Mathematical City Proof Forge
MATHEMATICAL CITY · RECURSIVE INTELLIGENCE / E47
Proof Forge
PF-FPV20C
120/120 PASS
Every plate opens a live destination sheet. Open lands on the Roll or Drive certificate; copy is the fallback when a tab is blocked.
ROLL OF CITIZENSENROLMENT BUREAUPATH TO CITIZENSHIPPROOF FORGEKARTEKEYA 09CITY
CITIZEN-PROVING CFPV20 FLIGHTE47 RECONSTRUCTION
FLIGHT FOLDERMONOGRAPHPYTHON WITNESSCERTIFICATE JSONMANIFESTZIP ARCHIVE
CARRIER
125 → 47
ΩC
47/125
Ρ*
15/17
Ε*
1/99144
Source citizens
LIVE ROLL RECORDS · TAP A PLATE TO OPEN
Enrolled from this flight
DISTINCT THEOREM IDENTITIES · CIVIC 341–346
Foundations
20/20 · 2 new
Representation Theory
20/20 · 1 new
Spectral Theory
20/20 · 0 new
Graph Theory
20/20 · 2 new
Verification
20/20 · 0 new
Quantum Information
20/20 · 1 new
ALL DISPOSITIONS120 shown · 6 new · E0+E1
PF-FPV20C-FOUND-001 · NEWEuler homogeneous-function identityOPEN
PF-FPV20C-FOUND-002 · RECONCILEDInverse dilation of a monomialOPEN
PF-FPV20C-FOUND-003 · RECONCILEDLog-additivity of homogeneous monomialsOPEN
PF-FPV20C-FOUND-004 · RECONCILEDDegree of monomial compositionOPEN
PF-FPV20C-FOUND-005 · RECONCILEDWeighted bihomogeneous scalingOPEN
PF-FPV20C-FOUND-006 · NEWExact quadratic Taylor descent identityOPEN
PF-FPV20C-FOUND-007 · RECONCILEDDiscrete Richardson Lyapunov on the complementOPEN
PF-FPV20C-FOUND-008 · RECONCILEDCommuting Richardson maps commuteOPEN
PF-FPV20C-FOUND-009 · RECONCILEDSimultaneous diagonalization of commuting HermitianOPEN
PF-FPV20C-FOUND-010 · RECONCILEDSpectral-radius equality for a commuting productOPEN
PF-FPV20C-FOUND-011 · RECONCILEDStrict convexity of an SPD quadraticOPEN
PF-FPV20C-FOUND-012 · RECONCILEDZero-homogeneity of the kernel projectorOPEN
PF-FPV20C-FOUND-013 · RECONCILEDPositive homogeneity of the Euclidean normOPEN
PF-FPV20C-FOUND-014 · RECONCILEDMetric gradient-flow decrease identityOPEN
PF-FPV20C-FOUND-015 · RECONCILEDLyapunov exponent of Richardson on the complementOPEN
PF-FPV20C-FOUND-016 · RECONCILEDKernel of a commuting Richardson productOPEN
PF-FPV20C-FOUND-017 · RECONCILEDQuadratic-form scale covarianceOPEN
PF-FPV20C-FOUND-018 · RECONCILEDInterior step remains contractive under commuting productOPEN
PF-FPV20C-FOUND-019 · RECONCILEDCritical point of a positive quadratic is the originOPEN
PF-FPV20C-FOUND-020 · RECONCILEDBilinear scale covariance of the Euclidean pairingOPEN
PF-FPV20C-REP-001 · RECONCILEDGauge invariance of the projector traceOPEN
PF-FPV20C-REP-002 · RECONCILEDFrobenius square of an orthogonal projector equals its rankOPEN
PF-FPV20C-REP-003 · RECONCILEDWeyl dimension of SU(2) spin-2OPEN
PF-FPV20C-REP-004 · RECONCILEDTensor-cube carrier dimensionOPEN
PF-FPV20C-REP-005 · RECONCILEDC5 character at k=1 is the golden ratio inverseOPEN
PF-FPV20C-REP-006 · RECONCILEDTrace of C5 adjacency vanishesOPEN
PF-FPV20C-REP-007 · RECONCILEDSpectral mapping of the squareOPEN
PF-FPV20C-REP-008 · RECONCILEDPolynomial spectral mapping t^2−tOPEN
PF-FPV20C-REP-009 · RECONCILEDUnitary conjugation preserves spectrumOPEN
PF-FPV20C-REP-010 · RECONCILEDAdjoint action of a rotation on a full-rank frameOPEN
PF-FPV20C-REP-011 · RECONCILEDDirect-sum dimension of the E47 sectorsOPEN
PF-FPV20C-REP-012 · RECONCILEDSingle-copy Casimir is centralOPEN
PF-FPV20C-REP-013 · RECONCILEDCasimir-dimension partition of the carrierOPEN
PF-FPV20C-REP-014 · RECONCILEDHermitian spectrum is realOPEN
PF-FPV20C-REP-015 · RECONCILEDDegenerate eigenframe gaugeOPEN
PF-FPV20C-REP-016 · NEWFourier intertwiners of C5 are circulantOPEN
PF-FPV20C-REP-017 · RECONCILEDProjector uniqueness for a full ONBOPEN
PF-FPV20C-REP-018 · RECONCILEDPolynomial functional-calculus homomorphismOPEN
PF-FPV20C-REP-019 · RECONCILEDSpectral mapping of Richardson powersOPEN
PF-FPV20C-REP-020 · RECONCILEDTrace of the spin-2 CasimirOPEN
PF-FPV20C-SPEC-001 · RECONCILEDSpectral mapping of RichardsonOPEN
PF-FPV20C-SPEC-002 · RECONCILEDSpectral mapping of K squaredOPEN
PF-FPV20C-SPEC-003 · RECONCILEDIsolation of the selector polesOPEN
PF-FPV20C-SPEC-004 · RECONCILEDComplementary gap is recoveredOPEN
PF-FPV20C-SPEC-005 · RECONCILEDOperator norm of Q is recoveredOPEN
PF-FPV20C-SPEC-006 · RECONCILEDComplementary contraction factorOPEN
PF-FPV20C-SPEC-007 · RECONCILEDSpectral mapping of Richardson powersOPEN
PF-FPV20C-SPEC-008 · RECONCILEDKernel of K is the Γ-eigenvalue 1OPEN
PF-FPV20C-SPEC-009 · RECONCILEDInterior complementary spectrum is strictly contractiveOPEN
PF-FPV20C-SPEC-010 · RECONCILEDCharacteristic polynomial of the two-mode kernelOPEN
PF-FPV20C-SPEC-011 · RECONCILEDSpectrum of a commuting Hermitian sumOPEN
PF-FPV20C-SPEC-012 · RECONCILEDSpectral reconstruction residual of COPEN
PF-FPV20C-SPEC-013 · RECONCILEDHermitian resolvent identityOPEN
PF-FPV20C-SPEC-014 · RECONCILEDCondition number of the model quadraticOPEN
PF-FPV20C-SPEC-015 · RECONCILEDCauchy interlacing on a path LaplacianOPEN
PF-FPV20C-SPEC-016 · RECONCILEDSpectral radius of a Richardson mapOPEN
PF-FPV20C-SPEC-017 · RECONCILEDSelector annihilates E47OPEN
PF-FPV20C-SPEC-018 · RECONCILEDExponential functional calculus on the two-mode kernelOPEN
PF-FPV20C-SPEC-019 · RECONCILEDMinimax complementary radius is extreme-attainedOPEN
PF-FPV20C-SPEC-020 · RECONCILEDCritical Richardson step kills the top modeOPEN
PF-FPV20C-GRAPH-001 · RECONCILEDGolden-ratio cycle eigenvalueOPEN
PF-FPV20C-GRAPH-002 · RECONCILEDOriented incidence realizationOPEN
PF-FPV20C-GRAPH-003 · RECONCILEDDiscrete Dirichlet energy on P2OPEN
PF-FPV20C-GRAPH-004 · NEWDirichlet–incidence polarizationOPEN
PF-FPV20C-GRAPH-005 · NEWKirchhoff matrix-tree theorem on C5OPEN
PF-FPV20C-GRAPH-006 · RECONCILEDKirchhoff matrix-tree theorem on P2OPEN
PF-FPV20C-GRAPH-007 · RECONCILEDIncidence rank of P2OPEN
PF-FPV20C-GRAPH-008 · RECONCILEDIncidence rank of C5OPEN
PF-FPV20C-GRAPH-009 · RECONCILEDOriented incidence kernel is the constantsOPEN
PF-FPV20C-GRAPH-010 · RECONCILEDC5 adjacency spectrumOPEN
PF-FPV20C-GRAPH-011 · RECONCILEDAlgebraic connectivity of C5OPEN
PF-FPV20C-GRAPH-012 · RECONCILEDAlgebraic connectivity of P2OPEN
PF-FPV20C-GRAPH-013 · RECONCILEDC5 is 2-regularOPEN
PF-FPV20C-GRAPH-014 · RECONCILEDC5 is not bipartiteOPEN
PF-FPV20C-GRAPH-015 · RECONCILEDP2 is bipartiteOPEN
PF-FPV20C-GRAPH-016 · RECONCILEDHandshaking lemma on C5OPEN
PF-FPV20C-GRAPH-017 · RECONCILEDFiedler vector of P2OPEN
PF-FPV20C-GRAPH-018 · RECONCILEDGraph energy of C5OPEN
PF-FPV20C-GRAPH-019 · RECONCILEDDirichlet–incidence polarization on P3OPEN
PF-FPV20C-GRAPH-020 · RECONCILEDIncidence reconstruction of the C5 LaplacianOPEN
PF-FPV20C-VERIFY-001 · RECONCILEDRecovered rank equals 47OPEN
PF-FPV20C-VERIFY-002 · RECONCILEDCasimir multiplicity tableOPEN
PF-FPV20C-VERIFY-003 · RECONCILEDCasimir dimensions sum to the carrierOPEN
PF-FPV20C-VERIFY-004 · RECONCILEDSelector sectors sum to 47OPEN
PF-FPV20C-VERIFY-005 · RECONCILEDC5 cube Laplacian kernel is not E47OPEN
PF-FPV20C-VERIFY-006 · RECONCILEDBinary64 machine-epsilon contractOPEN
PF-FPV20C-VERIFY-007 · RECONCILEDRecovered Q-normOPEN
PF-FPV20C-VERIFY-008 · RECONCILEDRecovered complementary gapOPEN
PF-FPV20C-VERIFY-009 · RECONCILEDKernel-annihilation residualOPEN
PF-FPV20C-VERIFY-010 · RECONCILEDProjector annihilates QOPEN
PF-FPV20C-VERIFY-011 · RECONCILEDIdempotence of POPEN
PF-FPV20C-VERIFY-012 · RECONCILEDHermiticity of POPEN
PF-FPV20C-VERIFY-013 · RECONCILEDTrace of POPEN
PF-FPV20C-VERIFY-014 · RECONCILEDFrobenius square of POPEN
PF-FPV20C-VERIFY-015 · RECONCILEDComplement annihilates POPEN
PF-FPV20C-VERIFY-016 · RECONCILEDIndependent reconstruction checksumOPEN
PF-FPV20C-VERIFY-017 · RECONCILEDSelector is a polynomial in COPEN
PF-FPV20C-VERIFY-018 · RECONCILEDCasimir reconstruction residualOPEN
PF-FPV20C-VERIFY-019 · RECONCILEDdtype contract of the projectorOPEN
PF-FPV20C-VERIFY-020 · RECONCILEDEvidence-class lockOPEN
PF-FPV20C-QI-001 · RECONCILEDvon Neumann entropy of the normalized E47 projectorOPEN
PF-FPV20C-QI-002 · NEWPurity of the normalized E47 projectorOPEN
PF-FPV20C-QI-003 · RECONCILEDvon Neumann entropy of a pure state vanishesOPEN
PF-FPV20C-QI-004 · RECONCILEDUnitary invariance of von Neumann entropyOPEN
PF-FPV20C-QI-005 · RECONCILEDBinary entropy of a diagonal qubitOPEN
PF-FPV20C-QI-006 · RECONCILEDFidelity of identical pure statesOPEN
PF-FPV20C-QI-007 · RECONCILEDTrace distance of orthogonal puresOPEN
PF-FPV20C-QI-008 · RECONCILEDUnitary Schrödinger evolution preserves purityOPEN
PF-FPV20C-QI-009 · RECONCILEDMaximum entropy on E47OPEN
PF-FPV20C-QI-010 · RECONCILEDRelative entropy of a state to itself vanishesOPEN
PF-FPV20C-QI-011 · RECONCILEDConcavity instance of von Neumann entropyOPEN
PF-FPV20C-QI-012 · RECONCILEDPartial trace of a product pure is pureOPEN
PF-FPV20C-QI-013 · RECONCILEDProjector-filter trace lawOPEN
PF-FPV20C-QI-014 · RECONCILEDSingle-Kraus rank of the projector filterOPEN
PF-FPV20C-QI-015 · RECONCILEDPurity of a pure state is oneOPEN
PF-FPV20C-QI-016 · RECONCILEDvon Neumann entropy of a qubit maximally mixed stateOPEN
PF-FPV20C-QI-017 · RECONCILEDKernel entropy is strictly below carrier entropyOPEN
PF-FPV20C-QI-018 · RECONCILEDEntropy of a computational-basis projectorOPEN
PF-FPV20C-QI-019 · RECONCILEDIso-spectral states have equal entropyOPEN
PF-FPV20C-QI-020 · RECONCILEDRank-deficient states do not saturate log dimOPEN
FOUNDATIONS · E0 + E1
Euler homogeneous-function identity
For f(x)=x^D on x>0, x f'(x)=D f(x).
WITNESS
Δ=0.00e+00
RESIDUAL
0.000e+0
PARENTS
BOUNDARY
Smooth monomial on the positive ray; not a PDE Euler theorem.
LIVE DESTINATIONS
ROLL · CIVIC 341 · EULERPARENT SCALE · CIVIC 332FOUNDATIONS LEDGER (DRIVE)FLIGHT MONOGRAPH (DRIVE)PYTHON WITNESS (DRIVE)CERTIFICATE JSON (DRIVE)FLIGHT FOLDER (DRIVE)ZIP ARCHIVE (DRIVE)
Transfer does not upgrade evidence class.
Recovered rank P = 47 · gap 11664 · ||Q|| 186624RollDriveKARTEKEYA
