No all-E8/P1 no-go or exclusion of covariant density channels, open outcomes, noninvariant preparation or spontaneous branches. No identification of real reconstruction functional with physical potential. Existing polar-fibre/clock theorem remains comparison; new source gives unmarked geometry, not physical selection.
Read the exact result, assumptions and evidence
Result
Six OPE-reconstructed axes give15 equivalent rank2 pair planes. None equals actual originalP2; minimum squaredHS distance is(21−6sqrt6)/25>0. Full logical field-mode imageM5 is irreducible with centerC, no distinguished3+2 superselection. With all exterior data invariant, fully contracted LINEAR code return/memory kernels stay scalarI5 by native irreducibility even with every exterior path. Nontrivial uncontracted OPE tensors remain and are not excluded.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
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.
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 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.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Analytic theorem for finite unitary Cartan-Weyl-only histories and original neutral code-Fock embedding. Not general nonunitary field products, root currents, interleaved stress/current histories, open processes with memory or all E8/P1 operations. No original P1 time law or new code-preservation axiom. Do not unite separate exclusions.
Read the exact result, assumptions and evidence
Result
Actual CCR fixes [J(V),J(W)]=i sigma I and exp(iJ(V))exp(iJ(W))=exp(−i sigma/2)exp(iJ(V+W)). Every finite ordered Cartan-Weyl history is phase times total displacement. Every nonzero total displacement turns any nonzero finite Fock polynomial into exponential nonpolynomial in Bargmann realization. Exactly code-preserving endpoint forces zero total displacement; neutral zero modes are trivial and only common phase remains. Entire stated class provides neither marked R5 nor3+2 selection. Nonzero individual profiles may cancel in total.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
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.
Full original Cartan-current insertion and specified Weyl class
In existing neutral Cartan-Fock module use full original current field and its actual CCR, all smooth real8-vector profiles with Vhat_-n=conjugate Vhat_n and h0=0. Ordered unitary classification uses only finite exp(iJ(V)) histories of these currents. Explicit mathematical class in given source net, not raw-P1-derived permission, field coupling, physical time or code=H_adm identification. Root currents, general field products and mixed stress histories are outside.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Pure original canonical stress histories in given source frame only; not all geometry/metric variations, affine KZ histories with other field insertions, noncanonical/nonstress fields or general P1 processes. No physical time identification or union with prior separate zero-mode exclusions.
Read the exact result, assumptions and evidence
Result
All modes/words of given canonical T_E8 act in generated code cycle as common Virasoro representation tensor I5. Every code compression is scalar, including excursions to higher grades and return; code-preserving unitary endpoint is a common phase only. No such pure stress history implements given nonscalar R5 or selects P2. U_conf=exp(i pi L0/2) agrees with native J on4/5/20 seed carriers, but acts as+i on newly forced weight5 twenty whereas native J there remains-i. Common Casimir phase does not repair this relative discrepancy.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
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.
All modes of original canonical source stress tensor
In given E8_1 lattice vacuum use exactly T_E8=(1/2)sum:h_A h_A:,c=8, without improvement/background charge. Examine all Virasoro modes and well-defined pure stress histories in original neutral Cartan-Fock space. This is a mathematically specified geometric transport class, not P1-selected physical history or time. It differs from prior class of all neutral weight2 ZERO MODES; do not combine exclusions. First erasure Ward action uses existing a_a=bar u_a(1), no extra source, root or family choice.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Same specified single-beta response family only. Norm fraction is not an instrument probability. Rank lower bound10 is not sufficiency of a10D realization, particle count, spacetime or3+2 derivation. No separate n=0 feedthrough, time-dependent maps or nonlinear models in excluded class; no wholesale transfer to other source histories.
Read the exact result, assumptions and evidence
Result
Complete exact feedback Gram Delta=B*B satisfies Delta>=5120I5 and has rank5. Every nonzero code input obeys sharp ||Pi Lpsi||²/||Lpsi||²<=9/44, equality exactly span(f2,f3); at least35/44 of squared response norm is exterior. Hankel/Gram block[[I,K],[K,H]] has exact rank10. Hence any fixed linear realization M_n=C A^n E for n>=0 with time-independent input/output maps needs at least10state dimensions. Closed5D continuation of these moments is excluded even after fixed input/output changes.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Specified ordered response family of original single pair
Examine mathematically specified moments M_n=Pi L_beta^n Pi,n>=0, L_beta=o(W_beta)*o(W_beta), for same original doubled root(0,0,0,0,0,0,-2,-2). Pi/Q only split full amplitudes; no projection is executed. This tests composition/memory of the already determined source, not P1 selection of physical history, coupling, preparation or time. Full coherent multiroot processes must additionally retain nonneutral final charge sectors.
Original sum and coherent profiles with unchanged moduli; no physically selected execution or code-closure theorem for arbitrary new weights. Prior complete positive-profile erasure trace gap remains separately valid. Other higher source histories are not excluded.
Read the exact result, assumptions and evidence
Result
For unchanged original unrenormalized root-input basis, Lsum=sum_beta S_beta* S_beta and <q,Lsum f0>=-2092/sqrt3 with leakage norm²>=4376464/3. All4 original family omissions give same exact witness. Independent targeted original-data check confirms35736-343776/4=-50208 for unnormalized witness. Full coherent S* S sum has additional charged cross terms, which vanish exactly in neutral q/f0 matrix element. Thus coherent profiles with |a_beta|=1 also fail code closure regardless of phases.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Specific full adjoint two-insertion return in original code embedding. Rank5 Gram stays correct; no global E8/P1 or all-history impossibility claim.
Read the exact result, assumptions and evidence
Result
Earlier positive rank5 matrix is Pi L Pi, not full operation L=S_beta* S_beta. Original doubled root(0,0,0,0,0,0,-2,-2) has S_beta h=0 for h=x0^4/sqrt24. Normalized code-orthogonal q=(2/sqrt3)(h-f0/2) gives <q,L f0>=-188/(3sqrt3) and ||(I-Pi)L f0||²>=35344/27. Thus full operation is not code preserving. a0 commutes with S_beta and its adjoint; no omitted Ward term repairs this erasure branch.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Common original normalization, positive adjoint two-insertion returns with original real v_beta. Nonadjoint return fields, new complex transverse fields, independent relative20/5 calibration, longer histories and general physical channels are outside.
Read the exact result, assumptions and evidence
Result
For every original root and real transverse v,4trK5-trK20=(43/12)||v_parallel_Jbeta||²+(25/4)||v_orth||²>0 for v!=0. Full7x7 trace forms and actual native240-root transitivity prove the theorem; all240 computed code traces agree. Original aggregates:trK5=18400,trK20=46848,gap26752. Charge orthogonality gives Kd(a)=sum|a_beta|² Kd,beta for every coherent profile of original W_beta. Thus no nontrivial positive reweighting repairs common unrenormalized erasure continuation.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Common unrenormalized positive-return erasure test
The tested hypothesis reads actual positive K5 and K20 of the same source response with common original normalization as complete branchwise erasure continuation: K20(rho tensor I4)K20=K5 rho K5 tensor I4 for all rho, equivalent under positivity to K20=K5 tensor I4. This is a tested candidate identification, not a claim every correlation is a physical instrument. Independent relative20/5 recalibration is outside this fixed map.
Actual neutral Sym3 trimer, not charged E8 F20 block. Specific response branch, not classification of all combined histories or instruments.
Read the exact result, assumptions and evidence
Result
Original W20 has Fock columns g_(i,a)=partial_a f_i, all20 orthonormal. Same source channel for doubled root(0,0,0,0,0,0,-2,-2) has K5 rank5, actual trimer K20 rank13 and operator-Schmidt rank4. HS² residual from decoder lift is124096/3. It kills g00=x0³/sqrt6 while decoder lift gives188/3 there. This positive unrenormalized paired response is not a common complete branchwise erasure lift.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Common unrenormalized positive-return erasure test
The tested hypothesis reads actual positive K5 and K20 of the same source response with common original normalization as complete branchwise erasure continuation: K20(rho tensor I4)K20=K5 rho K5 tensor I4 for all rho, equivalent under positivity to K20=K5 tensor I4. This is a tested candidate identification, not a claim every correlation is a physical instrument. Independent relative20/5 recalibration is outside this fixed map.
Excludes direct or spectral identification of these concrete kernels with existing mark, not every joint source history or mixed operator algebra.
Read the exact result, assumptions and evidence
Result
None of194 nonzero individual returns commutes with original P2. Sum spectrum is3581,4191,3419²,3790 and commutes with tau but not sigma or P2. Exact witnesses [Ksum,sigma]12=772 and [Ksum,P2]01=(488sqrt2-61sqrt3)/5. Its spectral functions therefore do not give original P2; all4 supplied family variants leave sum unchanged.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
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.
Original positive adjoint two-insertion response
Compute o(W_beta), W_beta=E_beta,0 R_neut, with unchanged original real transverse v_beta. Ordered return is positive Fock Gram o(W)*o(W) between code or original trimer states without intermediate projection. Allow W=sum a_beta W_beta for arbitrary complex input coefficients; distinct lattice charges force nonnegative weights |a_beta|². Nonadjoint returns, other complex transverse fields, longer histories or physical instruments are not thereby selected.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Complete exclusion of this neutral local weight-two zero-mode class including temporary code exits. Do not unite with separate inner E8 exclusion: mixed root/quadratic histories, individual mode roundtrips and higher fields remain outside. R_neut itself is not zero as a field.
Read the exact result, assumptions and evidence
Result
The full lattice-neutral weight-two space is8 derivatives plus36 symmetric quadratic fields. On original quartic code o(T_A)=dGamma(A), compression=(trA)/2 I5. Exact leakage sum is4||Ac-trA I8/8||²+(5/2)||Aa||²; real Gram relative to matrix HS metric has spectrum0^1,4^15,(5/2)^20 and kernel only A=aI. Original R_neut compresses0 with universal leakage bounds240..384, B48 compresses48I and B64 acts64I. Any sequence solely of these neutral zero modes acts by U8 on mode1; a code-preserving endpoint forces the U4 stabilizer and logical phase-G31 action, excluding marked R5.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Actual Clifford identification and finite-overgroup theorem
Retain the actual concrete identification of <G31,zeta8 I4> with complex Clifford X2. Apply NRS6.5 only to the proved finite determinant slice; a group-order match alone does not suffice.
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.
Original neutral root-pair moment fields
Use existing E8_1 neutral_source_response reader:64 chirally selected roots, original omission of one SU4 family weight line, B48=12T_E8+R_neut, AR=4P_A2-8P_U1. Family omission is an explicit existing input, not derived here from P1; neither it nor the R port or physical coupling is newly selected.
Solely neutral local weight-two zero modes
Consider energy-preserving zero modes o(v)=v_(wt(v)-1) of all Hermitian lattice-charge-zero weight-two fields in given vacuum and temporal sequences solely of these generators. Grant the mathematical class without claiming P1-derived physical intervention permission, time or projections. Alternating root-current operations, individual K48 mode roundtrips, nonneutral fields and higher mode products are different classes.
Actual J-positive canonical Cartan Fock embedding in given lattice vacuum and compact inner E8 zero-mode operations. Not an exclusion of higher modes, nonlinear mode products, other derived field maps, non-automorphism interventions or all P1 physics; no physical preparation or selection of the embedding proved.
Read the exact result, assumptions and evidence
Result
The original lattice vertex law gives root PBW component f(b)alpha(-3)ealpha/3. The actual five quartics have no common projective zero; all240 root zero modes therefore leak from the neutral code. Distinct charge sectors prevent cancellation. The stabilizer has Lie algebra Cartan8 and H0=T8; its components normalize T8 and preserve the actual H+ four-plane. The full native U4 code-stabilizer theorem restricts its logical action to phase-G31, outside which R5 lies. Arbitrary inner-group sequences returning to code are included in the exclusion. L0 acts as4I5; conformal time and Casimir shift do not enlarge the logical action.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Actual Clifford identification and finite-overgroup theorem
Retain the actual concrete identification of <G31,zeta8 I4> with complex Clifford X2. Apply NRS6.5 only to the proved finite determinant slice; a group-order match alone does not suffice.
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.
Compact inner E8 current operation class
Consider exponentials of compact weight1 current zero modes and arbitrary sequences preserving the given code at the endpoint. Optional conformal L0 propagation commutes with them. Nonlinear Hamiltonian polynomials, higher modes and non-automorphisms are not identified with or excluded as this class.
Excludes this literal charged four-current identification with unchanged tensor intertwiner, not the actual Cartan four-space or every derived composite field map.
Read the exact result, assumptions and evidence
Result
Under literal C4/register identification all three source clock branches act as -I20 on three C currents but as R5 tensor I4 on F20. The actual W intertwiner has squared HS residual48. Every traceless Q(H) already acts0 on C and its products but nontrivially on F. Thus finite cover agreement is not a full field-algebra map.
Required assumptions
Given local E8_1 vacuum representation and explicit cocycle
Positive level-one E8 lattice vacuum representation in orthonormal D5+D3 coordinates, declared simple-root cocycle, level-one Heisenberg Ward rules and internal quarter character v=(0^5,1/2^3). Insertions are separated. No raw-P1 pullback or physical time law is assumed or derived from this representation.
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.
Existing logical clock and charge marking
Retain the existing logical labels weak0/1, color2/3/4, source point5 and Y5,R5,sigma5. Equivalence under their stabilizer is not automatically an equivalence of lifts commuting with the original native four/P1 clock.
Original coupled determinant event lift
Compare all60 original events with h=exp(-i pi/4)r and A5=-rho5(r) on the coupled finite SU4 cover. This is not the unchanged order2 G31 word or a selected physical pulse.
Literal charged-current/register identification
The tested dictionary identifies the four original charged C_a currents with the unchanged native four-register and requires the actual erasure tensor intertwining under gl5 source operations. This is a tested hypothesis, not a P1-derived fact.