Excluded in the stated class
finding:original-a4-linear-quarter-does-not-supply-proposed-scalar-mu3-repair
The proposed minus-one times omega-squared repair requires a scalar mu3 holonomy on a V4 loop. Every actual A4 scalar character is trivial there, and quarter equivariance further leaves only the trivial character. The entire four-puncture mu3 character class has 27 members and only one cyclic-quarter invariant member. A marked extra line can give the desired value but is additional changed data.
Scope: Only the proposed scalar repair within the stated original class is excluded. No claim against marked lines, projective/antilinear/rank-two structures, actual Higgs/reader legs or physical CP as a whole. Do not infer reality of all structural projectors from real kernel parameters, or identify a bilinear evaluation rule with its argument or with the physical consumer.
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 - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock - Original hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contract
Established within the stated premises
finding:offdiagonal-hom-matches-a4-family-six-but-not-two-triplet-e8-product
Original s/R lifts and normalized two-torsion products give the explicit unitary A4 bundle map. The direct holomorphic two-triplet wedge has complex family rank three and is not six independent complex holomorphic components. Its fixed-quarter and generic SU4 counterexamples remain valid for that complex-linear map. Compact real completion must instead retain the actual adjoint and simultaneous D5 carrier conjugation, as reviewed in the subsequent correction.
Scope: A genuine restricted bundle connection and product exclusion for these two inputs, not a dimension dictionary. The original full K includes O; no singlet zero mode does not exclude full fields or existing seam/Hardy modes. Their actual spin, twist, mode and statistics must be checked. Do not substitute a bosonic E8 current for a Grassmann matter field. Fixed-quarter failure is not a universal fixed-marking requirement under whole-data transport, and no free singlet is added. Correction: no universal O-fermion gate follows for compact real completion. Family Hodge alone also does not prove full(10,6) with the carrier suppressed: direct C/X triplet inputs give30 real directions, full16xF inputs60. Subsequent carrier and restricted-D8 findings replace the old active O-input gate.
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 - Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
premise:recovered-genus-two-cover-with-retained-signed-coefficients - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock - Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
premise:given-split-carrier-and-actual-genus-two-q-sign-family - One E8 current trilinear as the same Weyl quadratic with one anchor mark only
Test only literal B_h=κ(x,[h,y]),h in(10,6),x,y in(16,4), as the local quadratic coefficient of the SAME left four-dimensional Weyl multiplet with Lorentz epsilon. In each fixed spin/charge channel the family form omega is skew. Allow linear combinations F(X)omega G(X) for only ONE X=diag(3,-1,-1,-1) and arbitrary polynomials. Other original family generators, independent Dirac variables, derivative vertices, multiple omega factors and different field maps are outside this class.
premise:one-e8-bracket-weyl-pairing-with-single-anchor-dressing
Established within the stated premises
finding:compact-e8-adjoint-completes-family-six-with-carrier-rank-retained
Actual compact adjoint induces canonical anti-linear Hodge reality on the family six and is native-quarter/SU4 covariant. No universal extra O-fermion input is required for real family completion. Dagger simultaneously reverses the D5 vector weight: restricted C/X|F gives15 complex and30 compact real directions, while full16xF inputs supply30 complex and all60 compact real directions. The missing carrier half comes from10xbar5, not family Hodge or10x10 alone.
Scope: Corrects both the universal O gate and the first overstrong full60 reading of family-only Hodge. Retain valid adjoint/SU4 identities. Does not identify geometric mu with complete spinor inputs or a finite Phi block; no physical scalar or whole-origin promotion. The separate D8 finding decides the entire restricted recursive class.
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 - Given original C/X current source with E8 cocycle and compact adjoint
Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjoint - Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
premise:given-split-carrier-and-actual-genus-two-q-sign-family
Established within the stated premises
finding:three-family-cx-recursion-closes-exact-d8-with-minimal-original-escape
Only original C/X family labels1,2,3 and adjoints give36 seed roots. Full recursive Chevalley closure is36,92,112, rank8 and exact D8. Missing10xF components remain unreachable;30 of60 target roots occur and30 never do. Depth-two new roots are10xO plus adjoints. Any single omitted original C0 or X_i0 root, with its adjoint for compact input, escapes to E8 with114,170,240. Thus this restricted recursive class is fully decided and its minimal original escape specified.
Scope: Complete finite zero-mode Lie closure and concrete different D8 frame in E8. Not a no-go for higher affine products, other original operations or the full original family four. No new species invented. Geometric mu access to the minimal existing escape current and actual finite consumer remain separate. Algebraic reachability is not state preparation or physical time; independent root-sum and source-cocycle audits agree.
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 - Given original C/X current source with E8 cocycle and compact adjoint
Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjoint
Established within the stated premises
finding:original-weak-current-coefficient-has-explicit-finite-oneform-consumer
The actual weak bar5 coefficient has an explicit quaternionic Higgs witness in the original finite algebra. Its evaluated one-form has LR=q(H)diag(Yup,Ydown), with correct SU2, hypercharge and grading and explicit nonzero lepton/quark entries. General sums retain a common2x2 matrix Q multiplying the already supplied Yukawas across generations and sectors. The separately evaluated central dz normal reader is finite-identity valued and does not create a family Hom matrix.
Scope: A genuine finite-slot coefficient witness, not a full geometric mu-to-current-to-Higgs identification. General complex-linear span gives Q in M2(C); quaternion conjugation constraints require an explicit real-algebra/reality contract and do not follow merely from self-adjoint completion. Preserve actual color projection and Pati-Salam scopes. Old v258 modular inversion is for a given covariance and records the physical seam compression as conditional, not an independently evaluated mu source. Next test the simultaneous common-Q times given-Y relation at the actual geometric sewing consumer. Crucial goal distinction: the QY test applies to inner fluctuations around a fixed supplied D_F, not to original generation of D_F and its Yukawa matrices themselves. Source reconstruction of the background may change those matrices and must neither be excluded by the fixed-background fluctuation class nor replaced by merely varying it. The reviewed further mandatory family-scalar mu-reader conclusion is unsupported. A bare C3 sum is not A4 invariant, and real D†D does not imply real full Pstr kernel with unchecked complex projectors.
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 - Given original C/X current source with E8 cocycle and compact adjoint
Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjoint
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:original-d5-zero-mode-closes-triplet-carrier-and-fixed-glue-is-minimal-escape
The restricted D8 contains only20 of40 original D5 roots. An original grade-zero D5 zero mode gives the explicit cocycle-correct word into the missing carrier half, preserving glue grade2. Full original D5 action with the triplet seed closes to all240 roots; its Weyl orbit completes15 to30 complex target directions and adjoints to all60. No new O fermion or freely supplied full16 input is needed. Original marked glue lambda maps in the fixed chart exactly to C0 dagger, with its adjoint the minimal D8 escape pair. The D8 vacuum lattice VOA preserves its coset; distinguish its new Z2 parity from old mu4 grades.
Scope: Positive actual operator connection at the given P2/E8 current level; replaces the extra-carrier/O gate. Not primitive P1 realization, physical zero-mode history, geometric mu-to-current or simultaneous-QY consumer derivation. Original quarter twist still lacks the localized charged glue-vertex identification beyond its conditional neutral eight-copy kernel. Accept The reviewed independently matching D8/D5 step, not its further exchange/CP or normal-carrier-selection conjectures. Do not count existing total Hom character compensation twice.
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 - Given original C/X current source with E8 cocycle and compact adjoint
Use the actual supplied level-one E8 current source C in1x4 and X inbar5x4, original cocycle and compact adjoints. The expressly restricted initial seed keeps only family labels1,2,3. Check current Lie words without presupposing geometric q/p access, a finite Phi coefficient or physical P1 source selection.
premise:given-original-e8-cx-current-cocycle-and-compact-adjoint - Original D5 base-current action on supplied P2 and E8 carrier
Original D5_1 x A3_1 base net and explicit P2 Clifford carrier supply full45-dimensional D5 operator action including20 non-U5 roots. Its zero modes act with the existing Chevalley cocycle on the supplied compact E8 currents; no primitive P1 preparation or history selecting a word is presumed.
premise:original-d5-base-current-action-on-given-p2-e8-source
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:mixed-spin-full-deck-has-no-rank-three-projector
In natural spin frames s*mu_ab=-mu_ba and R*mu_ab=rho^-1 mu_(b+1,a+1); the antisymmetric half is the positive U6-cube sheet after orbit phase calibration. The diagonal-A4 coefficient coisometry and bare positive K3 calculation are exact but do not define a global triplet subsource: six distinct V4q times V4p characters, together with transitive R, have scalar commutant. A displayed sign element exchanges antisymmetric and symmetric pairs. The original base map and v117 pullback already exist.
Scope: Complete finite result only for the bare six global section channels with independent original deck signs and R. Not an obstruction to coupled endpoint kernels, Bmu, diagonal response or P1. A4-only coefficients are a restricted category. Marked S conjugation transports a supplied triplet matrix rather than producing a global triplet subsource; retain canonical-form and endpoint factors. Read the early bridge report only together with its corrected addendum. Completed The reviewed and the reviewed source identify bare mu channels with Gamma paths, but matching labels do not compose their actual q/p endpoint and canonical-form types. The actual Bmu response is the source-supported replacement.
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 - Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
premise:recovered-genus-two-cover-with-retained-signed-coefficients - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:actual-reverse-hom-diagonal-supplies-global-q-hodge-response
The actual B=GqJ* composition T(u,v)=B(u,v)mu(v) cancels the full intermediate p signs and retains q input/output covariance. On existing smoothing same-face diagonals, the original bilinear skew projection and oriented Hodge map yield a global canonical-form-valued Fq response, retaining normal and D5 operators without new line, state or normalization. The given scalar common-quarter collar at Phi=0 already has a nonzero response to original off-diagonal insertions, using its actual positive diagonal Fourier kernel and invertible endpoint factor, without input Yukawas.
Scope: Positive global coefficient/form response of the supplied whole source. No pointwise Hodge at unmatched bilocal endpoints. Its integrable diagonal is not automatically a bounded full L2 composite, holomorphic section or finite Yukawa matrix. Scalar Phi=0 test does not trivialize actual Fuchs monodromy. At D_F=0 the original finite one-form vanishes while this response may not; the actual P1 variation or sewing operation must select and turn it into a background generator. No universal fixed-background QY gate. Wrel alone does not select J* M_mu. In an exact supplied graph block the second CAR cumulant9/25 differs from affine-logdet second derivative−16/25 and mean product16/25; retain actual source coupling. This is not a complete TFPT countermodel.
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 - Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
premise:recovered-genus-two-cover-with-retained-signed-coefficients - Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
premise:given-split-carrier-and-actual-genus-two-q-sign-family - 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
Established within the stated premises
finding:bare-c3-kernel-diagonal-yukawas-have-common-real-frame
The same D=diag(1,omega,omega²) conjugates every positive bare H3 and its inverse square root to real symmetric matrices. Real diagonal left/right readers commute with D, so all such Yukawas are simultaneously real and all weak flavor CP-odd invariants vanish. No parameter or genetic search within this fully classified bare class can change the result.
Scope: Only the specified bare kernel class without additional relative readers or noncommuting actual holonomy words. No general TFPT CP obstruction, Majorana/theta claim or identification with full Pstr. Singular parameters are outside the inverse-square-root domain. Outside the common-real class, twisted contributions in both sectors are not necessary for algebraic CP: invariant Yu and one-sector twisted Yd=I+Pdiag(1,2,i) have Tr([Hu,Hd]^3)=-1440i. This is not an original TFPT mass derivation.
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 - Bare positive C3 kernel with real diagonal Yukawa readers
For this restricted analytic class only, take the displayed positive circulant H3 with real parameters and strictly positive eigenvalues, and Y_f=L_f H3_f^-1/2 R_f with real diagonal readers. This is not assumed to be the original P1 consumer or full Pstr compression.
premise:bare-c3-positive-kernel-with-real-diagonal-yukawa-readers
Established within the stated premises
finding:original-primitive-action-is-present-highpass-is-not-finite-selector
the reviewed source correctly quoted the original primitive relative-action formula and its bound reference/relative split. Do not reject it by substituting a different relative-trace convention. The actual primitive projector is seam-even times a spectral high-pass and retains infinitely many circle modes, so it does not by itself select finite Hcar or generate Yukawas. The displayed master variables and hypercharge Y are distinct from Yukawa matrices.
Scope: Preserve the original action and supplied full GNS/state/time source. Not an exclusion of every possible variation or renormalization; reuse existing coupled reference/reflection/gap/domain/projector/eta variation results. Old first-order-bound and D4 corrections are not rediscovered. This checks only the claim that primitive projection/stationarity already generated the finite background.
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 - 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
Non-scientific attribution omitted from public display.
Established within the stated premises
finding:atlas-detail-retrieval-recovers-existing-d4-solution
The actual natural D4 request reached the correct large problem, but full-JSON detail ranking let source metadata hide the existing solution. The small existing Rust retrieval now prioritizes semantic coverage and result text while preserving exact IDs and metadata fallback; bilingual tokens and continuation packing were repaired. Three regressions and all19 research-module tests pass. A fresh actual run.sh mcp request retrieves the existing D4 repair first with seven sources and within budget at the same data revision.
Scope: Retrieval software repair, not a new theory proof or direct graph edit. Existing old MCP processes do not hot-reload; fresh isolated connection was actually verified without stopping other clients. No full server-suite claim. Until normal reconnect, use exact IDs or the existing fresh stdio path rather than interpreting missed retrieval as scientific openness.
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:original-poisson-normal-trace-fixes-whole-calderon-graph
For the supplied homogeneous selfadjoint collar, its Poisson range graph(exp(-ell h)) and original positive boundary metric uniquely determine the full bounded orthogonal projection G with A=(1+exp(-2ell h))^-1 and X=(2cosh ellh)^-1. Both normal traces of the antiperiodic Green formula give G directly. An invertible periodic realization yields an oblique projection with the same range and thus the same orthogonal G. Functional calculus includes unbounded h; no extra AP-selection gate is needed.
Scope: Exact bridge for the supplied homogeneous source. Bulk Green kernel and boundary projection are related by the proved normal-trace map, not literal equality. No equality of h with longitudinal quarter time. Wrel defines generic source derivatives but does not alone select J_geom* M_mu; the supplied source and specified insertion fix its response.
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 - Complete data of both product-collar faces
A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.
premise:actual-product-collar-two-face-data
Established within the stated premises
finding:induced-original-hardy-defect-gives-finite-whole-source-reader
Actual signed G columns prove F_v117=Ind_V4^A4 chi0=pi_*L0q. The old spin cable is the correct induced family bundle without extra copies. Its given NS Hardy unit-shift defect has family rank three and transports by V_h into the whole graph, giving M_rs=<JE_r,M_mu E_s>. The actual induced mu01 input at Phi=0 gives nonzero M02=(4X*/pi)I Pgamma+, X*=(2cosh(ell_NS/2))^-1, I=0.1258739334853158906973-0.4697679151157443151336i. Actual q2/p1 open arcs add by their Kummer signs while diagonal pairs cancel. A closed primitive and strict analytic lower bound prove nonvanishing. Independent root checks give zero exact derivative remainder and continuous-branch quadrature residual below3.2e-76.
Scope: Existing mathematical NS Hardy source contract, not a newly proved physical finite P1 selection. The graph-lifted shift differs from both-face diagonal shift and relative matching; the whole-annulus shift has index zero. Graph membership alone does not establish finite time stationarity. The evaluated response is neutral and grading even, retaining all D5/charge slots, not an odd Higgs/Dirac source. NS frequency1/2 and quarter1/4 are related only via the old double-frame map with ell_quarter=2ell_NS and both quarter sectors for the seam shift; no physical scale/time equality is inferred.
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 - Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
premise:recovered-genus-two-cover-with-retained-signed-coefficients - Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
premise:given-split-carrier-and-actual-genus-two-q-sign-family - Relative spin and reference Hardy cable on original three-cover
Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-cover - Complete data of both product-collar faces
A selfadjoint B occurs in an exact normal-independent product equation. The full orthogonal L2 Cauchy graph projection of both labeled faces, their actual fiber identification and independently known positive normal length ell are supplied. Selection of these data from P1/P2 is not presumed.
premise:actual-product-collar-two-face-data
Established within the stated premises
finding:original-weak-quartic-action-has-nonzero-nonlinear-response
Original Metrology already contains E_rel=-R I48/4-(Phi*Phi)P2+gammaF/2 and the weak E2 potential. Along admissible Phi=s varphi the first E response vanishes, second equals-2(varphi*varphi)P2; the potential has explicit nonzero second and fourth responses and a nonzero radial minimum for positive coefficients. The supplied scalar collar crossblock likewise has zero first but explicit nonzero second variation. No new free quartic ansatz is needed.
Scope: Retains given E2 admissibility and Yukawa seed. Euclidean GammaD4 and stated potential use distinct sign conventions. Zero first X derivative is not a no-go for whole G responses. Bound primitive variation retains reference, gap, reflection, eta and domains. Does not prove that B_mu is the E2 tangent or impose fixed-background QY as a universal origin condition.
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 gap-normalized relative P1 action
Original source defines chi_seed=1/lambda_1^+(|B_Sigma|), S_prim=Tr f(D_rel/chi)-Tr f(D_ref/chi)+i pi Deltaeta/2 for declared spectral test profile. D_rel/ref are geometric odd/even parts; varying reflection, boundary domains, reference, state and eta must be retained. This is the given source function, not a new coupling or physical event rule. Scalar quarter CAR realization and NS/native field dictionary remain explicitly conditional.
premise:original-gap-normalized-primitive-relative-action - Given finite SM representation with symbolic Yukawa inputs
Use only the existing v252/v254 representation with C⊕H⊕M3, already supplied color/weak modules and four symbolic complex3×3 Yukawa blocks. No physical values are chosen or fitted. Classify the particle LR one-form block; no proof of the full real96-dimensional fluctuation with antiparticles, JAJ and Majorana sector is claimed.
premise:given-finite-sm-triple-yukawa-inputs
Excluded in the stated class
finding:all-common-leading-distance-clutches-fail-original-flavor-lengths
Original diagonal TOTAL lengths Lu=(7,3,0),Ld=(7,5,2),Le=(8,5,3) have sorted gap ratios3/4,3/2,2/3; separate numeric left/right lists are not supplied. A common single-leg list requires one ratio. For equal-weight same-list two-leg readers, normalize x=(0,1,t): all six relative S3 permutations are degenerate or give only t-1 and its reciprocal. No arbitrary real triple reproduces all three original rows. Entire class is analytically decided.
Scope: Only shared leading distances with the stated equal weighting. Different q/p spectra, unequal weights, full mode sums and actual sector-dependent original C6 residue packets with additional length-six windings remain outside the exclusion. Frobenius exponents are not a boundary clutch without an actual operator dictionary.
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 - Common leading triple distances with equal two-leg weights
Restricted candidate class only: arbitrary shared real triple x, sector positive scales/offsets and permutations, single leg or equal-weight same-list two legs. Not a P1 axiom. Different lists/weights, full sums and extra operator histories lie outside.
premise:common-leading-distance-flavor-readers
Established within the stated premises
finding:actual-hardy-response-has-weak-clifford-odd-and-ko-real-completion
For the actual nonzero Hardy coefficient and marked original weak P2 creators, the exact commutator gives a nonzero grading-odd color-neutral weak doublet of hypercharge+1/2, rank16 for each component in the declared whole-96 comparison. All45 D5 Clifford bilinears commute with the even Hardy projection. Adjoint completion alone has rank32 and fails finite reality. Full original KO6 completion has rank64, is selfadjoint, grading odd and J_F real, with D_KO^2=|kappa|^2(E00+E22) tensor I32. All four sectors retain the same family matrix but fixed quark/lepton signs and antiparticle conjugations; no Majorana block. Actual checker replays and independent root algebra pass. Crucially, original carrier008 already contains the primitive exterior-volume coupling. Its actual up-quark channel reads the new directed coefficient as+kappa; the fixed signed KO Hilbert convention gives-kappa because compact conjugation reverses the complementary wedge. No phase is fitted. The original weak carrier consumer is therefore present.
Scope: Exact operator and original carrier consumer under the declared family/96 P2 comparison. Original wedge contraction corrects the earlier overly broad claim that no original weak Clifford application exists; read the two earlier operator reports with this addendum. Original family coefficients are already prescribed by Hol(nablaF*)Kstr. It remains to compare the actual Hardy contribution with the relevant entry, actual variation or path summand, without imposing equality to the whole Ybr as a universal condition or treating original Y as arbitrary free v252 inputs. Keep mixed E8 family leg, fixed-background limits, C0 versus J_F, internal versus field CAR parity, and NS versus physical quarter time distinct. A correct finite block is not the complete physical source derivation. General addendum: identical familyM on all96slots yields S=M+M^T. Two directed edges give equal nonzero singular values, not unique polarCKM. Different bare doublet-component coefficients violate fixedSU2. Typed original sector-specific readers remain allowed.
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 oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
premise:oriented-p2-exterior-carrier - Alternative chiral comparison of q columns with actual v252 P2 carrier
For this explicitly alternative comparison identify actual G columns(L0,L2,L1) with supplied generation slots through whole signed P2 dictionary. D_E acts on gamma_F positive,barD_E on negative. Retain unchanged full_D with Y and symmetricMR,F5 structure,faces,graph state and given time. Do not silently replace earlier particlewise hypothesis. No P1 selection,global trivialization,new state/time or physicalE8gauge action assumed.
premise:declared-q-column-to-v252-chiral-slot-comparison - 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 - Original D5 base-current action on supplied P2 and E8 carrier
Original D5_1 x A3_1 base net and explicit P2 Clifford carrier supply full45-dimensional D5 operator action including20 non-U5 roots. Its zero modes act with the existing Chevalley cocycle on the supplied compact E8 currents; no primitive P1 preparation or history selecting a word is presumed.
premise:original-d5-base-current-action-on-given-p2-e8-source - Relative spin and reference Hardy cable on original three-cover
Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-cover - Original hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contract
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-PRIMITIVE-WEDGE-CONSUMER-HARDY-REVIEW.txt, lines 1–123
Source SHA256: f830ec1e84b614b175918fd7aad5659121c3f53d9f12693ab0bed602e4d4f87c
bounded-excerpt · current-at-snapshot
- documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/008-source.tex, lines 155–245
Source SHA256: aa2731355579b961ea9de47532cb0a4cb3db6e1c29e0f18965b517d1280d8d85
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- documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/004-source.tex, lines 180–244
Source SHA256: 107d525221eb816043dbf4fb1a3c7e8244d3e24a5a5bcbfe1c2c34d8ee192f4a
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HARDY-BMU-WEAK-CLIFFORD-ODD-LIFT-REVIEW.txt, lines 1–176
Source SHA256: 2840c19c6f80ad23c88011194c21dbc02905538891fb4b0ac4384e165783c975
bounded-sanitized-excerpt · current-at-snapshot · 18 administrative lines explicitly omitted
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/HARDY-BMU-KO-AND-FOUR-SECTOR-COMPLETION.txt, lines 1–178
Source SHA256: 6548f713daafb6c76d0ba195bbd16a0a0f1d7ac28b235a38854239533d97bb89
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_hardy_bmu_weak_clifford_lift.py, lines 1–193
Source SHA256: 5e2cbc4cda9dfd3ccbb35df45b13b796861e42545e3c6b9729c666925b7787e8
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_hardy_bmu_ko_completion.py, lines 1–184
Source SHA256: 4b4702bf9911db2e100c4db18799e0145efcbcc0c7c4a4faf84a7a67f8c61204
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-HARDY-CLIFFORD-AND-MODEL-REVIEW.txt, lines 1–69
Source SHA256: 7d0e548953e7e52e56a6da43dce2c71e5387376e189c966f2b2be08bb9cd174a
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/CLAUDE42-GENERAL-FAMILY-KO-AND-SU2-REVIEW.txt, lines 1–170
Source SHA256: 5029b23a17a31856d3b1cf74348fc2b83484f3f38e83ace5a3ecd01fa22c6904
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-C6-KO-CANDIDATE-REVIEW.txt, lines 1–70
Source SHA256: f691ed00544966a616cebfa260517a6a464ef7d68bc805f4e1ca6a0122e84a03
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Excluded in the stated class
finding:two-entry-hardy-adjoint-hierarchy-fails-full-ko-and-su2
For arbitrary complex3x3M identically lifted to actual96family slots, full originalKO6 completion of A=[X,MP+]=MXgamma is D=(M+M^T)Xgamma−(M†+barM)X†gamma. For M=aE02+bE21 the symmetric coefficient has singular values(r,r,0),r²=|a|²+|b|²; fullD has rank64. Independent symbolic characteristic polynomial and actual96replay confirm this. RawM/M† Grams are diagonal; fullKO has a degenerate two-space, not a unique polarCKM prediction. Actual[T+,Xw2]=Xw1 forbids unrelated bare matrices on this fixed doublet.
Scope: Complete stated identical-M lift/two-edge class, independent of uncalibrated second-ray sign. Not a universal restriction on originalYukawas. Typed sector-specificHolK readers,H/conjugateH intertwiners and complete mixed-current family legs remain outside. Originalwedge consumer is present. Rayquadrature is not calibration of actualM21. No physicalmass/CPclosure.
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 oriented exterior carrier
Given E=C5=E3⊕E2, a Hermitian metric, volume orientation, S± and Y=(-1/3)^3⊕(1/2)^2. Internal carrier labels are not physical vacua; geometric seam reflection is not identified with carrier conjugation.
premise:oriented-p2-exterior-carrier - Alternative chiral comparison of q columns with actual v252 P2 carrier
For this explicitly alternative comparison identify actual G columns(L0,L2,L1) with supplied generation slots through whole signed P2 dictionary. D_E acts on gamma_F positive,barD_E on negative. Retain unchanged full_D with Y and symmetricMR,F5 structure,faces,graph state and given time. Do not silently replace earlier particlewise hypothesis. No P1 selection,global trivialization,new state/time or physicalE8gauge action assumed.
premise:declared-q-column-to-v252-chiral-slot-comparison - 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
Established within the stated premises
finding:actual-fuchs-halfpath-has-canonical-g-metric-c6-kernel-map
Actual originalv117 P/Q integration and separately exact unitarykernel now share a closed frame map using already proved algebraicG. Fixed H=G^-dagG^-1 source metric and actualsigned cycleCs give Cpair^-1TrawCpair=[[0,Cs],[I,0]] with Cpair=diag(Gx,PGx) an isometry. Sourceadjoint equalsinverse. ExplicitB and existingJ connect to originalM/U6. Actualpath,D,metricGram,Green and inverse square root share one isometricfinite map, independently replayed with realP/Q residuals<1.3e−12. EvenwordCs² reads certifiedκE02 contribution; barepositiveK branch weights give v±κ. These are evaluated contributions, not an assertion that the complete originalsource inserted them. Stronger common marked closure: originalGbase/H0 gives H0^1/2Gbase=e^(7pi i/12)Bstar with explicitly fixed unitaryBstar. The sameBstar intertwines both actualCs to originalM0 and inverseKQ to originalU, hence all four markedmeridians. Exactly BstarE02Bstar†=M0P0 and BstarE22Bstar†=P0. CertifiedHardy contribution is thusκM0P0 in the common originalmarked frame with the existing quarter-fixede0 input. Six exact rootidentities and literalGbase normalization replay confirm it. The fixed markedendpoint is explicitly P0=(I+U²)/2; separately reviewed findings continue this same channel through the actualreal delta jet and allfour originalopenpaths. Positive actualspine consumer: originalP/Q fold is realized by P=T3,Q=T0^-1 and fixedC, with sameJ carrying inversefold to originalU6. OriginalD_y/fullGram/positivefunctionalcalculus and every already givenPstr transport isometrically; eight independent rootsymbolic checks pass. Recovered original v118 consumer reads det(I-tM0)=1-t³; native t=1/2 gives16/7,4/3,7/6. Later v121/FLAV.H2.04 uniquely pins recorded R under declared margins anddet8 among17 candidates, independently re-enumerated.
Scope: Positive finite ORIGINALpath with transported endpoints and every already givenPstr. No fitted/free metric or rawEuclideanadjoint identification. Read preliminarytype review with positiveGmetric addendum. Transportfiber pair need not equalF5faces; sheetparity is not automaticallyCalderonpolarization. No equality of geometricR/nativeclock/U6 by order. Wordtraces concern only certifiedcontribution. ActualZadm/blockedT insertion,entireD4spine and originalendpoints/compression remain at their originalconsumer. K is coupling,not a universalCARmap. GivenwholeG/W state/reflection/time remain; fullphysicalorigin/time derivation is not proved. StrongerBstar also retains originalquartermark; a single-M eigenbasis match alone would not. Common scalarphase cancels in endomorphisms. Transport full96J_F/Clifford/marks with the complex basis. κP0 is not identified with entirepositiveKstr, and actual originalsource insertion remains to execute. diag(kappaM0P0,0) is explicitly a comparisonembedding, not a derivedwhole6Hardysource or physicalzero for otherbranches. Any already givenwhole6operator andcross/adjointlegs share the sameEfold. Do not reopen nine free addresses or a new Hitchin PDE. Retain conditional margin provenance, distinguish native1/2 from later delta_ph, and do not turn scalar readout into whole-Yukawa or insertion provenance.
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 - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock - Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
premise:recovered-genus-two-cover-with-retained-signed-coefficients - Supplied split carrier with actual q sign lines on genus-two cover
Given existing split carrier E3⊕E2 with unitary split connection onX and actual unitary flat q linesL0,L1,L2 on old coverC:w³=(z²−1)/(z²+1),η²=1−w⁶,product1 andπ*Fv117=L0⊕L1⊕L2. Pull these data toX×C and combine with declared alignment to mA slots. This does not selectX,E,mA or alignment as original P1 quantum source.
premise:given-split-carrier-and-actual-genus-two-q-sign-family - Relative spin and reference Hardy cable on original three-cover
Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-cover - Original hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contract
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ACTUAL-FUCHS-PATH-C6-HARDY-CONSUMER.txt, lines 1–190
Source SHA256: 99d7aafa1e204f344f00b6d1fc6344ed7895295b01f847674422a97784735ed8
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FLAVOR-PATH-TRANSPORT-SOURCE-TYPE-REVIEW.txt, lines 1–120
Source SHA256: 23e11fb0309b5260c8cf9049b438a567724ab8342e77d18940289f5017257067
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FLAVOR-PATH-TRANSPORT-G-METRIC-ADDENDUM.txt, lines 1–118
Source SHA256: 2630f1de582645bef554537c6c16aa8004dfeff83631097a4850aa502c85c443
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ACTUAL-PATH-G-METRIC-REVIEW.txt, lines 1–78
Source SHA256: bd84febd1cd122b5145bb918553f6d9cdab5c4e89fb6601c1f3da11b51b184f0
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt, lines 1–174
Source SHA256: 3a57907902631b58e0abee61e9a424c3ac03ff7a8fa074cc4d27e3379b406cf3
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- tfpt_explorer/flavor_path_transport.py, lines 70–199
Source SHA256: 82b4fab94138ab3f5122cf40d507e7a4b7c8a5da25393d4f42dcd35259a9de92
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-COMMON-MARKED-FUCHS-HARDY-REVIEW.txt, lines 1–50
Source SHA256: a085f6735da10cafa35e31d9548323d83de628c6ae304cc5ae1c78056fc57bb9
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/FULL-MARKED-G-FRAME-AND-ORIGINAL-OPEN-WORD.txt, lines 1–160
Source SHA256: 1090dbaa4bb2ab7bf3ed1f6cebbe4498bf794cd51e6e103502948c9f614e914e
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt, lines 1–143
Source SHA256: d98da73f0023e1de696a31874d73b1df547564cec70205c07e5a54f3e0dc0fc5
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-REVIEW.txt, lines 1–45
Source SHA256: fb1d8858d1e90ac5cad5b80777b620162bfb8c14b0ebffbe6112e7bf661fef14
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-CHECK.json, lines 1–11
Source SHA256: c18e4e48e8d4bba9bab3a0aef23a4078774ef8ceaae5b4b9e42962a086f99a43
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/RECOVERED-ORIGINAL-RESOLVENT-AND-WORD-READOUT.txt, lines 1–51
Source SHA256: d44c6f0172c5030a7b84056849a61d74d70346fed35b933a5f2bd919763d9d26
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-RECOVERED-V118-V121-READOUT-CHECK.json, lines 1–64
Source SHA256: 9eb5a7f60c898f99bbc6a09321c8c68bdee83b023c180531d3def2ecff19d06b
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- documents/tfpt_research_contracts/sections/006-source.tex, lines 236–258
Source SHA256: a93b3c1fd9be52521a3eea6ca82b6bddd16e15c2447382f274d3542a36a0382b
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- verification/v118_hexagon_family_dictionary.py, lines 54–138
Source SHA256: 48b7a05bcd877afe13f0a92cce4087e86c23172823e605cda21c6a8ceafa6e37
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- verification/status_ledger.csv, lines 205–205
Source SHA256: 8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4
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Established within the stated premises
finding:original-real-delta-jet-reads-same-marked-hardy-open-word
Actual common original frame identifies certified kappaM0P0 with the marked component of the ORIGINAL delta derivative. The original real-adjoint determinant consumer reads both sign branches and all three cusps. Paired marked-leg current is4delta^5/(y6-delta6), whole family derivative three times it. At exact original nonzero delta_star the full first response is exactlyzero; the same action has positive dimensionless curvature417.71513194757964. Independent symbolic identities and numerical replay confirm it.
Scope: Actual original operator direction and executed real consumer. Does not insert the complex Hardy coefficient into Zadm/Y merely by direction matching. P0 is the marked endpoint, not Pstr or determinant-sector projector. Imaginary kappa is not a free real delta variation. Curvature is not physical mass/time. Preserve the already complete given seed.
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 - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock - Relative spin and reference Hardy cable on original three-cover
Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-cover - Original hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contract - Original closed real delta transport action
Original EM3 action on its invertible closed epsilon0 branch with real delta, fixed U6 and all three cusps. Use actual common Gbase dictionary U6=diag(M0,-M0) and fixed marked P0. This is not a newly chosen independently projected physical variation.
premise:original-closed-real-delta-transport-action
Established within the stated premises
finding:four-actual-fuchs-spine-edges-recover-marked-meridians-and-nonzero-open-word
Actual algebraicG produces all four original diagonal0-to-infinity transports and fixed endpoint metrics. Their different source/target quarter actions give T_k=V^kT0U^-k and ALL FOUR adjacent return loops recover the exact original markedmeridians in the normalized sourceframe. The covariantly rotated open-word sum is nonzero: -6sqrt30/5 E10 with normalized input and -2sqrt2 E10 with target also normalized, while frozen insertion sums tozero. An initial raw/normalized mix was caught and corrected before registration. Fourteen exact identities and independent root integration of all four genuine original paths confirm it. Positive actualspine consumer: originalP/Q fold is realized by P=T3,Q=T0^-1 and fixedC, with sameJ carrying inversefold to originalU6. OriginalD_y/fullGram/positivefunctionalcalculus and every already givenPstr transport isometrically; eight independent rootsymbolic checks pass. Complete addendum: T_hat,k M_k=T_hat,k-1, so the covariantword sum equals the unweighted edge sum. Actual four-edge tuple retains four nonzero Fourierchannels of ranks(1,2,1,2) and metric squarednorms(1/2,1,1/2,1). Complete inverse transform reconstructs all actualpaths/meridians. Only the invariant linear single-Hom compression is one-dimensional; whole covariant packaging is not automatically this compression.
Scope: Four actual original path classes with typed open endpoint action. Preserve explicit geometric reading when identifying their diagonal theta4 graph with the unnamed original geodesicspine. HolomorphicD4 alone is not the larger real-reflection symmetry. Nonzero four-path expression is an explicit consumer comparison, not a claimed originalsum prescription or nine-address table. Execute originalHol_G packaging/coefficientinsertion without inventing it. Full physical closure and time origin are not proved. diag(kappaM0P0,0) is explicitly a comparisonembedding, not a derivedwhole6Hardysource or physicalzero for otherbranches. Any already givenwhole6operator andcross/adjointlegs share the sameEfold. Rank1 sum is not established as the original complete physical consumer. RawkappaM0P0 also fails nonzeroSU3 holonomy tangency since trace(M0^-1deltaM)=kappa; this is not an obstruction to differently typed field or additiveV_adm responses.
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 - Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
premise:actual-original-a0star-fuchsian-connection-and-c4-clock - Relative spin and reference Hardy cable on original three-cover
Compare holomorphic Hardy shifts M_z on S0 tensor L and the same degree-zero coefficient line L over the original pi:C→P1_z. Spin half-forms give boundary norm; Fredholm convention is det kernel tensor inverse det cokernel. Relative line is spin line tensor inverse reference line. This defines a mathematical sewing contract, not an established identification with physical D_rel/D_ref or state.
premise:relative-spin-scalar-hardy-cable-on-original-three-cover - Original hard-holonomy contract with pure closed-triangle trace
Read original45 flavor sources defineY from canonical minimal paths of a Hermitian family connection andPi_triangle=Hol12Hol23Hol31 as ordered closed holonomy,delta=argtrace. DisplayedPi includes neitherKstr nor extraZ6operator. Nonreal asymptotic is a readout contract to test,not completed physical derivation. Active source retains absolute wall selector;no automatic physicalconnection=v117.
premise:original-hard-holonomy-and-closed-triangle-readout-contract - Four original diagonal paths with regularized endpoints
Actual original v117 connection and already proved G along the four diagonal0-to-infinity classes, regularized target z^-D and fixed G metrics. Geodesic reading uses canonical complete hyperbolic metric of the given conformal class, or original real-reflection invariance; not an arbitrary physical metric. No original four-path summation prescription is assumed.
premise:four-original-diagonal-paths-and-regularized-endpoints
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ACTUAL-DIAGONAL-SPINE-ENDPOINT-TRANSPORT.txt, lines 1–160
Source SHA256: 8d9cd72f553b68854ce94bd101a847df6f2b9777225518361515b3c05732e0da
bounded-excerpt · current-at-snapshot
- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-ORIGINAL-JET-AND-FOUR-PATH-REVIEW.txt, lines 1–101
Source SHA256: a917b2333628aa580666adec61c99f1701823cfe308cc47085bc1188cc565f68
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Source SHA256: 46787929dff0f7517949d225263fb4301bb4d3fe553b7bdfb4b937c6b6beae7d
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-FOUR-OPEN-PATH-ODE-CHECK.json, lines 1–68
Source SHA256: 9fb2c3dd60364c2342298635a39664e77cfcecc2fb2840613529d5f0fe7b6be1
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- documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/004-source.tex, lines 140–244
Source SHA256: 107d525221eb816043dbf4fb1a3c7e8244d3e24a5a5bcbfe1c2c34d8ee192f4a
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-FUCHS-ALGEBRAIC-FRAME.txt, lines 1–174
Source SHA256: 3a57907902631b58e0abee61e9a424c3ac03ff7a8fa074cc4d27e3379b406cf3
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/SPINE-ORIGINAL-PQ-FOLD-KERNEL-ADDENDUM.txt, lines 1–143
Source SHA256: d98da73f0023e1de696a31874d73b1df547564cec70205c07e5a54f3e0dc0fc5
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-REVIEW.txt, lines 1–45
Source SHA256: fb1d8858d1e90ac5cad5b80777b620162bfb8c14b0ebffbe6112e7bf661fef14
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ROOT-SPINE-FOLD-C6-CONSUMER-CHECK.json, lines 1–11
Source SHA256: c18e4e48e8d4bba9bab3a0aef23a4078774ef8ceaae5b4b9e42962a086f99a43
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ACTUAL-SPINE-FOURIER-AND-ABSORPTION-REVIEW.txt, lines 1–83
Source SHA256: 3b69102fad712ea9dcacdd39e941eafc4542d1811b0539138f9bb324e8a0b7be
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/check_actual_spine_fourier_consumers.py, lines 1–73
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- experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/actual-spine-fourier-consumers-results.json, lines 1–29
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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