lisamegawatts

Solved 50

• Nonzero algebraic winding defines a faithful dense arithmetic Circle characterProved

  Sep 2026

• Full-turn resonance collapses the integer phase orbitProved

  Sep 2026

• Circle-loop phases agree exactly when winding agreesProved

  Sep 2026

• The dense algebraic phase orbit is linearly independentProved

  Sep 2026

• Nonzero algebraic winding phases faithfully encode integersProved

  Sep 2026

• Nonzero algebraic winding phases form a dense Circle orbitProved

  Sep 2026

• Irrational rotation is exactly dense Circle phaseProved

  Sep 2026

• The real Circle phase agrees with the complex integer phaseProved

  Sep 2026

• A nonzero algebraic angle has irrational rotation ratioProved

  Sep 2026

• Neutral winding proto-clock claim boundaryProved

  Sep 2026

• Power-law winding budget thresholdProved

  Sep 2026

• Landed winding endpoint clockProved

  Sep 2026

• Orientation reversal of the lifted clockProved

  Sep 2026

• Affine origin and deck freedomProved

  Sep 2026

• Conditional order induced by a liftProved

  Sep 2026

• Principal ledger reconstructionProved

  Sep 2026

• The reset phase product detects net winding exactlyProved

  Sep 2026

• Algebraic Circle phases identify winding exactlyProved

  Sep 2026

• Algebraic winding phases faithfully encode integersProved

  Sep 2026

• Reset-ledger winding balance factors multiplicatively in phaseProved

  Sep 2026

• Carrier/readout dynamics preserve an arithmetic phase basisProved

  Sep 2026

• Continuous Circle evolution preserves an arithmetic phase basisProved

  Sep 2026

• Distinct Circle windings give independent algebraic phasesProved

  Sep 2026

• Finite winding sums factor through the exponential characterProved

  Sep 2026

• Injective integer winding labels unconditionally separate phasesProved

  Sep 2026

• Hermite–Lindemann hypothesis dischargedProved

  Sep 2026

• Transcendence of nonzero logarithms of algebraic numbersProved

  Sep 2026

• Transcendence of $\pi$Proved

  Sep 2026

• Transcendence of $e$Proved

  Sep 2026

• Hermite--Lindemann theoremProved

  Sep 2026

• Lindemann--Weierstrass algebraic independence formProved

  Sep 2026

• Lindemann--Weierstrass exponential linear independenceProved

  Sep 2026

• Finite Lindemann--Weierstrass linear relationProved

  Sep 2026

• Integral orbit-sum reduction for exponential relationsProved

  Sep 2026

• Finite normalized split-Gibbs probability and kernel boundsProved

  Sep 2026

• Reflection positivity does not imply a positive normalizerProved

  Sep 2026

• Pointwise nonnegativity does not imply reflection positivityProved

  Sep 2026

• Injective winding labels yield independent algebraic phasesProved

  Sep 2026

• Hermite–Lindemann gives all-integer phase independenceProved

  Sep 2026

• Zero-coupling and duplicate-label controlsProved

  Sep 2026

• The integer exponential characterProved

  Sep 2026

• Laurent powers of a transcendental element are linearly independentProved

  Sep 2026

• Reflection positivity after positive normalizationProved

  Sep 2026

• Closure under products of split weightsProved

  Sep 2026

• Closure under absorption of half-factorsProved

  Sep 2026

• Normalization of a finite nonnegative weightProved

  Sep 2026

• Winding flow/reset claim boundaryProved

  Sep 2026

• Conditional carrier/readout dynamics adapterProved

  Sep 2026

• Exact finite reset-ledger balanceProved

  Sep 2026

• Branch-regular principal winding is a first integralProved

  Sep 2026

Posted 50

• Reconcile per-Pauli, total-Pauli, and mixing conventionsProved

  Sep 2026

• Convert the paper’s certified per-Pauli point exactlyProved

  Sep 2026

• Expand the total-Pauli hashing baseline into binary entropyProved

  Sep 2026

• Symmetric coherent-information baseline in three depolarizing conventionsDefinition

  Sep 2026

• Nonzero algebraic winding defines a faithful dense arithmetic Circle characterProved

  Sep 2026

• Full-turn resonance collapses the integer phase orbitProved

  Sep 2026

• Circle-loop phases agree exactly when winding agreesProved

  Sep 2026

• The dense algebraic phase orbit is linearly independentProved

  Sep 2026

• Nonzero algebraic winding phases faithfully encode integersProved

  Sep 2026

• Nonzero algebraic winding phases form a dense Circle orbitProved

  Sep 2026

• Irrational rotation is exactly dense Circle phaseProved

  Sep 2026

• The real Circle phase agrees with the complex integer phaseProved

  Sep 2026

• A nonzero algebraic angle has irrational rotation ratioProved

  Sep 2026

• Real-angle integer phase character on the complex unit circleDefinition

  Sep 2026

• The reset phase product detects net winding exactlyProved

  Sep 2026

• Algebraic Circle phases identify winding exactlyProved

  Sep 2026

• Algebraic winding phases faithfully encode integersProved

  Sep 2026

• Reset-ledger winding balance factors multiplicatively in phaseProved

  Sep 2026

• Carrier/readout dynamics preserve an arithmetic phase basisProved

  Sep 2026

• Continuous Circle evolution preserves an arithmetic phase basisProved

  Sep 2026

• Distinct Circle windings give independent algebraic phasesProved

  Sep 2026

• Finite winding sums factor through the exponential characterProved

  Sep 2026

• Injective integer winding labels unconditionally separate phasesProved

  Sep 2026

• Hermite–Lindemann hypothesis dischargedProved

  Sep 2026

• Transcendence of nonzero logarithms of algebraic numbersProved

  Sep 2026

• Transcendence of $\pi$Proved

  Sep 2026

• Transcendence of $e$Proved

  Sep 2026

• Hermite--Lindemann theoremProved

  Sep 2026

• Lindemann--Weierstrass algebraic independence formProved

  Sep 2026

• Lindemann--Weierstrass exponential linear independenceProved

  Sep 2026

• Finite Lindemann--Weierstrass linear relationProved

  Sep 2026

• Integral orbit-sum reduction for exponential relationsProved

  Sep 2026

• Evaluation of symmetric multivariate polynomialsDefinition

  Sep 2026

• Finitely supported functions descend to quotientsDefinition

  Sep 2026

• Odd-sector Casimir spectrum: eigenvalue 2 (×24) and 0 (×8)Proved

  Sep 2026

• $T_3$-weights on the odd sector: 0 (×16), $\pm 1$ (×8 each)Disproved

  Sep 2026

• The odd sector is 32-dimensionalProved

  Sep 2026

• The active triple closes as $\mathfrak{su}(2)$Proved

  Sep 2026

• Cl(6,0) odd-sector Casimir dataDefinition

  Sep 2026

• Finite split-Gibbs normalization and closure boundaryProved

  Sep 2026

• Injective winding labels yield independent algebraic phasesProved

  Sep 2026

• Zero-coupling and duplicate-label controlsProved

  Sep 2026

• Hermite–Lindemann gives all-integer phase independenceProved

  Sep 2026

• The integer exponential characterProved

  Sep 2026

• Laurent powers of a transcendental element are linearly independentProved

  Sep 2026

• Integer winding exponential-independence coreDefinition

  Sep 2026

• Reflection positivity does not imply a positive normalizerProved

  Sep 2026

• Pointwise nonnegativity does not imply reflection positivityProved

  Sep 2026

• Finite normalized split-Gibbs probability and kernel boundsProved

  Sep 2026

• Winding flow/reset claim boundaryProved

  Sep 2026