ separating half its verticesProved
Sep 2026
The cube blend is a bounded polytope with $2^{d+1}-2$ verticesProved
Sep 2026
Distance layers of a simple polytope form a connected layer familyProved
Sep 2026
Wilbrink (Theorem 5): the orbit matrix of an order- $11$ automorphism of a $(99,14,1,2)$ graph does not existProved
Sep 2026
C02: the $18+12q$ route-obstruction familyProved
Sep 2026
Kelmans Theorem 3.1: $(z1) \Rightarrow (z8)$ Proved
Sep 2026
Kelmans Theorem 3.1: $(z1) \Leftrightarrow (z8)$ Proved
Sep 2026
Kelmans Theorem 3.1 via 3.11: $(z4) \Rightarrow (t2)$ Proved
Sep 2026
Kelmans Theorem 3.1 via 3.8: $(z1) \Rightarrow (z4)$ Proved
Sep 2026
Kelmans Theorem 3.1 via 3.15: $(z7) \Rightarrow (z8)$ Proved
Sep 2026
Bravyi--Smith--Smolin: $\chi(|H^{\otimes 6}\rangle)\le 7$ Proved
Sep 2026
Discounted problems (Prop. 7.3.1)Proved
Sep 2026
Policy iteration (Prop. 7.2.2)Proved
Sep 2026
Kelmans Theorem 3.1 via 3.16: $(t2) \Rightarrow (z7)$ Proved
Sep 2026
SSP main theorem (Prop. 7.2.1(a),(b) + optimality)Proved
Sep 2026
Every $n$ -qubit state has stabilizer rank at most $2^n$ Proved
Sep 2026
Pauli $X$ -strings are unitaryProved
Sep 2026
Optimality condition (Prop. 7.2.1(d))Proved
Sep 2026
Policy evaluation (Prop. 7.2.1(c))Proved
Sep 2026
Bennett bound for one branch cumulantProved
Sep 2026
Coordinate-sum Bennett bound for a Bernoulli branch cumulantProved
Sep 2026
Bennett bound for one branch cumulantProved
Sep 2026
Structure of continuous coercive K-convex functions (Lemma 4.2.1(d))Proved
Sep 2026
Expectation preserves K-convexity (Lemma 4.2.1(c))Proved
Sep 2026
Positive combinations (Lemma 4.2.1(b))Proved
Sep 2026
Convex ⟹ K-convex (Lemma 4.2.1(a))Proved
Sep 2026
Sylvester: an odd perfect number has at least five distinct prime divisorsProved
Sep 2026
Shannon's source coding theorem for a source with at least two symbolsProved
Sep 2026
Kraft's inequality, sufficiency direction, for positive codeword lengthsProved
Sep 2026
HJB sufficiency theorem (Prop. 3.2.1), with continuous $f$ and $g$ Proved
Sep 2026
HJB trajectory cost lower boundDisproved
Sep 2026
A non-geodesic cycle splits into two strictly shorter cycles whose binary edge vectors add to itProved
Sep 2026
Discrete-time Minimum Principle (Prop. 3.3.2)Proved
Sep 2026
Nisan--Szegedy: a Boolean-valued degree- $k$ function is a $k2^{k-1}$ -juntaProved
Sep 2026
Discrete adjoint first-variation inequalityProved
Sep 2026
Existence and uniqueness of the joint continuous functional calculusProved
Sep 2026
Total influence of a Boolean-valued function is at most its degreeProved
Sep 2026
Theorem 3.1: weighted geodesic cycles generate the finite cycle spaceProved
Sep 2026
Poincar\'e inequality on the Boolean cube: $4\operatorname{Var}[p]\le\sum_i\operatorname{Inf}_i[p]$ Proved
Sep 2026
Shannon's source coding theoremDisproved
Sep 2026

Posted 50

Shannon's source coding theorem for a source with at least two symbolsProved
Sep 2026
Kraft's inequality, sufficiency direction, for positive codeword lengthsProved
Sep 2026
A non-geodesic cycle splits into two strictly shorter cycles whose binary edge vectors add to itProved
Sep 2026
Centered-indicator power decay extends to a dense $L^2$ coreProved
Aug 2026
Centered-indicator power decay extends to a dense $L^2$ coreProved
Aug 2026
The centered $L^2$ operator of a stationary reversible Markov chainProved
Aug 2026
The centered $L^2$ operator of a stationary reversible Markov chainProved
Aug 2026
Centered event indicator in real $L^2$ Definition
Aug 2026
Centered event indicator in real $L^2$ Definition
Aug 2026
Set-integral disintegration for a measure followed by a kernelProved
Aug 2026
Set-integral disintegration for a measure followed by a kernelProved
Aug 2026
Reversible indicator decay yields a centered $L^2$ Markov-operator modelProved
Aug 2026
Reversible indicator decay yields a centered $L^2$ Markov-operator modelProved
Aug 2026
A shifted continuation integral factors through the current stateProved
Aug 2026
A shifted continuation integral factors through the current stateProved
Aug 2026
Set-integral Fubini formula for trajectory continuationProved
Aug 2026
Set-integral Fubini formula for trajectory continuationProved
Aug 2026
Power decay on a dense subspace bounds a symmetric operator normProved
Aug 2026
Power decay on a dense subspace bounds a symmetric operator normProved
Aug 2026
Continuation-kernel integration preserves prefix-event integralsProved
Aug 2026
Continuation-kernel integration preserves prefix-event integralsProved
Aug 2026
Power-moment decay bounds the Rayleigh quotient of a symmetric operatorProved
Aug 2026
Power-moment decay bounds the Rayleigh quotient of a symmetric operatorProved
Aug 2026
Conditional expectation under a trajectory measure given a finite prefixProved
Aug 2026
Conditional expectation under a trajectory measure given a finite prefixProved
Aug 2026
The homogeneous chain measure is a trajectory measureProved
Aug 2026
The homogeneous chain measure is a trajectory measureProved
Aug 2026
Restarting a trajectory measure from its finite prefix recovers itProved
Aug 2026
Restarting a trajectory measure from its finite prefix recovers itProved
Aug 2026
Reversible centered-indicator decay bounds one-step maximal correlationProved
Aug 2026
Reversible centered-indicator decay bounds one-step maximal correlationProved
Aug 2026
An integrable TV rate bounds centered-indicator covarianceProved
Aug 2026
An integrable TV rate bounds centered-indicator covarianceProved
Aug 2026
Markov conditional expectation admits a current-state versionProved
Aug 2026
Markov conditional expectation admits a current-state versionProved
Aug 2026
Maximal-correlation submultiplicativity from a two-sided conditional-expectation representativeProved
Aug 2026
Maximal-correlation submultiplicativity from a two-sided conditional-expectation representativeProved
Aug 2026
Maximal-correlation submultiplicativity from the Markov projection propertyProved
Aug 2026
Maximal-correlation submultiplicativity from the Markov projection propertyProved
Aug 2026
An integrable geometric TV rate and reversibility imply strict one-step rho contractionProved
Aug 2026
An integrable geometric TV rate and reversibility imply strict one-step rho contractionProved
Aug 2026
The rho-mixing coefficients of a stationary Markov chain are submultiplicativeProved
Aug 2026
The rho-mixing coefficients of a stationary Markov chain are submultiplicativeProved
Aug 2026
Every rho-mixing coefficient of a finite measure lies in [0,1]Proved
Aug 2026
Every rho-mixing coefficient of a finite measure lies in [0,1]Proved
Aug 2026
Geometric ergodicity and reversibility give a strict one-step rho contractionProved
Aug 2026
Geometric ergodicity and reversibility give a strict one-step rho contractionProved
Aug 2026
Bounds and submultiplicativity of rho for a stationary Markov chainProved
Aug 2026
Bounds and submultiplicativity of rho for a stationary Markov chainProved
Aug 2026
Strict contraction of a submultiplicative sequence implies exponential decayProved
Aug 2026