Excluded in the stated class
finding:native-whole-five-ground-space-needs-four-register-interaction
rho_C=Pi_C/5 andrho_S=Pi_sym4/35 have exactly equal reductions on all4+6+4 subsets of sizes1,2,3; each three-register reduction isPi_sym3/20. Their global trace distance is6/7. Every Hermitian at-most3-local Hamiltonian on the same four registers therefore has equal mean energy. If the ENTIRE codeC has minimal energyE0, positivity ofH−E0I forces the full35-dimensional symmetric space to be ground as well. An exact five-dimensional code ground space is impossible. The existing4-local moment parent attains the necessary interaction order.
Scope: Only exact energetic selection of the ENTIRE original five-code on the same four registers. Arbitrary Hermitian terms and frustration allowed. Does not exclude one selected code state,ancillas,thermodynamic systems,effective four-body interactions,open dynamics or approximate selection. Marginal equality is for the two mixed states,not all pure code inputs. No physical-origin derivation.
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors
Established within the stated premises
finding:old-cover-winding-reconstructs-local-quarter-current-net
The old stress formula gives J_n=2(L_n^(3/4)−L_n^(1/4)) on the same CAR generators for every n including0. The comparison within the existing cut-cover source is not free: u_cov W0=W1 and u_cov W1=W0 u_base give U=[[0,u_base],[I,0]],rank[C,U]1 and phase-independent adjoint Fock transport AdGamma(U). The first arrow preserves factor seas and Wick ordering. Hence on factor0 J(f)=2(AdGamma(U)^−1 T_(3/4)(f)−T_(1/4)(f)). Existing self-adjointness/energy bounds and the stable unitary Trotter sequence show that this transported stress pair generates exactly the local U1 current net on every base interval. The full winding remains charged and is not globally vacuum-preserving because of the second arrow.
Scope: Complete operator and local-net theorem in the GIVEN original cut-cover CAR realization. Support is the two-preimage region, not a single cover arc. The later eightfold fold, cross-arc CAR transporters and original P1 support/Theta/collar/reference map do not follow from this scalar current-net theorem alone. No time interpretation of product parameters or physical gate closure.
Required premises and original source excerpts
- Existing full cut-cover CAR source with actual winding and sea
The already constructed NS double-cover source Hcov=W0K⊕W1K is given, with common negative sea m<0 and original winding U=[[0,u_base],[I,0]], u_base e_m=e_(m+1). Quarter stress fields retain their original CAR coefficients and Wick ordering. Base intervals carry two cover preimages. This assumes the mathematical source realization and does not derive its physical P1 field map or descent into a fixed Pin collar domain.
premise:existing-cut-cover-car-with-actual-winding-and-sea - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Excluded in the stated class
finding:untransported-independent-quarter-stress-pair-is-not-current
For the untransported two-factor difference D_n=2(L_n^+⊗I−I⊗L_n^−),c±1,h±1/32,the ground-state commutator is exactly n(4n²−1)/6. Values1/2 and5 at n1,2 contradict a level1 current with1,2;no common rescaling works. Every real self-adjoint linear combination aLplus+bLminus has cubic coefficient(a²+b²)/12 and thus can yield a Heisenberg algebra only trivially. The proved actual winding transport above avoids this false replacement.
Scope: Complete exclusion of the named real linear class of independent stress factors. No exclusion of the transported common CAR factor,general nonlinear source operations or P1. Finite CAR checks are not asserted to be full finite CCR representations.
Required premises and original source excerpts
- Existing full cut-cover CAR source with actual winding and sea
The already constructed NS double-cover source Hcov=W0K⊕W1K is given, with common negative sea m<0 and original winding U=[[0,u_base],[I,0]], u_base e_m=e_(m+1). Quarter stress fields retain their original CAR coefficients and Wick ordering. Base intervals carry two cover preimages. This assumes the mathematical source realization and does not derive its physical P1 field map or descent into a fixed Pin collar domain.
premise:existing-cut-cover-car-with-actual-winding-and-sea - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:current-public-paper-bytes-and-binding-source-gaps-recovered
Directly downloaded current public introduction and tfpt_research_contracts PDFs are byte-identical to website/public/papers,with SHA256 d564ea7b…c7b9 and5c08d585…9b93. Old search-engine views return differing earlier editions and do not prove a deployment defect. The reviewed current TYPEIII.CHARGED original remains open. Its binding ALG2 correction withdraws the Vandermonde inference to the microscopically generated algebra and requires FE-GEN or the precise projected-algebra route. The old technical companion CMB section does not supply this P1 field map either. The positive old stress/winding composition is instead reused as F1.
Scope: Targeted current public sources and original passages on26October2026. Not a theorem that every archive lacks another solution. Neutral W8 retains positive older results;the charged TYPEIII extension is not imposed as an extra prerequisite.
Required premises and original source excerpts
- Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:winding-charge-conjugation-descends-fixed-pin-domain-but-not-full-dirac-sea
In the given flat Moebius comparison,A=e^(i pi x)sigma1K is an antiunitary involution of the same fixed(c,b) H1 domain and preserves cover support. Exactly A D A=−D+pi sigma1. Centering D−(pi/2)sigma1 would change flat/Pin data. For the full D sea the PH polarization mismatch has at least n/4 frequency contributions of4/(13n²) on every n≥4;the HS level sum≥1/(13n) diverges. Thus this PH Fock lift does not exist in this full two-dimensional sea. The old transverse zero branch instead retains its finite rank1 defect. A is not a bulk D solution intertwiner;Calderon boundary-range invariance follows neither positively nor negatively from that and remains separately open.
Scope: Positive fixed-domain descent;proposed Theta/state/same-time identification excluded in the named full flat D-sea contract. No exclusion of all P1 kernels or reduced circle sources;no new physical Theta or general Calderon theorem.250 finite grid controls accompany the analytic divergent lower-bound proof.
Required premises and original source excerpts
- Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
premise:given-flat-mobius-dirac-boundary-family-and-full-sea - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:native-fourth-root-frame-has-signed-collective-sixty-mode-dual
Columns z_a^tensor4 define F and K=F*F with spectrum3^5,(3/2)^30,0^25. F/sqrt3 literally identifies its top five with the native code. Each row contains1 once,1/16 thirty-two times,−1/4 twelve times and0 fifteen times. Actual triangle0,1,2 has invariant product−1/64. Magnitude replacement |K| instead has a unique Perron mode at6;|K|² is strictly positive.
Scope: Finite duality of the same supplied frame; no physical sixty-site world or coupling. Only the magnitude replacement is excluded,not all classical/nonlinear self-organization. Central J acts trivially in quartic degree.
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors
Excluded in the stated class
finding:native-root-gram-spectrum-is-not-canonical-source-energy-selection
Normalized local quartic fields have the actual vacuum two-point functionK_ab/(z−w)^8. YetL0F=4F andF*L0F=4K,so the generalized energy problem hasE=4 on all35 source directions. ExactlyK+=(7K−2K²)/9 andFK+F*=Pi_sym4. Positive candidatesL_t=(3I−K)(I+tK),t>=0,share the five-kernel with different remaining rates;the finite correlation alone selects no physical generator.
Scope: Only identification of this covariance spectrum with canonical c8 stress energy is excluded. Intrinsic frame anisotropy remains. No executed whitening,no identification ofL0 with P1 time,no exclusion of original quarter states,other interactions or full P1 models. The older full W/Gamma generating functional remains available.
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
premise:full-existing-local-e8-field-hull-observer-code - Actual positive Cartan quartic Fock embedding
Use original Construction-A roots with physical metric dot/2 and u_j=(h_2j-i h_2j+1)/sqrt2 as J=+i basis. Canonically embed the actual five Sym^4 code support sums as neutral grade4 Heisenberg polynomials in the given E8_1 lattice vacuum. No physical preparation follows.
premise:literal-native-positive-cartan-quartic-fock-embedding
Excluded in the stated class
finding:identical-overlapping-native-five-codes-have-no-common-state
ForA=V_1234 tensorI andB=I tensorV_2345,exactlyA*B=(1/4)S for a factor permutationS. Their image intersection is0. The auxiliary projector penalty2I−AA*−BB* has minimum3/4;the actual native parent sum is>=3/8. Since overlappingS4 groups generate symmetry on the union,the same zero intersection follows for identical code constraints overlapping in1,2 or3 registers.
Scope: Only rigid identical code constraints in a shared register frame. No new P1 code-closure axiom. No classification of differently rotated codes,disjoint blocks,approximate/open processes,frustrated phases or the full E8 field. The auxiliary penalty is not presented as a native extensive Hamiltonian spectrum.
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors
Excluded in the stated class
finding:horizontal-e8-invariant-octic-cannot-isolate-native-five-ground-space
For the actual normalizedf0=sum(u_a.h(-1))^4/sqrt96 and original rootalpha=sqrt2e0,E_alpha(0) has charged PBW componentalpha.h(-3)|alpha>/(3sqrt96) with squared norm1/144,outsideC5. Thus an operator commuting with horizontal E8 zero modes cannot have preciselyC5 as an isolated eigen/ground space on the full grade4 source. The existing screenedW8 obeys[E_alpha(0),o(W8)]=0 and therefore fails this necessary condition as a sole exact-five selector.
Scope: Finite canonical c8 source with the same positive Gaussian polarization;no claim of full affine invariance. Does not exclude W8 contributions to larger E8 multiplets,broken symmetry,quarter references,state responses or full TFPT. The observer code need not be a full-source ground space and this is not imposed.
Required premises and original source excerpts
- Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension - Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
premise:native-clock-complex-reflection-and-quartic-subspace - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
premise:full-existing-local-e8-field-hull-observer-code - Actual positive Cartan quartic Fock embedding
Use original Construction-A roots with physical metric dot/2 and u_j=(h_2j-i h_2j+1)/sqrt2 as J=+i basis. Canonically embed the actual five Sym^4 code support sums as neutral grade4 Heisenberg polynomials in the given E8_1 lattice vacuum. No physical preparation follows.
premise:literal-native-positive-cartan-quartic-fock-embedding - Fixed octic completion in the existing current space
In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed.
premise:declared-original-octic-quantum-completion-ansatz
Established within the stated premises
finding:longitudinal-reflection-preserves-fixed-pin-domain-and-full-dirac-sea
Theta_x=K R_x is an antiunitary involution of the same(c,b) H1 domain for both c=±i and b=±1. Deck inversion compensates conjugation:bar(c)^−1=c. Exactly D Theta_x=Theta_x D;all real spectral functions,the complete D sea and quasifree vacuum ray are preserved. Block-diagonal antiunitary Fock implementation needs no PH mixing or HS repair. D time and longitudinal translations are reversed. Original operational Theta is distinct from normal deck lift and Calderon polarization;longitudinal reflection is a correctly typed candidate,not yet an identified P1 field map.
Scope: Concrete flat boundary family and its given D sea. State invariance does not imply Green reflection positivity;P1 locality,time and kernel need an actual map. Do not identify the three reflection types.
Required premises and original source excerpts
- Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
premise:given-flat-mobius-dirac-boundary-family-and-full-sea - Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
premise:original-p1-seed-boundary-and-local-restriction-definitions - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Excluded in the stated class
finding:single-fixed-pin-minus-green-kernel-fails-neutral-os-positivity
The actual invariant simple transverse branch has D0=−i b partial_x,q=cb=±i. Its exact Green kernel Gq is q/(q−1) for0<s<1 and1/(q−1) for−1<s<0. The equivalent normalized one-mode trace has z=−q^−1 and omega(N)=1/(1−q)=(1±i)/2. The neutral number word is phase-independent under standard antilinear charge-exchanging word reflection. Its smeared positive-time OS square is not real. Thus the complete free Green realization in one fixed Pinminus sector is not RP. Linear Clifford reflection sends c to−c and is not an endomorphism there;K R_x as D-sea symmetry does not replace it.
Scope: Only this given charged Gaussian Green realization and standard charge-exchanging word reflection on a single fixed Pinminus sector. No P1 no-go,no exclusion of the positive NS cover source or arbitrary other kernels. Sector exchange prevents transporting the neutral witness as an isolated OS square in the cover state.
Required premises and original source excerpts
- Given free Green quantization of the flat Pin Dirac operator on its NS cover
Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel.
premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:full-original-ns-orientation-cover-has-all-mode-charged-green-rp
Original doubled Pin deck action forces beta2 in the existing length convention. H=i sigma3 partial_w is selfadjoint on the same b boundary domain,with simple spectrum nπ/2,n inZ. For L=partial_x+H,S(t)=e^(−tH)(1+e^(−2H))^−1 is the entire antiperiodic Green kernel. Both charge blocks factor exactly:−S(−t−s)=B_t*B_s and S(t+s)=Btilde_t*Btilde_s,with B_t=e^(tH)(1+e^(2H))^−1/2 and Btilde_t=e^((1−t)H)(1+e^(2H))^−1/2 for0<t,s<1. Both are bounded. Explicit source-order minus and charge-exchanging word reversal give full free CAR RP through Wick/Gibbs limits. Relative thermal Z=2 product_n≥1(1+e^(−nπ))² converges. Linear Clifford reflection exchanges the actual c=±i deck spaces;their zero kernels jointly give NS value±1/2. Every transverse excitation is retained.
Scope: Proved for the given free charged Green quantization on the existing whole orientation cover. No additional field-species doubling,no mixture of independent complex states,no identification with P1 kernel or previous W8 vacuum. Cover trace period2 is not the global relative C12 cover result. Jaffe/Ritter is not applied with unchecked boundary hypotheses;the concrete proof is direct.
Required premises and original source excerpts
- Given free Green quantization of the flat Pin Dirac operator on its NS cover
Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel.
premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:cover-green-thermal-state-is-not-original-quarter-hardy-vacuum
The full cover Green realization quantizes x as Euclidean time and has thermal covariance C=(1+exp(2H))^−1 on the w-section L2 space,with simple zero-mode value1/2. The D sea on L2(x,w) and old quarter Hardy state on the longitudinal circle are spectral projections. Mere covariance-preserving one-particle unitary identification is impossible:projections have only0,1 while C has1/2. Spaces and time coordinates must be transported. Enlarged purification or local net embedding is not excluded. v526 already assumes the chiral NS kernel and half algebra;its thermal success does not supply this original two-dimensional P1 identification.
Scope: Type check of the specified free sources. No ban on local state maps in enlarged cyclic spaces and no requirement of surjective full Hilbert-space identification. Same geometry or numerical temperature is not yet same field action and time.
Required premises and original source excerpts
- Given free Green quantization of the flat Pin Dirac operator on its NS cover
Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel.
premise:given-flat-pin-dirac-free-green-quantization-and-ns-cover - Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
premise:given-flat-mobius-dirac-boundary-family-and-full-sea - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:declared-recursive-native-som-is-u35-equivariant
For every U in U(35),the stipulated update is exactly covariant under X->XU,W->WU: norms,distances,winners,means and normalization are preserved. After5000 directly executed steps the relative signal error is1.36e-14. Original code weight.9809168 becomes.1324321 for actively rotated input with FIXED readout; passive readout transport restores.9809168.128 orientations transported by the proved covariance give mean.1417688 near5/35. Three generic complex starts also compress without the high native code weight.
Scope: Exact mathematical symmetry of the chosen update plus finite numerical checks. Generic U(35) does NOT preserve native tensor powers/field products;not a countermodel to full TFPT origin. Given native initial alignment may be justified upstream.
Required premises and original source excerpts
- Explicitly chosen recursive SOM rule on60 native signal cells
Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws.
premise:declared-recursive-native-som-update - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
Established within the stated premises
finding:declared-recursive-native-som-clocks-depend-on-chosen-rates
Nine prescribed beta/eta pairs around the original settings were executed5000 steps each. Three reach numerical rest,six retain motion. At beta=.25,changing eta=.15 to.075 changes frozen-response periods from11201/64540 to18551/106907 iterations. For all9 states,the observed frozen120x120 response reproduces the next1000 nonlinear steps with relative error<8e-14. Normal and-OO runs produce identical result bytes.
Scope: Finitely tested property of the expressly chosen learning rule. Frozen response is not the full Jacobian;no general attractor theorem,no identification with physical time or an original TFPT Clock.
Required premises and original source excerpts
- Explicitly chosen recursive SOM rule on60 native signal cells
Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws.
premise:declared-recursive-native-som-update - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
premise:native-even-e8-gaussian-clock-and-sign-extension
Established within the stated premises
finding:existing-c2-dividing-real-forms-realize-moebius-annulus-tower
The complete affine census of eight h^a Q^b kappa has precisely two dividing members:hQkappa and hQ³kappa. With O=(0,i),T=(1+i)/2,Qz=iz,hz=−z+T,kappaz=−i bar z+T. Their halves have width1/2,circumference1 and Q exchanges them. Delta=hQ² is the unique free involution among h,Q²,hQ²;on the annulus it acts(t,s)->(1/2−t,s+1/2),with Moebius quotient. The earlier kappa-only nondividing statement is correctly scoped. v507 half-period origin,v510 free-deck/Fock class and v519 free RP are reused results.
Scope: Exact theorem only in the named h,Q,kappa subgroup and its eight-member anti coset. There the unordered OS annulus pair is canonical. Full already marked D4 lift has16 antiholomorphic members and an additional equatorial dividing pair;earlier unqualified full canonicity is narrowed by finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots. No square-modulus derivation or physical P1 cover identity. Free-deck uniqueness only among h,Q²,hQ².
Required premises and original source excerpts
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks - Existing marked cyclic cover tower and compact elliptic images
Use only existing C_n:u_n^n=x^4-1 with fixed x base,deck Delta_n and already forced compiler clock R12=Q12 Delta12^4=(ix,omega s),Q12=(ix,s). Compare compact algebraic curves over C and pullback function fields. A comparison of punctured local systems must retain its removed points,peripheral loops,spin and field transports.
premise:existing-marked-cyclic-cover-tower-with-compact-elliptic-images - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:raw-ns-elliptic-glide-has-projective-spin-commutator-and-quarter-descent
For the untwisted NS NS line and raw complex-linear coefficient pullbacks,U_delta²=chi(1+i)=+I and U_rho U_delta=−U_delta U_rho,because universal lifts differ by the A cycle. The glide g=delta_E rho=−bar z+T has g²=z+i and U_g²=−I. With fixed sigma_s²=I,A=sigma_s U_g is Dirac covariant,A²=−I,and has c=±i spaces with involutive c^−1 A descent. Anti-linear Real j_g is distinct:(sigma_s j_g)²=+I and has no complex ±i eigenspaces. Q invariance allows only(+,+),(−,−);a genuine transported A4 Spin/Pin relation forces(−,−),without a separate no-zero-mode rule.
Scope: Raw flat spin pullbacks with explicit Clifford convention. Additional spin minimality requires genuine Spin/Pin bundle transport up to real central sign;an arbitrary projective U1 phase is another linearization. Do not identify Q,half translation,Pin operator and OS Real structure.
Required premises and original source excerpts
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks - Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
premise:original-p1-seed-boundary-and-local-restriction-definitions - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:canonical-elliptic-annulus-reproduces-original-quarter-boundary-tuple-and-kms
Unitary theta=2pi s identifies domains and actual operators:B_Sigma/(2pi)=Bcov=2(B1/4 direct_sum B3/4),V=T_pi,u_cov=[[0,u_base],[I,0]]. Q rotates cut charts and is not V. At canonical width W=1/2,the second chiral Calderon compression is C_A=(1+exp(2pi Bcov))^−1,hence geometric beta_angle=2pi without fitting. C_A is a mixed traceclass perturbation of the Hardy sea at distance<0.086590;relative covariance/Fredholm factor remains1−z,and(1−z)² for double winding. Known two-boundary graph reconstruction is specialized to the actual existing C2 cut. The old full flat Moebius test has modulus1,this one1/2;units cannot identify their full Dirac problems.
Scope: Proved for the given one-particle boundary tuple and declared free chiral CAR interpretation. No equality with Hardy vacuum,original P1 measure/time identification,or EM/Quillen response from the relative covariance determinant. v813 index-four response normalization remains open;E8 compiler and existing W8 are not relabelled as new. Continuation:This boundary-tuple identity is not literal identity with the full marked equator pullback,which is a ramified V4/E8 graph. Retain full Real group and both original slots.
Required premises and original source excerpts
- Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
premise:existing-c2-group-with-untwisted-raw-flat-spin-pullbacks - Free chiral Cauchy quantization of the canonical elliptic annulus
Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.
premise:free-chiral-cauchy-quantization-of-canonical-elliptic-annulus - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
premise:original-p1-seed-boundary-and-local-restriction-definitions - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Excluded in the stated class
finding:finite-crosscap-cauchy-state-is-not-original-quarter-vacuum-by-normal-filtering
In the declared flat Pin model,the crosscap Cauchy covariance on each lambda,−lambda pair is the graph with t=−c exp(−2Llambda). Its commutator with signed boundary B has norm lambda/cosh(2Llambda)>0. Fock energy variance is lambda²/cosh²(2Llambda),so the finite-L state is nonstationary. Further normal collars filter in trace norm to the tree NS vacuum,which loses c,b marks. The loop quarter operator still follows from cb=±i,but this limit supplies neither its Hardy state nor W8 source dictionary. Cauchy data remain free before imposing physical local b boundary conditions;imposing them would instead solve the different zero-kernel problem.
Scope: Only identifying this finite crosscap state or its normal tree vacuum limit with the original quarter Hardy state under the claimed same time is excluded. No P1 no-go and no exclusion of actual open/closed sewing maps with appropriate state/time transport.
Required premises and original source excerpts
- Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
premise:given-flat-mobius-dirac-boundary-family-and-full-sea - Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
premise:original-p1-seed-boundary-and-local-restriction-definitions - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures
Established within the stated premises
finding:native-quartic-relative-arc-charge-excludes-additive-density-stress-insertion
In the actual M/O/quarter dictionary,each degree8 CAR arc-charge Gram has rank5 and determinant498159/262144,normalized166053/4294967296. All four index-difference classes have rank5. Every nonzero native quartic responds to every nonconstant real infinitesimal arc phase;the common phase remains trivial. These phases pointwise fix the restricted additive scalar density/stress subnet. Native field distributions cannot be generated there. The full original CAR algebra already contains the required transfers.
Scope: Exact highest CAR degree;subnet conclusion assumes the expressly restricted insertion algebra. Closed-operator affiliation needs an appropriate realization and common core. No exclusion of full CAR or arbitrary P1 maps,no claim for every finite phase,and no physical event selection.
Required premises and original source excerpts
- Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
premise:original-quarter-car-fold-current-subalgebra - Original displayed J-equivariant root isometry
Use existing S=_SIMPLE and T=_TARGET_SIMPLE from cartan_source._glue_deck_character_certificate: O=T S^-1/sqrt2 maps actual Construction-A roots r/sqrt2 to original Chevalley roots r/2, preserving metric and J. This is the existing concrete map, not a newly fitted embedding; physical P1 selection stays separate.
premise:original-displayed-j-equivariant-cartan-root-isometry - Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
premise:native-symmetric-quartic-and-erasure-constructors - Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
premise:typed-source-structures - Additive scalar density and stress algebra on eight original arcs
The restricted insertion candidate is the additive original scalar density/stress subnet on eight proper arcs with disjoint closures. Full neutral interarc CAR products are not automatically included.
premise:original-eight-arc-additive-density-stress-restriction
Open questions preserve their achieved subresults
Each research problem has its own scope. A resolved task does not close its whole physical parent. Historical tasks remain explicitly historical in the source record.
Future quotient and positive GNS reconstruction
What is determined by complete future behavior, and what additional positive word-kernel source is needed to reconstruct a cyclic operator realization?
- Resolved in scope: Future quotient from complete rRead result
- Resolved in scope: Conditional GNS reconstruction from supplied KRead result
- open: Select complete K from the original source
Historical: common source, state and event selection
Outside the active mathematical research program since the user's23Oct2026 decision. Historical question: Do the original principles derive a common physical source together with its state, dynamical events, and physically observed fields?
Seam connection and family action
Does the joint discrete theorem determine a concrete connection and a family coupling compatible with the determinant seam action?
- Resolved in scope: Separate classes from actual transportRead result
- open: Derive the common connection from the original source
Physical time and complete transfer
Do the original reflection/projector structures determine the full physical time generator and required field transfer?
- Resolved in scope: Reuse the sign-projector counterexampleRead result
- Resolved in scope: Reuse conditional full-transfer reconstructionRead result
- open: Identify the physical complete TFPT transfer
- Resolved in scope: Reuse complete collar reconstructionRead result
- Resolved in scope: Classify homogeneous GKLS embedding of the shared register familyRead result
- Resolved in scope: Decide every homogeneous GKSL logarithm of the fixed M4 channelRead result
Flavor ratio and absolute amplitude scale
Which flavor quantity is fixed on the derived discrete stratum, and which requires the continuous holonomy anchor?
- Resolved in scope: Reuse the derived flavor ratioRead result
- open: Determine the absolute holonomy amplitude
Alpha: derived terms, unique root and physical EM identification
Where do the factors and closed alpha equation come from, which provenance steps are proved, and which precise physical EM identification remains open?
- Resolved in scope: Separate root calculation from source selectionRead result
- open: Derive the actual EM functional variation and Thomson identification
- Resolved in scope: Establish the unique global positive rootRead result
Geometric flow and gravity normalization
Do common matter-only observations derive geometric horizon flow and the area response from the original gravity source?
- Resolved in scope: Record scope of fixed original functionalRead result
- open: Derive geometric modular response and area coefficient
Clocks and complete neutral source response
Which complete quadratic response can the actual clock images reconstruct?
- Resolved in scope: Reconstruct all neutral quadratic matrix directionsRead result
- open: Derive physically admissible probe access
Clock action on charge, time and quarter transition
How does the actual Gaussian J act on the complete marked source?
- Resolved in scope: Construct original J lift with complete time/charge actionRead result
- open: Derive physical meaning of the frame orbit
Which responses distinguish charged time action?
Which data separate sources with identical complete neutral vacuum response?
- Resolved in scope: Determine twist blindness completelyRead result
- Resolved in scope: Reconstruct twist from charged responsesRead result
- open: Derive actual charged source probes
Which seam action distinguishes native opposite charges?
Can existing native charge fields produce the quarter-twist time response of the seam?
- Resolved in scope: Check native fields and response discriminatorRead result
- open: Derive actual marked seam/state action
Constructive seam search: operators, state and source compatibility
What does the complete phase search decide, and which additional state information prevents a false source solution?
- Resolved in scope: Finite search closed, actual winding and parity equivalenceRead result
- Resolved in scope: Positive finite-word state extensionRead result
- Resolved in scope: E8 current group conditionally determines the P signRead result
- Resolved in scope: The same shift functional hides distinct ground statesRead result
- Resolved in scope: No phase hit realizes the unchanged sourceRead result
Which partner actually belongs to the original seam?
Which charge, state type and time action belong to the root partner and original sheet pairing?
- Resolved in scope: Concrete pair operator; source neutrality is not hypercharge neutralityRead result
- Resolved in scope: Fixed quarter time splits the color/weak multipletRead result
- Resolved in scope: Explicit conjugation for the existing sheet pairingRead result
- Resolved in scope: Actual partner map between quarter domainsRead result
- Resolved in scope: Bilinear sheet pairing is not Hermitian kernel selectionRead result
- Resolved in scope: Actual quarter conjugation transports the supplied markingRead result
- Resolved in scope: No time-stabilizing orthogonal repair of the fixed markingRead result
- Resolved in scope: Spinor16 is a state sector, not a 16-real one-particle fieldRead result
Automated construction of operator maps and sources
Which tools generate operator maps, learn counterexamples, and can search for the full positive source?
- Resolved in scope: Calibrate new search without supplying the target mapRead result
- open: Synthesize a joint field, marking and transfer dictionary
- open: Search for the positive common source kernel itself
- Resolved in scope: Automatically construct, certify and distinguish finite kernelsRead result
- Resolved in scope: Repair search conditions against source types and collar controlsRead result
- Resolved in scope: Reconstruct multi-field sewing of the canonically identified boundary sourceRead result
- Resolved in scope: Retain absolute reference amplitude in searchRead result
- Resolved in scope: Integrate supplied free source including boundary response and scalarRead result
- Resolved in scope: Convert the full finite CAR kernel into a link functionalRead result
- Resolved in scope: Close original recursive word reconstruction with memoryRead resultRead result
- Resolved in scope: Retain whole original caller through scale and readoutRead resultRead result
- Resolved in scope: Execute actual shared Higgs source with full matter words and local RPRead resultRead result
- Resolved in scope: Reduce whole constant original Higgs spectral fiberRead result
- open: Resolve original geometric Higgs residue sign and field map
- Resolved in scope: Evaluate local original Higgs heat identification and whole finite consumerRead resultRead result
- Resolved in scope: Execute whole variable bound Higgs reference and original scale mapRead resultRead result
- Resolved in scope: Execute whole inner Higgs scale/source and normal kernel transportRead resultRead result
- Resolved in scope: Execute given whole superconnection and normal spectral readerRead resultRead result
- Resolved in scope: Determine own-admissibility and whole total-chiral spectral readersRead resultRead result
- Resolved in scope: Derive whole scale-energy map,normal profile and relative flowRead resultRead result
- Resolved in scope: Execute original Green energy producer and mixed scale readoutRead resultRead result
- Resolved in scope: Match current action argument and common Higgs/gravity weightsRead resultRead result
- Resolved in scope: Execute whole original curvature consumers and Higgs radial sourceRead resultRead resultRead result
- Resolved in scope: Execute original whole four-ghost source and geometric type testRead resultRead result
- Resolved in scope: Execute original moving normal kernel derivative and whole source responseRead result
- Resolved in scope: Decide fixed original O1 source and normal operator placementRead result
- Resolved in scope: Compare whole Higgs mixture and covariance reader on invariant four-field witnessRead result
- Resolved in scope: Test exact bounded cutoff on whole ordinary Higgs volumeRead result
- Resolved in scope: Test whole original circle joint mode and IR Higgs normalizationRead result
- Resolved in scope: Test original O1 mode covariance against whole Higgs-law classRead result
- open: Reconstruct original localization from the whole process
- Resolved in scope: Test bare native-code word compression against actual localityRead result
- Resolved in scope: Decide original geometric local-time class and execute actual interval readerRead resultRead result
- Resolved in scope: Execute actual regional two-face partner and supported charged wordRead resultRead result
- Resolved in scope: Execute original color marginal, modular field law and complete class readerRead resultRead resultRead result
- Resolved in scope: Reconstruct common Higgs law from whole original quarter source towerRead resultRead resultRead result
- Resolved in scope: Execute original record action on Doily and ordered whole source responseRead resultRead resultRead resultRead result
- Resolved in scope: Locally implement original record process and test unchanged exterior sourceRead resultRead resultRead result
- Resolved in scope: Execute original elliptic insertion,whole source and causal responseRead resultRead resultRead result
- Resolved in scope: Evaluate actual joint Higgs and color group sourceRead resultRead result
- Resolved in scope: Execute whole original graph color reader with typed original center selectorRead resultRead result
- Resolved in scope: Execute original color fixed source and first inherited grading testRead resultRead result
- Resolved in scope: Execute actual original color-spinor CAR four-word and complete spin-sector sewingRead resultRead result
- Resolved in scope: Decide actual color admissibility of density operations and coordinate regionsRead resultRead result
- Resolved in scope: Execute actual whole seam-operation class and two-face responseRead resultRead result
- Resolved in scope: Execute entire original C6 word expansion with source amplitudeRead resultRead result
- Resolved in scope: Execute original collective Higgs force source and entire mean dualRead resultRead resultRead result
- Resolved in scope: Execute original all-mode force with actual time and whole sourceRead resultRead result
- Resolved in scope: Execute original local space/time force source and causal liftRead resultRead result
Origin reverse selection, field dictionary and original P1 kernel
What does reverse selection of P1/P2 give for concrete local fields and multi-field responses, and which identification with the original P1 kernel has actually been proved?
Observable reality: minimal conditions and counterworlds
Which operational conditions are independently required, which inequivalent models satisfy them, and which observable distinctions remain for selection?
Formal carrier core: unbounded Pascal uniqueness and finite glue
Which carrier and glue statements are already present in the papers and Lean sources, and which physical selection does not follow?
- Resolved in scope: Classify the unbounded Pascal proofRead result
- Resolved in scope: Classify the formal finite glue scopeRead result
Active mathematical program: marked seam monodromies and lattice lifts
Which marked seam/lattice transport geometries, lift classes and local-coefficient invariants arise from existing clock/reflection/quartic data? First complete case: sign lifts of fourJ representation on CP1 minusμ4.
- Resolved in scope: Define marked seam category and factor formulaRead result
- Resolved in scope: Completely classify quarter-clock four-puncture liftsRead result
- Resolved in scope: Determine central class and all subgroup restrictionsRead result
- Resolved in scope: Determine full G0 cocycle and classRead result
- Resolved in scope: Determine native4/5/6local cohomologyRead result
- Resolved in scope: Classify unrestricted G31 reflection monodromiesRead resultRead result
- Resolved in scope: Determine lift class beyond G0Read result
- open: Classify additional reflection/clock equivariance and mapping-class quotients
- Resolved in scope: Equivariant lifting and divisibility by eightRead result
- Resolved in scope: All62clock obstructions and central transport variantsRead result
- Resolved in scope: Actual group comparison and central pushout exclusionRead result
- Resolved in scope: Complete invariants and explicit collisionsRead result
- Resolved in scope: Compare E6 and E7 slices with the actual quarter clockRead resultRead resultRead resultRead result
- Resolved in scope: Classify original character-valued G31monodromy liftsRead resultRead result
- Resolved in scope: Determine E7-pair action on all original lattice fieldsRead result
- Resolved in scope: Completely connect E6/E7 cuts to the original compilerRead result
- Resolved in scope: Compare common covers and actual clock carriersRead result
- Resolved in scope: Prove shared representation consequence for48,4/3 and5/4Read result
- Resolved in scope: Completely decide joint compiler-field-cover constructionRead resultRead resultRead resultRead result
- Resolved in scope: Reconstruct canonical local compiler field source from C4Read resultRead result
- Resolved in scope: Eliminate redundant sector and multiplicity assumptionsRead result
- Resolved in scope: Classify native equivariant markingsRead result
- Resolved in scope: Classify pure quarter clock mapping class quotientRead result
- Resolved in scope: Determine complete cut algebra and lossless tetrahedron transformRead resultRead resultRead resultRead result
- Resolved in scope: Completely compare scalar glue and actual native compiler classRead resultRead resultRead resultRead result
Common clock sectors, quartic geometry and operational reconstruction
Which previously separate data of the original TFPT core follow from a common clock and representation geometry, and which complete finite measurement classification follows without asserting physical source selection?
Automatic joint origin hypotheses and source responses
Which simple joint rules connect the existing P1 source chain,double cover,information and compiler,and which whole candidate classes can be decided automatically using actual source consequences?
- Resolved in scope: Decide even-matter word class and check actual AI operator expressionsRead resultRead result
Existing TFPT derivations and correction of repeated gap diagnoses
Which common source/reconstruction chain already exists in the old original papers, and which purported global gaps arose from reducing P1 or choosing an optional CAR route?
Complete physical Hamiltonian source with Gauss sector and thermal word limit
Which whole source is constructed on the original local Hamiltonian route, how do physical constraints and thermal words follow, and how is its actual IR response distinguished from the original covariant geometric source branch?
Original TFPT source versus DET16 mirror vertex
Does the same original TFPT source produce the concrete DET16 generator and whole responses,or is a computable parent supplied as extra input?
Whole original source and canonical vacuum attachment
Which vacuum joins are already in the whole original source,and how do H ground source and R104 field/Gauss source join completely without second state choice or parent change?
Craig chiral measure and the original whole TFPT source
Which concrete operator and Berezin measure map preserves the original TFPT source when connecting Craig overlap measure?
- open: Compare original4D fermion Hessian and measure line with Craig
Cyclic quantum universe and original Genesis connection
Does original TFPT dynamics yield the exact cyclic quantum return in the September/October press lead and a geometric Genesis transition?
- open: Test periodicity and Genesis response on the same whole source
Physical constants as joint constraints on the TFPT source
Which independent constants constrain the original common source, and can one relative heat product supply gravity and vacuum energy together?
- open: Evaluate original volume, curvature and gauge responses together