Established within the stated premises
finding:actual-graded-hypercharge-trace-rejects-quark-lepton-sign-intertwiner
The actual real unimodular v252 gauge lift gives Tr(gammaY³)=0, quark−9/2 and lepton+9/2. gamma_prime=gamma(2q−I) gives−9, excluding every unitary simultaneously preserving Y and intertwining those two fixed gradings. Weak KO6/operator signs alone allow gamma_prime, while the original fixed graded charge tuple is not equivalent. The complete four sector-sign choices have distinct cubic/fifth graded trace pairs: (0,10/3),(-9,-95/12),(9,95/12),(0,-10/3). Only the original (+,+) preserves the fixed joint dictionary.
Scope: Finite trace proof and actual rational96 gauge-lift computation with ten controls. Excludes only the specified simultaneous dictionary intertwiner. Does not derive physical PF or reject every other intrinsic grading on the same normal fibre image, extra sectors or inflow; anomaly cancellation is not treated as sufficient source selection.
Required premises and original source excerpts
- Actual full v252 gauge lift and original P2 comparison
Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.
premise:actual-full-v252-unimodular-p2-gauge-lift - Actual v252 SM coefficients and internal KO6 structure
Original v252 full_D, rep, grading and Kswap, arbitrary Yukawas and symmetric Majorana, SM connection and quark-preserving momentum. No extra quark-lepton mixing or full normal real structure is assumed.
premise:actual-v252-sm-coefficients-and-internal-ko6-without-extra-mixing
Established within the stated premises
finding:separable-normal-real-maps-compose-to-given-deck-and-quarter-image
Exactly four normal real types in the stated separable product ansatz. Their product JS JR is the existing Clifford deck, old linear and new antilinear. Scalar quarter shifts violate J-oddness and map to the existing inverse-holonomy source rather than an endomorphism of the same periodic bundle.
Scope: Analytic coefficient/domain result with46 actual controls. Not every96 antiunitary, physical OS reflection or archived inv/Gamma dictionary is classified.
Required premises and original source excerpts
Established within the stated premises
finding:actual-gauge-real-frames-leave-carrier-phase-as-coordinate-freedom
All rephased Etheta intertwine the fixed JS and JF. The fixed P2 gauge/grading/real dictionary admits constant U(3)^6 frame freedom, real dimension54, with negative-grade action determined by J. Actual-slot generators preserve all24 left algebra basis elements and therefore the opposite action. These are coordinate equivalences, not additional physical couplings.
Scope: Completeness uses the six original inequivalent irreps and Schur. Extra fixed Phi, connection or clocks require intersecting their stabilizers. Does not derive physical PF.
Required premises and original source excerpts
- Given normal-independent product collar, internal KO6 and separable normal antiunitary ansatz. J-odd actual gauge connection and scalar quarter image transport are separate premises and cases.
Given normal-independent product collar, internal KO6 and separable normal antiunitary ansatz. J-odd actual gauge connection and scalar quarter image transport are separate premises and cases.
premise:separable-normal-real-map-with-actual-jodd-gauge-and-typed-quarter-image - Fixed actual v252 left/opposite algebra, graded real P2 gauge representation, gamma and J. Six inequivalent positive-grade irreps with family multiplicity3. Constant coordinate frames are classified, without claiming they fix extra numerical Phi/clock/family operators.
Fixed actual v252 left/opposite algebra, graded real P2 gauge representation, gamma and J. Six inequivalent positive-grade irreps with family multiplicity3. Constant coordinate frames are classified, without claiming they fix extra numerical Phi/clock/family operators.
premise:actual-p2-six-multiplet-gauge-real-coordinate-frame-class
Established within the stated premises
finding:original-higgs-family-has-one-complex-kk-class-but-different-whole-sources
The original bounded radial Higgs perturbation preserves complex graded K-homology on the common compact product domain, while inverse Fermi functional calculus distinguishes every actual h_r and whole source. trPhi_r² distinguishes amplitudes1 and2 from fixed-dictionary frame changes. The boundary reader is not gamma-odd.
Scope: Analytic bounded homotopy with actual96 controls. Does not reconstruct K_car representation/connection, assert realKO without quarter-domain data or vary free Yukawa parameters.
Required premises and original source excerpts
Established within the stated premises
finding:signed-one-particle-modular-weight-is-not-the-positive-even-heat-operator
The given two-sided signed circle generator has positive unbounded exp(-k), whereas even heat operators are bounded. A two-level exact test separates them. Finite Fock and GNS modular densities act on different spaces. Valid v259 moment arithmetic is retained, while literal untransported operator equality cannot derive the heat profile.
Scope: Only the literal operator comparison, not every correctly defined source transport or the supplied KMS theorem. Exponential domain controls the negative tail and is neither simply H1 nor a subset of all Sobolev domains.
Required premises and original source excerpts
- Constant odd circle-source coefficient with existing sea and full boundary graph
In the existing Clifford chart on L2(S1,K) with finite K let h0=(-i∂theta+alpha)gamma,alpha=1/4 or3/4,gamma*=gamma,gamma²=I. Supply constant selfadjoint odd Phi,{gamma,Phi}=0,and V=-i gamma Phi,h=h0+V on common periodic H1. Compare given CAR sea projectors P_-(h0),P_-(h) and complete pure two-face projector G_ell(h),ell>0,including crossings. This is the existing source class with classical background, not physical selection from P1 or quantization of dynamic bosons.
premise:constant-odd-quarter-circle-source-sea-and-full-graph - 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:three-moments-select-one-exponential-exactly-in-positive-laplace-class
Across the entire positive Laplace cone, the moment determinant is nonnegative and vanishes exactly for one point measure, selecting the exponential for moments1,1,1. Variance supplies an automatic concentration bound. General smooth positivity alone is insufficient, as the exact same-moment polynomial counterprofile demonstrates; it is not completely monotone.
Scope: Complete analytic class/equality proof with shared27 controls. Original Bernstein and current action variables still require identification and independently derived moment values. v259 computes moments after inserting exp(-u), so its outputs are not independent selection premises. No new UV kernel or physical state is postulated.
Required premises and original source excerpts
Established within the stated premises
finding:existing-ap-positive-source-factor-has-oriented-poisson-heat-bridge
The existing source is exactly reconstructed from its signR and positive AP factorQ, including the crossing block. Q alone loses orientation. In the explicitly squared argument, this same factor is the diffuse positive subordinated profile exp(-sqrt(u)), with moments1,2,12 and amplitude/scale invariant shape ratio3, whereas every pure exponential has ratio1.
Scope: Analytic whole-spectrum result with18 new exact and actual96 controls. Constructs a bridge for a supplied source without selecting a new source/action. Physical action argument, K_car origin, reference and eta remain required. Does not impose Sbos=fermion logdet or exclude whole TFPT; linear-energy arguments require their own moment convention.
Required premises and original source excerpts
- Existing AP source factor and explicitly squared-energy comparison
Given self-adjoint invertible tangent reader of the constant original quarter class, beta=2ell and existing AP gluing factor Q=exp(-beta|h|), with full orientationR. Squared u=(beta|h|)^2 is an explicit comparison variable, not an assumed physical whole bosonic action identification.
premise:existing-ap-positive-source-factor-and-declared-squared-energy-comparison - Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison.
Positive finite Laplace measure and three finite positive moments. Identification of the original profile variables and independent physical moment values is explicitly not supplied by this mathematical comparison.
premise:positive-laplace-profile-finite-three-moment-comparison
Established within the stated premises
finding:actual-v252-entire-compatibility-family-has-generic31-dimensional-quotient
At actual v252 all84 independent real directions and their whole real family pass the specified compatibility equations. Actual54 U(3)^6 Lie generators have generic orbit rank53, certified by a nonzero exact53 minor and universal baryonic U(1). Generic quotient dimension31. Enumerating the same compatibility predicate cannot select a unique source. This checks the known31 dimensional finite NCG moduli on the implementation.
Scope: Entire family within the specified finite v252 form; basis plus linearity, Gaussian integers and exact rational rank;15 controls passed. Does not impose whole TFPT source/action selection or exclude original provenance; no new Lean theorem/ledger status. Binary2^84 subfamily is covered, not individually enumerated.
Required premises and original source excerpts
- Whole original v252 family under finite compatibility conditions
Four arbitrary complex3x3 Yukawas and complex symmetric3x3 MR in original full_D, with fixed original algebra,gamma,JF. Impose only Hermiticity,gamma oddness,JF reality and order zero/one. Generic quotient uses only R014 constant U(3)^6 coordinate changes. No whole TFPT source rule, extra fixed clock or action selector assumed.
premise:actual-v252-entire-yukawa-majorana-family-with-compatibility-only
Established within the stated premises
finding:full-memory-schur-reconstruction-preserves-every-ordered-word-under-nesting
For M=I-sum x_a A_a in formal free variables, F_P(F_R(M))=F_P(M) exactly for P<=R with identical variables and order. All block inverses have identity constant term. Full exterior feedback and input/output legs preserve every word coefficient. Gram positivity follows from actual word-vector norms. Minimal representation can be structurally fixed while responses change; stationarity or physical time does not follow.
Scope: Coefficientwise theorem on supplied domain; familiar Schur/Feshbach mathematics. No physical source selection, general analytic UV closure or noncommutative determinant. Whole original Z and unobservable factors are not inferred from a single boundary response; reuse completed F1.M1-M3.
Required premises and original source excerpts
Established within the stated premises
finding:original-return-and-native-j-have-minimal68-dimensional-all-word-memory
Exact original Fock polynomials close under L,J,Jdagger in dimension68. Actual positive metric and adjoint closure prove reachability, observability and minimality for all word lengths in this alphabet. Code5 needs memory63 with J multiplicities18,14,17,14 at1,i,-1,-i. Positive original forms F_w give both old defect Delta=sum F_w and new rank5 clock defect sum(w-1)F_w=-2(F_-1+F_i), with F_i=F_-i and ranks4,5,5,5. Original unit f4 has L² response6144 and LJL response0; bare repeated code compression gives1024. Full nested Schur reconstruction through10 equals direct reduction to5 exactly.
Scope: Complete linear realization for specified original single-beta L/J alphabet on neutral grade4:204 exact original-vector identities, positive metric,15 source controls and6 structure controls.68 is neither spacetime dimension nor whole E8 source. Values are response amplitudes, not event probabilities. No new Lean formalization, ledger promotion or full physical origin. Old rank10 was only a lower bound.
Required premises and original source excerpts
- Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
premise:local-e8-current-response-realization - Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
premise:native-g31-concrete-event-representation - 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 - 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 - Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
premise:original-neutral-root-pair-moment-fields - 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 - Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
premise:original-positive-adjoint-two-insertion-response-profiles - Specified ordered response family of original single pair
Examine mathematically specified moments M_n=Pi L_beta^n Pi,n>=0, L_beta=o(W_beta)*o(W_beta), for same original doubled root(0,0,0,0,0,0,-2,-2). Pi/Q only split full amplitudes; no projection is executed. This tests composition/memory of the already determined source, not P1 selection of physical history, coupling, preparation or time. Full coherent multiroot processes must additionally retain nonneutral final charge sectors.
premise:specified-original-pair-ordered-response-composition - Original single-root return with native Cartan J
Same complete original single-beta S and actual Fock adjoint as SOURCE-RETURN-MEMORY.txt, L=Sdagger S on neutral grade4 dimension726 with the original five quartics. Native linear J with Ju=i u,Jubar=-i ubar and its adjoint retained. Algebraic word responses of this supplied source only; no selected physical history or full E8 alphabet claimed.
premise:original-single-beta-return-with-native-cartan-j-word-alphabet
Established within the stated premises
finding:original-full-source-regulator-flow-retains-normalized-kernel-and-vacuum-factor
Original v42 integral gives partial_t Z=-D_dotR Z. For q=Z/Z[0],ell=logZ[0],a=(D_dotR q)[0], partial_t q=-D_dotR q+a q and partial_t ell=-a. Exact reweighting and conditional factors retain all original field responses and reference normalization through actual fibers without Gaussianizing. Keep mixed exterior legs. Gamma=Gamma_norm-ell retains geometric scalar response; at J=0, Gamma[phi_bar]+V_R[phi_bar]=-ell, not generally Gamma[0]=-ell. Reuses prior null-source result in the actual v42 flow.
Scope: Whole functional identities for supplied original integral; no existence proof of complete physical source. All8 even-density and6 bilinear-regulator Grassmann coefficients checked exactly; bosonic inverse heat series requires convergence. Retain geometry,reference,eta and original given time. Native68 state space is not configuration field space. No Lean or ledger promotion.
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 - Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
premise:historical-original-circle-and-transfer-source-passages - Whole original source caller with actual measure and legs
Original v42 Z_k integral exp(-S_adm-V_R+Jphi) with fixed original action,measure,domain and reference. Analytic statements require finite relevant integrals/derivatives and nonzero Z_k[0]; otherwise coefficientwise only. Actual field fibers retain Jacobians and Berezin ordering. Distinguish structural P_adm, configuration readout, positive-time half and state projection. No new measure or original source coupler assumed.
premise:original-regulated-full-source-with-actual-measure-and-legs
Established within the stated premises
finding:full-reflected-quadratic-regulator-cone-preserves-every-rp-source
In specified finite class exp(-phi R phi/2) preserves every original positive RP measure iff C is negative semidefinite. Bounded reflected feature expansion gives sufficiency; RP product Gaussian with Gcross=((I+A+C)^-1-(I+A-C)^-1)/2 and inversion order gives necessity, without simultaneous diagonalization. Cone closed under addition; R_k to zero recovers original source by finite dominated convergence. Exact RP baseline C0=[[1,1/2],[1/2,1]],R=ones,P_adm=I gives reflected response-1/16 despite ordinary positivity and structural commutation. Existing generic spectral-weight exclusion is reused, not recounted as new proof.
Scope: Complete universal preservation theorem only for specified bosonic two-half class. Known RP-cone mathematics specialized to original IR caller. Not necessary for every regulator of one fixed source, not full P1 countermodel or proof of original S_adm RP.18 controls together with source flow; analytic class proof separate. No new physical model optimization.
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 - Finite reflected positive quadratic IR regulator class
Two real bosonic halves with no fixed-plane fields, reflection swaps them. Real symmetric A,C and PSD R=[[A,C],[C,A]]. Universal preservation over all finite positive RP original measures; no silent extension to complex/graded fermionic cases. A fixed original source can admit additional regulators. IR regulator is not a physical selector.
premise:finite-reflected-positive-quadratic-ir-regulator-class
Established within the stated premises
finding:original-shared-higgs-source-induces-fixed-yukawa-mixed-matter-words
All288 real coefficient basis images of actual full96 one-form consumer match four H derivatives exactly with adjoints,grading and JF. Same supplied H fiber gives exact affine Z_H[J-j|A],all cumulants and absolute factor. Induced ordered nu/up four-fermion action coefficient is -G_h2barh2 Ynu_ab conjugate(Yu_dc),no factor2; third/fourth boson cumulants give6/8 fermion terms. Retain all extra H dependent fermion vertices,which can also alter four-fermion coefficient. Fermion-first evaluation uses actual det/Pf weighted full source polynomials,with minors at singular fibers rather than inverse division.
Scope: Actual original field consumer and whole finite source identity for supplied boson moments. Reuses old one-form and kinetic Pfaffian/determinant bridges. No new physical H measure,naive96 independent fermion integrations,full connected/1PI amplitude or universal nonzero coefficient at degenerate G/Y.17 controls including288 original identities; general proof analytic. Preserve Yukawa/Flavor/Alpha and free g+ results.
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 - Actual full v252 gauge lift and original P2 comparison
Given the full unchanged v252 constructor pi,J_F,gamma_F,D_F and its symbolic Yukawa/Majorana inputs. Compare real gauge lift U=pi(u)J_F pi(u)J_F^-1 on the connected unimodular branch lambda det(m)=1 with original oriented P2 carrier E3+E2,Y=(-1/3)^3+(1/2)^2. No full Spin10 source action is presumed. A cyclically fixed neutral family line is considered only with an expressly supplied sigma=(123) and eigenvalue1; its original physical selection is not assumed.
premise:actual-full-v252-unimodular-p2-gauge-lift - Actual shared real Higgs consumer and supplied boson fiber
Original real AF one-form convention q(H)=[[barh2,h1],[-barh1,h2]] with supplied four Yukawa matrices across all families/colors. Keep distinct lepton and quark matrices. H fiber is an argument of same full original S_adm with measure,reference,regulator,eta and higher vertices. Finite Berezin algebra and required finite boson moments; analytic limits separate. Affine shift applies to affine Yukawa coupling; retain any additional H dependent fermion vertices as actual insertions. No new physical measure or Yukawa selection.
premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber
Established within the stated premises
finding:local-even-yukawa-sewing-preserves-given-joint-graded-rp
Original v42 mixed RP inference does not follow from commutation and separately positive marginals. Strictly positive reflection-invariant logical control p=(1-r xminus xplus yminus yplus)/16 has RP product marginals and mixed reflected form-r. Constructive full replacement: for actual joint graded RP reference and even local half action B=exp(-Vplus), omegaY(ThetaF circ F)=omega0(Theta(BF) circ BF)/omega0(ThetaB B)>=0 with positive normalization and integrability. Handles whole supplied Yukawa class with adjoint partner wherever same actual reflection intertwines H/matter density. No pointwise positive determinant required.
Scope: Specialization of known RP half-action mathematics to actual Yukawa consumer,not new general RP theorem. Finite Euclidean graded path or proved integrable limit. Internal JF reality does not prove common spacetime reflection. No unchecked spectral/eta/gauge weights,fixed-plane/cross insertions. Logical marginal control is no TFPT countermodel. Old negative-cross criterion applies to regulator R,not Higgs propagator G. No original boson source selection or3+1D completion.
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 - Actual shared real Higgs consumer and supplied boson fiber
Original real AF one-form convention q(H)=[[barh2,h1],[-barh1,h2]] with supplied four Yukawa matrices across all families/colors. Keep distinct lepton and quark matrices. H fiber is an argument of same full original S_adm with measure,reference,regulator,eta and higher vertices. Finite Berezin algebra and required finite boson moments; analytic limits separate. Affine shift applies to affine Yukawa coupling; retain any additional H dependent fermion vertices as actual insertions. No new physical measure or Yukawa selection.
premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber - Supplied joint graded RP reference and even local reflected half action
Given actual joint graded RP reference omega0, same original antilinear Theta,positive-half algebra and twisted product. In the supercommutative Euclidean path the actual even interaction is Vplus+ThetaVplus with strict half support and no unchecked fixed-plane/cross terms. B=exp(-Vplus),relevant coefficient integrals exist and omega0(ThetaB B)>0. A bosonic/fermionic RP product supplies one such reference; RP marginals of a coupled source alone do not. These hypotheses are not declared derived physical original data.
premise:original-graded-rp-reference-and-even-local-reflected-half-action
Established within the stated premises
finding:whole-original-constant-higgs-orbit-has-reduced-majorana-spectral-response
For all H and supplied Y,Phi(H)=V(q/r)(rDY+DMR)V*,weak left rotation with same JF/gamma and unchanged MR.84 real Y/MR basis images on actual original96 confirm block proof. det96(z+Phi²) reduces exactly to charged3x3 powers12,12,4 and squared6x6 neutrino determinant Bnu=[[rYnu,0],[MR*,rYnu^T]]. First u jet is4/z Tr(3Yu*Yu+3Yd*Yd+Ye*Ye)+4Tr[(z+MR MR*)^-1Ynu*Ynu],retaining necessary Majorana cross-resolvent term. On supplied quarter circle the whole absolutely convergent mode sum is evaluated by s_alpha(v)=pi/sqrt(v)sinh(2pi sqrt(v))/(cosh(2pi sqrt(v))-cos2pi alpha).26 controls pass.
Scope: Whole constant original coefficient class and named1D product circle,no new physical parameter choice. Internal96 spectral multiplicity is not96 independent fermion integrations. No free Yukawa search,whole4D Z master or full dynamic H covariance. Nonconstant H,fixed nontrivial A and global projections retain original connection,domain and source transport. Existing weak-connection mixing response remains valid.
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 - Actual shared real Higgs consumer and supplied boson fiber
Original real AF one-form convention q(H)=[[barh2,h1],[-barh1,h2]] with supplied four Yukawa matrices across all families/colors. Keep distinct lepton and quark matrices. H fiber is an argument of same full original S_adm with measure,reference,regulator,eta and higher vertices. Finite Berezin algebra and required finite boson moments; analytic limits separate. Affine shift applies to affine Yukawa coupling; retain any additional H dependent fermion vertices as actual insertions. No new physical measure or Yukawa selection.
premise:actual-shared-real-higgs-yukawa-consumer-and-given-boson-fiber - Original constant Higgs fiber and symmetric Majorana spectral consumer
Given actual whole v252/v254 real96 q(H) one-form consumer,four fixed complex3x3 Y and complex symmetric MR between right neutrino singlets. Constant H,real coordinates without1/sqrt2,no fixed nontrivial weak connection. Matrix spectral shift z>0. All-mode result uses supplied scalar-quarter product circle h=(n+alpha)gamma-i gammaPhi,alpha1/4 or3/4 with its original domain and mu²>0. Extension to global Padm,reference or APS requires established common unitary transport.
premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer
Established within the stated premises
finding:archived-geometric-higgs-residue-bulk-needs-coefficient-identification-repair
Printed -6chi²ED+GammaD4 gives bulk +chi²u/(8pi²)+u²/(16pi²) at R0. Equal quadratic/quartic signs match neither printed target potential -mu²u+lambda u² nor its -V reading. Positive canonical/sheet normalization and common action/Wick sign cannot repair relative sign. For same u,+V requires original remainder -chi0²(1+wH²)u/(8pi²),-V requires chi0²(wH²-1)u/(8pi²)-u²/(8pi²). Required source responses,not permitted new addends. H-independent U(chi) or constant source denominator at fixed chi do not help. Keep FPzeta(0) distinct from -zetaPrime(0),and M(xi) distinct from H-source/Legendre/bare actions.
Scope: Exact failure of a literal identification of specifically named archived local formulas. No TFPT countermodel,physical vacuum-instability claim or exclusion of existing Yukawa/Flavor/Alpha. Full relative source,reference,eta,scale and continuation can carry further H contributions and must be evaluated. Existing local target quartic and its conditional responses remain; direct derivation from this printed bulk is not established. No new Lean theorem or ledger status.
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 - Literal archived residue and common Higgs-field comparison
Compare exactly printed bulk coefficients in archived v42 section013 and v45 metrology source002,ED_bulk=-R/(24pi²)-u/(48pi²),GammaD4_bulk=kin/(16pi²)+u²/(16pi²)+Ru/(96pi²),Gamma_grav=-6chi²ED+GammaD4,and stated target potential with muPhi²(chi0)=chi0²wH²/(8pi²)>0,lambda=1/(16pi²). Same field normalization u=Phi*Phi>=0,fixed positive chi0,flat R0 background. Remaining complete relative/reference/eta/zero-source terms are not presumed zero. No automatic Wick or Legendre identification,no claim this exhausts current theory.
premise:literal-archived-geometric-residue-and-common-higgs-field-comparison
Established within the stated premises
finding:original-local-higgs-residue-linear-coefficients-fail-same-trace-heat-ratio
Literal local Erel=-R/4-X gives coeff_ED(u)=-12 coeff_Gamma4(Ru),independent of rank/common linear trace weighting,including subtraction of two same-type Dirac producers. Named archived printed values -1/(48pi²),+1/(96pi²) give-2,a factor6 mismatch. With ordinary48 trace and rank2,whole printed ED bulk equals a2/6 while quartic/Ru match a4;conditional normalization diagnosis,not new original definition. If displayed E is complete and connection H-independent,integrated a4 gives no Higgs kinetic term;Delta u is a total derivative. Fixed boundary/reference data and s-independent iEta cannot repair real ED jet. Actual bound-reference variation is deck-even part of operator jet and may be frozen only upon established deck-oddness.
Scope: Excludes specifically named literal local heat identification,not whole TFPT or existing target action,Yukawas/gravity. Nonlocal Padm,different symbol,moving domain or additional original curvature terms require their actual producer. R029 sign problem is separate;+6 alone does not repair ratio.
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 - Literal archived residue and common Higgs-field comparison
Compare exactly printed bulk coefficients in archived v42 section013 and v45 metrology source002,ED_bulk=-R/(24pi²)-u/(48pi²),GammaD4_bulk=kin/(16pi²)+u²/(16pi²)+Ru/(96pi²),Gamma_grav=-6chi²ED+GammaD4,and stated target potential with muPhi²(chi0)=chi0²wH²/(8pi²)>0,lambda=1/(16pi²). Same field normalization u=Phi*Phi>=0,fixed positive chi0,flat R0 background. Remaining complete relative/reference/eta/zero-source terms are not presumed zero. No automatic Wick or Legendre identification,no claim this exhausts current theory.
premise:literal-archived-geometric-residue-and-common-higgs-field-comparison - Local common Higgs residue contract and conditional product consumer
Local source test assumes P=-(nabla²+E),R positive on spheres,same local linear trace for Res1 and FP0,E=-R/4-X(H),no extra H-dependent curvature/connection terms,fixed smooth interior and unchanged boundary data. Relative subtraction requires both operators of same type. Boundary/eta/nullity results use explicitly fixed regular domain branch. Actual whole96 Higgs family with supplied Y and symmetric MR is additionally evaluated through explicitly conditional standard product Dirac with spin4. Original spacetime/compression/reference/continuation map is not thereby derived.
premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer
Established within the stated premises
finding:whole-original-higgs-moments-fix-conditional-local-kinetic-mass-quartic
Whole original96 family satisfies Tr(Phi²-DM²)=Au,Tr(Phi⁴-DM⁴)=Bu²+4Cu,Tr(dPhi)²=Akin,A=4Y2,B=4Y4,C=2Tr(Ynu*Ynu MR MR*)>=0. Generic block proof and unchanged v252 consumer confirm identities including four-real derivative Gram matrix. Explicitly conditional standard4D product Dirac with separate spin trace gives a2H=-Au/(4pi²),a4H=Akin/(8pi²)+Bu²/(8pi²)+Cu/(2pi²)+ARu/(48pi²).For cchi²a2+da4,Z=dA/(8pi²),mu_can²=2(c/d)chi²-4C/A-R/6,lambda_can=8pi²B/(dA²). At R0 negative quadratic requires cchi²A>2dC;c=-6,d=1 gives positive quadratic for all supplied Y/MR.28 direct controls pass;control numbers are not new physical parameters.
Scope: Whole original finite coefficient class and named conditional local consumer. No new Y choice,96 extra physical fermion integrations,derived original boson measure,physical pole mass or full H covariance. Finite96 trace,geometric48 E and compact P2 require actual common map;printed scalar quartic must not be renamed.
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 - Original constant Higgs fiber and symmetric Majorana spectral consumer
Given actual whole v252/v254 real96 q(H) one-form consumer,four fixed complex3x3 Y and complex symmetric MR between right neutrino singlets. Constant H,real coordinates without1/sqrt2,no fixed nontrivial weak connection. Matrix spectral shift z>0. All-mode result uses supplied scalar-quarter product circle h=(n+alpha)gamma-i gammaPhi,alpha1/4 or3/4 with its original domain and mu²>0. Extension to global Padm,reference or APS requires established common unitary transport.
premise:original-constant-higgs-fiber-and-symmetric-majorana-spectral-consumer - Local common Higgs residue contract and conditional product consumer
Local source test assumes P=-(nabla²+E),R positive on spheres,same local linear trace for Res1 and FP0,E=-R/4-X(H),no extra H-dependent curvature/connection terms,fixed smooth interior and unchanged boundary data. Relative subtraction requires both operators of same type. Boundary/eta/nullity results use explicitly fixed regular domain branch. Actual whole96 Higgs family with supplied Y and symmetric MR is additionally evaluated through explicitly conditional standard product Dirac with spin4. Original spacetime/compression/reference/continuation map is not thereby derived.
premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer
Established within the stated premises
finding:whole-variable-original-higgs-bound-reference-response-and-forced-clifford-factor
Fixed spin4 Clifford contract forces {gamma_mu,W}=0 hence W=gamma5 L(H),with gamma5=Z in given collar chart;H derivative in E follows by squaring. Put p=(H+Htau)/2,m=(H-Htau)/2,P=|p|²,M=|m|²,v=Re p*m,QS=P²+2PM+4v²,QT=M²+2PM+4v². Bound original references L(m),L(p)+DM give after H0 baseline:a2S=-A intP/(4pi²),a4S=int[A|Dp|²+BQS+4C(P+M)]/(8pi²)+A intRP/(48pi²);a2T=-A intM/(4pi²),a4T=int[A|Dm|²+BQT+4CM]/(8pi²)+A intRM/(48pi²). Normal derivative parity transported. Only reflected-pair quartic mean is nonnegative;raw local difference can be negative. S cannot repair R0 mass sign or ratio-12 in -6chi²a2+a4. T cancels entire unscaled same-geometry pair response for purely even H at every spectral order.
Scope: Whole variable fields and supplied finite coefficients in named local product/reference contract. No primitive lift selection,derived spacetime origin,deck/RP identification,RP proof from positive integrated action,or exclusion of separate original fermion source/full TFPT.
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 - Local common Higgs residue contract and conditional product consumer
Local source test assumes P=-(nabla²+E),R positive on spheres,same local linear trace for Res1 and FP0,E=-R/4-X(H),no extra H-dependent curvature/connection terms,fixed smooth interior and unchanged boundary data. Relative subtraction requires both operators of same type. Boundary/eta/nullity results use explicitly fixed regular domain branch. Actual whole96 Higgs family with supplied Y and symmetric MR is additionally evaluated through explicitly conditional standard product Dirac with spin4. Original spacetime/compression/reference/continuation map is not thereby derived.
premise:local-same-trace-higgs-residue-and-conditional-product-dirac-consumer - Whole variable Higgs response with bound reference and original scale sandwich
Given ordinary spin4 product realization with unchanged96 Y/MR,fixed Clifford connection,H only order zero,and no H-dependent first-order coefficient of its square. Evaluate separately already supplied full collar lifts S Rr and S gammaF Rr without selecting either. Common reflected double with invariant metric/trace,transported common full domain,unchanged Y/MR under supplied base pullback,covariantly constant DM. H changes compactly in interior or closed double. Local geometric full/reference pair,not primitive bounded-Drel contract. Original Dsigma=fDf,f=e^-sigma/2,holding sigma fixed in H variations;distinguish unscaled and jointly scaled reference. Scale test assumes Brel0 or already transported mass chart;actual Brel must be evaluated in complete original sum.
premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt, lines 1–108
Source SHA256: 13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt, lines 109–208
Source SHA256: 13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_higgs_bound_reference.py, lines 1–89
Source SHA256: 1a2790a3059d5e3c0949a56c17ae7953d425c36f8319b3c514f5a568423be951
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE.json, lines 1–41
Source SHA256: 653628ee0809b311c03753bef2a7bc5970f1c6a08d495f3b2b826a2de0ca6512
bounded-excerpt · current-at-snapshot
- verification/v252_full_finite_triple.py, lines 85–168
Source SHA256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DECK-REFERENCE-AND-ACTION.txt, lines 1–100
Source SHA256: d392cfc2c0b3b50d39a041c6c1ee8bd3a1e173f80e767f35e05ba82344eaf0f1
bounded-sanitized-excerpt · current-at-snapshot · 3 administrative lines explicitly omitted
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DECK-REFERENCE-AND-ACTION.txt, lines 101–197
Source SHA256: d392cfc2c0b3b50d39a041c6c1ee8bd3a1e173f80e767f35e05ba82344eaf0f1
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex, lines 1–146
Source SHA256: f03609effe2abf6629a0057fa024c29fba0c59176072588599bfa1646f48939e
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex, lines 39–96
Source SHA256: 313dade0e18117f8b4f5c7ad88d8e91caeaa11fe4a23cf32fc3f7bac238dab58
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex, lines 143–224
Source SHA256: 313dade0e18117f8b4f5c7ad88d8e91caeaa11fe4a23cf32fc3f7bac238dab58
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex, lines 122–154
Source SHA256: 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
bounded-excerpt · current-at-snapshot
Established within the stated premises
finding:original-symmetric-scale-map-fails-simultaneous-higgs-einstein-repair
Given4D spin realization gives Dsigma=fDf unitarily equivalent to Dirac_ghat+gamma5 exp(-sigma)Phi,ghat=exp(2sigma)g,U=exp(2sigma)F^-1. H and DM scale together. H-dependent a2=-A int exp(2sigma)|H|²/(4pi²);integrated a4H invariant up to divergence,including Majorana term. For deck-even sigma,UNSCALED bound reference,t=exp(2sigma):a2SrelH=-A int[tP+(t-1)M]/(4pi²),a2TrelH=-A int[tM+(t-1)P]/(4pi²),a4 as R032. t-1 not always positive. Constant sigma,pure even H,S branch gives H²/RH² ratio-12t. t=1/6 alone would match printed-2,but same ordinary positive trace/same bundle gives Einstein a2relR=-N(t-1)intR/(192pi²),POSITIVE at1/6 versus printed NEGATIVE for all N>0. Jointly scaled reference cancels pure Einstein response. Variable sigma adds -N int6t|dsigma|²/(192pi²). Complete Ksigma=fDgeof+Brel is not resolved by B0 test. Dsigma² differs from exp(-sigma)D²exp(-sigma).
Scope: Executed original scale map within named product realization/two explicit reference conventions. Not general exclusion of different original Brel/symbol/trace/domain data,no free Psi coupling,joint sigma backreaction,or whole H source integration. Read metrology owner names Brel without evaluating its H component there;not corpus-wide absence claim.29 direct controls,exact generic proofs,and actual The reviewed/Gemini/the reviewed source review.
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 - Literal archived residue and common Higgs-field comparison
Compare exactly printed bulk coefficients in archived v42 section013 and v45 metrology source002,ED_bulk=-R/(24pi²)-u/(48pi²),GammaD4_bulk=kin/(16pi²)+u²/(16pi²)+Ru/(96pi²),Gamma_grav=-6chi²ED+GammaD4,and stated target potential with muPhi²(chi0)=chi0²wH²/(8pi²)>0,lambda=1/(16pi²). Same field normalization u=Phi*Phi>=0,fixed positive chi0,flat R0 background. Remaining complete relative/reference/eta/zero-source terms are not presumed zero. No automatic Wick or Legendre identification,no claim this exhausts current theory.
premise:literal-archived-geometric-residue-and-common-higgs-field-comparison - Whole variable Higgs response with bound reference and original scale sandwich
Given ordinary spin4 product realization with unchanged96 Y/MR,fixed Clifford connection,H only order zero,and no H-dependent first-order coefficient of its square. Evaluate separately already supplied full collar lifts S Rr and S gammaF Rr without selecting either. Common reflected double with invariant metric/trace,transported common full domain,unchanged Y/MR under supplied base pullback,covariantly constant DM. H changes compactly in interior or closed double. Local geometric full/reference pair,not primitive bounded-Drel contract. Original Dsigma=fDf,f=e^-sigma/2,holding sigma fixed in H variations;distinguish unscaled and jointly scaled reference. Scale test assumes Brel0 or already transported mass chart;actual Brel must be evaluated in complete original sum.
premise:whole-variable-higgs-bound-reference-and-conformal-dirac-map
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt, lines 1–108
Source SHA256: 13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE-PROOF.txt, lines 109–208
Source SHA256: 13e79f2be052ca918fd2be8faf8cf6f1669fc3ad535ccf9a3fdff5b7c0b1b3c5
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_higgs_bound_reference.py, lines 1–89
Source SHA256: 1a2790a3059d5e3c0949a56c17ae7953d425c36f8319b3c514f5a568423be951
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-HIGGS-BOUND-REFERENCE.json, lines 1–41
Source SHA256: 653628ee0809b311c03753bef2a7bc5970f1c6a08d495f3b2b826a2de0ca6512
bounded-excerpt · current-at-snapshot
- verification/v252_full_finite_triple.py, lines 85–168
Source SHA256: 820254440e178430422e50605067775656236602996307f67c9e69124ba5d163
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DECK-REFERENCE-AND-ACTION.txt, lines 1–100
Source SHA256: d392cfc2c0b3b50d39a041c6c1ee8bd3a1e173f80e767f35e05ba82344eaf0f1
bounded-sanitized-excerpt · current-at-snapshot · 3 administrative lines explicitly omitted
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/DECK-REFERENCE-AND-ACTION.txt, lines 101–197
Source SHA256: d392cfc2c0b3b50d39a041c6c1ee8bd3a1e173f80e767f35e05ba82344eaf0f1
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/001-subsection-from-bridge-to-geometric-completion.tex, lines 1–146
Source SHA256: f03609effe2abf6629a0057fa024c29fba0c59176072588599bfa1646f48939e
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex, lines 39–96
Source SHA256: 313dade0e18117f8b4f5c7ad88d8e91caeaa11fe4a23cf32fc3f7bac238dab58
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--05_metrology_source/sections/002-subsection-closed-texorpdfstring-41-41-chain-after-famil.tex, lines 143–224
Source SHA256: 313dade0e18117f8b4f5c7ad88d8e91caeaa11fe4a23cf32fc3f7bac238dab58
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex, lines 122–154
Source SHA256: 7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79
bounded-excerpt · current-at-snapshot
Non-scientific attribution omitted from public display.
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