formal librarypublicsource:openai-ten-proofs

OpenAI

Native namespace openai-ten-proofs:comparator

12 source-native objects · 0 Repository bindings

Source-native objects

Stable native key order · 12 shown

Object	Kind	Availability	Source link
Sharp Cohn–Elkies sphere-packing asymptotics comparator:A_SpherePacking 4 declared theorems in SpherePacking	comparator profile	reference only
Strict improvement over the MRRW binary-code bound comparator:B_BinaryCodes 6 declared theorems in MetricCodes	comparator profile	reference only
Strict hierarchy of improved spherical-code bounds comparator:B_SphericalCodes 4 declared theorems in MetricCodes	comparator profile	reference only
Permanent lower bounds for formulas with division comparator:C_PermanentFormulaLowerBound 2 declared theorems in Permanent	comparator profile	reference only
Existence of a finitely presented non-sofic group comparator:D_NonSoficGroup 1 declared theorem in NonSoficGroup	comparator profile	reference only
Infinitely many nonisomorphic property-(T) groups with isomorphic factors comparator:E_ConnesRigidity 2 declared theorems in ConnesRigidity	comparator profile	reference only
Sharp Ehrhart volume inequality comparator:F_EhrhartVolumeInequality 4 declared theorems in EhrhartVolumeInequality	comparator profile	reference only
Uniform exponential quantum parallel repetition comparator:G_QuantumParallelRepetition 2 declared theorems in QuantumParallelRepetition	comparator profile	reference only
Polynomial-factor NP-hardness of the closest vector problem comparator:H_GapCVP 4 declared theorems in GapCVP	comparator profile	reference only
Explicit superexponential lower bound for multicolor triangle Ramsey numbers comparator:I_MulticolorTriangleRamsey 4 declared theorems in MulticolorTriangleRamsey	comparator profile	reference only
Quantitative counterexample to the Erdős–Simonovits compactness conjecture comparator:J_CompactnessConjecture 3 declared theorems in CompactnessAndDegeneracy	comparator profile	reference only
Quantitative counterexample for two-degenerate bipartite graphs comparator:J_TwoDegenerateGraphs 2 declared theorems in CompactnessAndDegeneracy	comparator profile	reference only

Sharp Cohn–Elkies sphere-packing asymptotics

comparator profile · reference only

comparator:A_SpherePacking

Strict improvement over the MRRW binary-code bound

comparator profile · reference only

comparator:B_BinaryCodes

Strict hierarchy of improved spherical-code bounds

comparator profile · reference only

comparator:B_SphericalCodes

Permanent lower bounds for formulas with division

comparator profile · reference only

comparator:C_PermanentFormulaLowerBound

Existence of a finitely presented non-sofic group

comparator profile · reference only

comparator:D_NonSoficGroup

Infinitely many nonisomorphic property-(T) groups with isomorphic factors

comparator profile · reference only

comparator:E_ConnesRigidity

Sharp Ehrhart volume inequality

comparator profile · reference only

comparator:F_EhrhartVolumeInequality

Uniform exponential quantum parallel repetition

comparator profile · reference only

comparator:G_QuantumParallelRepetition

Polynomial-factor NP-hardness of the closest vector problem

comparator profile · reference only

comparator:H_GapCVP

Explicit superexponential lower bound for multicolor triangle Ramsey numbers

comparator profile · reference only

comparator:I_MulticolorTriangleRamsey

Quantitative counterexample to the Erdős–Simonovits compactness conjecture

comparator profile · reference only

comparator:J_CompactnessConjecture

Quantitative counterexample for two-degenerate bipartite graphs

comparator profile · reference only

comparator:J_TwoDegenerateGraphs

Repository bindings

Exact local relationships · 0 shown

No Repository bindings on this page

A source observation does not create a local scientific record.

Source declarations, observations, source-native object rows, and Repository bindings record provenance. None creates scientific Standing; only an admitted local Claim can enter the attributed Decision path.