Precisedictionary/selectiongap,nogeneralabstractresetorno-goforactualstate-dependentfieldresponses. No max-overlap,minimization,newmeasurement/clock/couplingrule. Fullphysical3+2originopen.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
Original seam/state data on actual60 flags without fitted selection
User17Oct: test originalseam/statedata onactual60 flags P(q,S); no fittedclock,coupling,newselectionrule. Additional EXISTING data topreviousunmarkedobject: fullchargedinternalv=(0^5,1/2^3),deck square,originalE8vacuum; optionaloriginalR_neut/retained48familyomission explicitgivenpremise,all4cases. SEPARATEactualoriginalfoldphasesalpha1/4,3/4withfixedexistingM,d=M((j+alpha)/8−1/2);disshift/timediagnostic,notautomaticallyfullCARcovarianceorE8vacuumexpectation. Fullroot/fieldaction,nocompressiononly. NopostulatedphysicalTheta,field/state/normalorderingdictionaryorP1selection.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
Original seam/state data on actual60 flags without fitted selection
User17Oct: test originalseam/statedata onactual60 flags P(q,S); no fittedclock,coupling,newselectionrule. Additional EXISTING data topreviousunmarkedobject: fullchargedinternalv=(0^5,1/2^3),deck square,originalE8vacuum; optionaloriginalR_neut/retained48familyomission explicitgivenpremise,all4cases. SEPARATEactualoriginalfoldphasesalpha1/4,3/4withfixedexistingM,d=M((j+alpha)/8−1/2);disshift/timediagnostic,notautomaticallyfullCARcovarianceorE8vacuumexpectation. Fullroot/fieldaction,nocompressiononly. NopostulatedphysicalTheta,field/state/normalorderingdictionaryorP1selection.
Full internalE8Z4character(rootphasecounts52,60,64,64)hasactualG31stabilizer64/logicalimage16;decksquare3072/image48. Bothsplitthesixliteralquarticraysinto{0,1}|{2,3,4,5};exactly{0,1}amongall15globalpairsetsisinvariant. Originalglobaleventpairthereforefoundwithoutoldthreeclock/P2/coupling. Withqoutsidethispairremainfourflags(2,S),(3,S),(4,S),(5,S). LiteralexistingOframe,nofit.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
Original seam/state data on actual60 flags without fitted selection
User17Oct: test originalseam/statedata onactual60 flags P(q,S); no fittedclock,coupling,newselectionrule. Additional EXISTING data topreviousunmarkedobject: fullchargedinternalv=(0^5,1/2^3),deck square,originalE8vacuum; optionaloriginalR_neut/retained48familyomission explicitgivenpremise,all4cases. SEPARATEactualoriginalfoldphasesalpha1/4,3/4withfixedexistingM,d=M((j+alpha)/8−1/2);disshift/timediagnostic,notautomaticallyfullCARcovarianceorE8vacuumexpectation. Fullroot/fieldaction,nocompressiononly. NopostulatedphysicalTheta,field/state/normalorderingdictionaryorP1selection.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
Acceptedquartic/E8/adjointvacuumnormalization remainpremises.1+5+9 arecomposition/representationsectors,notspacetimedimensions orparticles. Gramcomparison doesnotidentifydifferent sourceweights. No new3+2/physicalselection.
Read the exact result, assumptions and evidence
Result
Actual local holomorphic multiplicationM:Sym²C5→fullsourceweight8 hasGram28^1,10^5,18^9. Canonicalprojectorsgive1+5+9; literalH_holo=10I15+(S2* S2)|Sym² with existingconjugatedoublecontractionOPE. Five-sector hasexplicitisometricintertwiner withsameactualnativerho5,notonlydimension5; all15quotientevents checked. Common smoothlocalvacuum smearing ofprimarycomposites preservesGram up toc_f. CentralidentityOPE coefficients aredataofsame*-fieldalgebra,notchosenGNSresponses.
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 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.
Intrinsic event geometry without marked clock as selector
User159c5316 17Oct replaces automatic instrument/whitening-origin next step with intrinsic structure test. In accepted full unitaryE8_1 fieldnet use actual quarticproducts,eventrelations,*-operation,centralOPEnormalization. No originalpolar/P2,desired3+2,markedq,selectedclock orphysicalrealstate rule as construction criterion. Compare originalgeometry/clocks only afterwards. Transportmetrics withbasis changes; distinguish centralalgebraicOPE data andstate-dependentGNS responses. Only states with definedcommonfieldmoments; positivefiniteenergycontrols not automaticallyRP/clustering/finiterelativeactionP1seeds. Retain full localproducts,composition,correlations; no assumed independenttensorphysics.
Given native E8 realization, clock and marked input, not physical selection of them. Positive normalization computable and unique WITHIN positive normalization class, not P1-derived execution/readout or3+2 matter. Three/two are originalsigma orbit sizes, not independent particle count. Injective r0 field-tensor map is not matrix-product homomorphism.
Read the exact result, assumptions and evidence
Result
Actual native reflections at givenq produce five local quartic difference fieldsDelta_j=F_nj−F_nq; full vacuumGramG=I+J, arbitrary common smooth local smearc_fG. All Wick classes/Taylor terms retained. Original three/two clockorbits give response tensorsKC=DQC D*,KW=DQW D* andR=KC+KW. Without insertingP2/targetangle, mathematical positive RELATIVE tensorR^−1/2 KW R^−1/2=UQW U* is exactly existing originalP2, U=D(I+J)^−1/2. Polar prescription thus has concrete common field/event-response interpretation as relatively normalized quantity.
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 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.
Original clock/simplex without an imposed polar mark
Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class.
Actual native event fields and distinct state controls
In accepted full E8 field net test actual native reflection automorphisms on reconstructed quartic fields and coherent difference against identity. Original sigma=(234),tau=(01),markedq=5 remain given comparison data; preparation ofq not derived. Vacuum and normalized marked source state are distinct mathematical controls. Difference of automorphism and identity is NOT assumed physically allowed intervention/instrument. Retain all local Wick/Taylor products and complete source states. Positive Gram/relative normalization is examined as computable tensor, never imposed as physical selection rule.
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.
Canonical stress now follows from given normalized full current OPE rather than independent stress premise. Level1/E8 realization remains input. Invariant source operator identity, not physical selected intervention/time law, particle clock or3+2. Correlated source constructions are not independent experiments.
Read the exact result, assumptions and evidence
Result
With actual cocycle dual sign full240-root OPE gives sum_alpha alpha tensoralpha=60I8 and h_dual30. Thus T_Sug=(1/62)sum248:J^AJ_A:=(1/2)sum8:h²:=T_E8,c8. Same stress follows within same source fromr3 quartic Wick ladder. ForT_n=sum248J^A_-nJ_A_n full endpoint factors onC5 atn0..3=(134,103/2,5,1/2), exterior-defect Grams=(100,225/4,9,1/4)I5. FULL source vectors obey(T0/2+T1+T2+T3)f_i=124f_i: exterior pieces cancel exactly, not just compressions. No root/family branch or fitted rate.
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.
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.
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.
Given original E8_1 vacuum source and coupled finite lift; no P1 source selection, physical time, instrument, polar minimization or physical field identification.
Read the exact result, assumptions and evidence
Result
Actual mixed Chevalley brackets give Q(H)|F20=H tensor I4, Q(H)|C4=trH/3 and kappa=trHK-trH trK/9. Noncommuting E+ responses exist. Separated Ward responses distinguish original polar and countermarks. Clock-current norm25/18 is constant throughout CP1 and selects no point. Three gl5 lifts of given R5 have full orders12,4,12; a genuine order4 source clock exists. All60 actual finite event charts match the native erasure twenty-action on the coupled determinant cover.
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 clock/simplex without an imposed polar mark
Retain actual normalized W6 simplex, sigma=(234), tau=(01), q=5. Consider ALL Hermitian rank2 projectors P with RanP inside Fixsigma, [P,tau]=0 and one positive/one negative tau eigenvalue on RanP. The original polar rule is a comparison point, not an imposed condition of this compatibility class.
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.