Coverage and source audit of available investigation documentation,not fresh independent validation of every proof.388 entries belong to the entire shared Atlas,not solely this conversation. Presentations and old save packets are not new scientific results. Original one-copy inverse point-norm selection,integral lattice origin and physical field/state/time map remain open. No ledger or physical proof status changes.
Read the exact result, assumptions and evidence
Result
A common overview and full manifest link all197 existing findings in the two relevant research problems. All1185 source references of388 stored findings were checked against497 current files for existence,SHA256 and line extents,with no discrepancy. Three previously local reports on real D4 comparison,conditional cyclic reconstruction and NS half-cover are now preserved byte-identically with two checkers and an existing result file. Historical scopes and later corrections are explicitly mapped. Active task reuses the completed complex module bridge instead of requesting it again; prior wording is retained.
Required assumptions
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.
Complex four-dimensional module closure for explicitly constructed Wq including full central action. Physical source selection of one inverse Nq copy remains open. Does not derive integral Gaussian E8 lattice,physical metric,W8 dynamics,or state rule.
Read the exact result, assumptions and evidence
Result
Spin-rigidified theta space is identified as complete complex Heisenberg and clock module. For L=O(2Theta),N={g in G(L):g⁴=1} is canonical order64 group with mu4 center. Every symplectic Phi lifts to N≅N64;Stone-von Neumann identifies Wq=H0(L) tensor Nq^(-1) with native C4 module. c lift has no remaining Pauli shift because1−Sigma invertible. alpha gamma alpha^(-1)=gamma^(-1) and trace(Ad gamma)=1 force trace(gamma)=1,hence exactly gamma->sigma without cube-root phase. Same intertwiner sends alpha to fully classified joint Clifford conjugacy class.
Required assumptions
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.
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.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
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.
Exact finite source identities and reconstruction of known mathematical connections. No proof of universal computation,physical noise,clocks,couplings,Born rule,or simulation. Marginal information loss concerns this mixed-state pair,not all pure codewords. A fully Clifford-invariant Hermitian generator is scalar on5/30 only in that class. Literature links toHamming/E8,QCA,transfer convergence and sufficient statistics remain background theorems under their own premises. The historicalF_a->deltaD_rel question was later sharpened for merely defining composites by the existing current reconstruction.
Read the exact result, assumptions and evidence
Result
The initial exact original-source calculation is now archived in the repository and replayed normally,optimized,and at its archived location with byte-identical results. Pi_native=Q_Pauli Pi_sym4 holds in the unchanged frame;ranks16,35,5 remain distinct. All64 one-register matrix-unit conditions give the existing erasure property. The60 original source rays have frame potentials1/4,1/10,1/20,1/32;the fourth Haar value is1/35 and HS moment defect3/1120. For the already known pair Pi_native/5 andPi_sym4/35,relative entropylog7 and global distance6/7 disappear in all proper marginals. The external standard-gate control compresses to diag(0,0,i,i,i),leaking2directions. The original comparison and known Clifford-commutant literature retain all premises and the physical selection boundary.
Required assumptions
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.
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.
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.
Excludes only explicitly tested fixed carriers and marks. No exclusion of all native E8 modules,other original transports or existing exact C12 theorem. P_nat/Q comparison is a named ansatz,not an assumed physical module identity.
Read the exact result, assumptions and evidence
Result
Fixed P_nat and v117 M are unmarked regular C3 modules,but ZP_nat=P_*Z together with ZQ=QZ or ZG=GZ has rank9 and only Z0. Natural Fermat deck has H10 multiplicities(0,2,1),H1(0,3,3);scalar cubic twists never give(1,1,1). Existing C12 Phi12 bridge has rank4 with(0,2,2). Same abstract C3 class or existing rank4 intertwiner does not replace a common marked rank3 dictionary.
Required assumptions
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Fixed three-slot permutation and original compiler comparison
Test the explicitly proposed fixed three-slot P_nat candidate from v417 against the P_* pullback of the v117 pair in the existing September dictionary. Q or G remain fixed on the same named comparison carrier. This coordinate identification is the tested ansatz, not an established physical identification of all native E8 representations or clock carriers.
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.
Only literal geometric identification of the full ramified equator pullback with the old single smooth seam circle preserving local marks is excluded. No ban on proved pushforward,local field intertwiner or originally derived smooth readout. No freely chosen vertex scattering and no P1 no-go.
Read the exact result, assumptions and evidence
Result
For Gamma=|x|1,exactly p^−1(Gamma)=Fix(rkappa) union Fix(hrkappa). Two horizontal and two vertical square-torus ovals at1/4,3/4 intersect at the four ramification points. Full pullback is a connected torus graph V4,E8,F4,b1=5,with local valence4. The old single smooth NS circle has valence2,so a marked collar homeomorphism cannot identify it with this full pullback. Normalization gives4 circles,radial push-off2 components. Selection,smoothing or vertex domain does not follow from the bare lift. Retain both source/Real types.
Required assumptions
Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
Original full four-mark inversion and distinct equatorial Real slots
The supplied marked base has x->ix and the inversion x->1/x already present in v512. Compare their actual lift to E:y²=x⁴−1,retaining the original four-marked base circle Gamma=|x|1. v510/v519 distinguish pointwise equatorial x->1/bar x from the OS family x->mu bar x acting along Gamma. These operations must not be identified in a source comparison. The old free carrier is named;no general physical P1 equality is presumed.
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
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.
Exact highest CAR degree;subnet conclusion assumes the expressly restricted insertion algebra. Closed-operator affiliation needs an appropriate realization and common core. No exclusion of full CAR or arbitrary P1 maps,no claim for every finite phase,and no physical event selection.
Read the exact result, assumptions and evidence
Result
In the actual M/O/quarter dictionary,each degree8 CAR arc-charge Gram has rank5 and determinant498159/262144,normalized166053/4294967296. All four index-difference classes have rank5. Every nonzero native quartic responds to every nonconstant real infinitesimal arc phase;the common phase remains trivial. These phases pointwise fix the restricted additive scalar density/stress subnet. Native field distributions cannot be generated there. The full original CAR algebra already contains the required transfers.
Required assumptions
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
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.
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.
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.
Additive scalar density and stress algebra on eight original arcs
The restricted insertion candidate is the additive original scalar density/stress subnet on eight proper arcs with disjoint closures. Full neutral interarc CAR products are not automatically included.
Proved for the given one-particle boundary tuple and declared free chiral CAR interpretation. No equality with Hardy vacuum,original P1 measure/time identification,or EM/Quillen response from the relative covariance determinant. v813 index-four response normalization remains open;E8 compiler and existing W8 are not relabelled as new. Continuation:This boundary-tuple identity is not literal identity with the full marked equator pullback,which is a ramified V4/E8 graph. Retain full Real group and both original slots.
Read the exact result, assumptions and evidence
Result
Unitary theta=2pi s identifies domains and actual operators:B_Sigma/(2pi)=Bcov=2(B1/4 direct_sum B3/4),V=T_pi,u_cov=[[0,u_base],[I,0]]. Q rotates cut charts and is not V. At canonical width W=1/2,the second chiral Calderon compression is C_A=(1+exp(2pi Bcov))^−1,hence geometric beta_angle=2pi without fitting. C_A is a mixed traceclass perturbation of the Hardy sea at distance<0.086590;relative covariance/Fredholm factor remains1−z,and(1−z)² for double winding. Known two-boundary graph reconstruction is specialized to the actual existing C2 cut. The old full flat Moebius test has modulus1,this one1/2;units cannot identify their full Dirac problems.
Required assumptions
Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
Free chiral Cauchy quantization of the canonical elliptic annulus
Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
Original P1, boundary, seed and local restriction definitions
Reviewed originals: P1 declares oriented seam, reflection-positive kernel, unit winding and c3; stronger T_boundary includes A_+ as data; operational seed takes A_loc, time, reflection, state, seam class and collar operator as inputs. A_adm(O) is A/A*-invariant restriction of supplied local insertions. Compare without P2/E8/target spinor assumptions and without presuming an original gauge/microscopic localization intertwiner.
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.
Finite canonical c8 source with the same positive Gaussian polarization;no claim of full affine invariance. Does not exclude W8 contributions to larger E8 multiplets,broken symmetry,quarter references,state responses or full TFPT. The observer code need not be a full-source ground space and this is not imposed.
Read the exact result, assumptions and evidence
Result
For the actual normalizedf0=sum(u_a.h(-1))^4/sqrt96 and original rootalpha=sqrt2e0,E_alpha(0) has charged PBW componentalpha.h(-3)|alpha>/(3sqrt96) with squared norm1/144,outsideC5. Thus an operator commuting with horizontal E8 zero modes cannot have preciselyC5 as an isolated eigen/ground space on the full grade4 source. The existing screenedW8 obeys[E_alpha(0),o(W8)]=0 and therefore fails this necessary condition as a sole exact-five selector.
Required assumptions
Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
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.
Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
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.
Fixed octic completion in the existing current space
In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed.
Only rigid identical code constraints in a shared register frame. No new P1 code-closure axiom. No classification of differently rotated codes,disjoint blocks,approximate/open processes,frustrated phases or the full E8 field. The auxiliary penalty is not presented as a native extensive Hamiltonian spectrum.
Read the exact result, assumptions and evidence
Result
ForA=V_1234 tensorI andB=I tensorV_2345,exactlyA*B=(1/4)S for a factor permutationS. Their image intersection is0. The auxiliary projector penalty2I−AA*−BB* has minimum3/4;the actual native parent sum is>=3/8. Since overlappingS4 groups generate symmetry on the union,the same zero intersection follows for identical code constraints overlapping in1,2 or3 registers.
Required assumptions
Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
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.
Finite original root lines,given J/metric and four native registers; no novelty claim for the old parent. First nonuniform projective moment does not exclude arbitrary nonlinear recognition. No physical time,dissipation,preparation,P1,3+2,clock or48c3^4 selection; E8 and J are not derived.
Read the exact result, assumptions and evidence
Result
The actual60 complex E8/J root lines obey exactly M1=I4/4,M2=Pi_sym2/10,M3=Pi_sym3/20 and40M4=Pi_C+Pi_sym4. Extracting40M4−Pi_sym4 without a five-dimensional target literally recovers the original code projector. The preexisting parent I−20M4 has spectrum0^5,(1/2)^30,1^221. Rebuilding the identity from the original Gaussian roots gives byte-identical normal/-OO results and two firing negative controls. Algebraically(20M4)^n=Pi_C+2^(−n)(Pi_sym4−Pi_C) for n>=1.
Required assumptions
Existing even E8 lattice, Gaussian J and sign lifts
Given existing even unimodular E8 with actual J(x0,x1,...)=(-x1,x0,...) and J²=-I, and the original ordered sign lattice cocycle. Sign automorphisms have kernel Hom(L,F2). Retain original integral ordered basis and generator phases; no enlargement to U1 characters except explicitly defined scalar pushouts.
Actual clock/complex-reflection subgroup and native quartic space
R=diag(-1,1,1,1) on Gaussian C4 is the complex reflection of root line(1+i)e0; G0=<J,R>=C4×C2. P5 is the existing five-dimensional symmetric quartic subspace in Sym4(V4), W6=exterior²V4. R is not a real codim1 E8 Weyl reflection; P5 is not the full fourth tensor power.
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.
Complete mathematical cyclicity in the GIVEN original source; concrete application of standard representation theory, no general novelty claim. No actual local P1 map, specified single physical intervention or local-net equality. A matching c1,h1/32 P1 stress module would conditionally give the cyclic state intertwiner but still needs original identification.
Read the exact result, assumptions and evidence
Result
For the same original quarter CAR source,p=alpha-1/2=plus or minus1/4 and c1 lowest weight h1/32. This is not a Kac weight m²/4. The injective Virasoro Verma map and equal partition characters prove at each grade that the full original stress cycle generates the entire fixed relative-charge sector. All W8 response components and their positive-semigroup smoothing are therefore in it. At original grade8 the first response is explicitly reconstructed by22 literal CAR stress words: all rational coefficients,residual0,full rank22 modulo three primes,and the identical complete Gram from independent c1 Sugawara calculation. All original modes and intermediate states are retained.
Required assumptions
Fixed octic completion in the existing current space
In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed.
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
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.
Targeted original-source review of the named claims, not an exhaustive archive theorem or rejection of positive compiler/microscopic results. Charged E8 extension and stronger typeIII exhaustion are not imposed as prerequisites for neutral W8.
Read the exact result, assumptions and evidence
Result
Reviewed originals retain the old circle, concrete microscopic neutral CAR field route and conditional E8 net extensions. v366 sets inclass=True and tests supplied copy counts and target constants; v464 uses a chosen sin(k) chain. v469 gives the extension route under its subnet hypotheses. v994 explicitly labels C7 cited/open; v1030 explicitly leaves microscopic generators and local word/adjoint tails unproved. The current SEAM.EQUIV.01 parent is open and its MMST branch conditional. The earlier complete Dirac vector cocycle cancellation is retained in its Lagrangian/CAR scope. None of these passages constructs the actual marked local P1 W8 image.
Required assumptions
Fixed octic completion in the existing current space
In the supplied positive c8 current space,seek W8 only in the declared17 dimensional space:H8=sum_roots(alpha.h_-1)^8-30Q11^4 and the16 weight8 Q_ab monomials. H8 leading coefficient is1;root zero mode and L1=L2 must vanish. This specifies a mathematical existence ansatz,not an extra physical source or preparation rule. Uniqueness beyond this space is not assumed.
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
Full existing local E8 field algebra with observer five-code
Accepted field-algebra scope: In accepted original E8_1 lattice vacuum use all existing Cartan/root currents, normal products, derivatives and local smooth smearings; native five-code is input/observer slice, not assumed dynamically closed. Retain all exterior charges/modes and both actual twenties. P,Q only decompose analytic endpoint/memory formulas, never execute intermediate projection. Global mode products of local fields are not localized instruments. PhysicalP1 pullback, intervention history, state/time stay separate. Intrinsic tensor/real-form/simplex reconstruction is not a postulated physical potential/state rule.
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.