Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Carrier, families and E8 closure
The published foundation in this area
32 authored claim references lead into the original ledger and paper sections. This source record remains available even where no separate reviewed research packet is attached.
The finite compiler combines a five-slot carrier, a selected half-spinor action, D5×A3 and Z4 glue into an E8 lattice closure. This establishes a mathematical construction within its stated choices, not the physical gauge group or a first-principles origin.
Starting structure in the Atlas orientation
Under the stated actions, D5×A3 with Z4 glue gives the even unimodular rank-8 E8 lattice; the half-spinor reading depends on the chosen group action.
Which connection is sought
Open items include physical boundary realization, a local interacting chiral 3+1D implementation, mirror decoupling, and derivation of the action from the origin.
How it connects
E8 carries internal clock, code, flavor, and arithmetic structures. Rank, representation, family count, and spacetime dimension remain distinct types.
Given free Green quantization and actual x-time cuts,not P1 seam or old circle time. Cauchy trace space is a mathematical extension,not new physical species. No exclusion of other P1 states,admissible subalgebras or differently derived local time maps.
Read the exact result, assumptions and evidence
Result
Actual NS half collar0..1 has graph(exp(-H))projection[[1-C,sqrt(C(1-C))],[sqrt(C(1-C)),C]],C=(1+exp2H)^-1;other NS half is complement. Pure quasifree boundary extension restricts under j=(0,I)state/time faithfully to given source. Neutral A=a0* a_m nevertheless has frequency-m*pi/2 and norm1/[2(1+exp(m*pi))]>0. Thus even a nonsurjective embedding of this entire neutral observable class in a positive ground source with same time is impossible;m2 also preserves spatial J parity.
Required assumptions
Given free Green quantization of the flat Pin Dirac operator on its NS cover
Given is the free charged Gaussian field realization with the Green operator of the concrete flat Dirac boundary family D=−i(sigma1 partial_x+sigma2 partial_w),w in[-1,1],sigma1 psi at boundary=b psi,b=±1. Original Pinminus c=±i forces psi(x+2,w)=−psi(x,w) on the orientation cover. The tested Euclidean kernel belongs to L=i sigma1 D=partial_x+H,H=i sigma3 partial_w. This Green quantization and x as Euclidean time are named premises,not identified with the D spectral sea,the old quarter Hardy state or original P1 kernel.
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.
Transfer is necessary structure for the existing native arc-charge test,not sufficient quartic/P1 identification. Second spectral Schur response is not new physical time or Hessian;full fields/composites,domains and profile/history selection remain needed.
Read the exact result, assumptions and evidence
Result
Exact second geometric Schur response at z0 contains R_h(k)=k/8 sum_m h_m²(pi*m)²/[k²+(pi*m)²]. Between actual disjoint quarter preimages I=(1/32,3/32),J=I+1/2,every nonzero cosine coefficient contributes a strictly positive multiple of(1-i). Thus transfer is nonzero for every nonconstant smooth real even profile. Concrete probe gives.001720549637597(1-i)as epsilon² coefficient;independent Fourier error7.09e-12. R_h(k)->0 is compact and cannot itself be a nonzero local folded multiplication current.
Required assumptions
Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
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.
Controlled conformal normal geometry of the given Pin Dirac source
For the authorized source study,the same given Dirac comparison D0 on its fixed(c,b)Pin/boundary domain is varied by smooth real even profiles h:g_e=exp(2e h)g0,D_e=exp(-e h/2)D0 exp(-e h/2)after unitary density transport. Profiles/amplitude are explicitly chosen diagnostic interventions,not a P1-selected history. Original pure D0 sea remains initial state;thermal Green quantization stays separate.
Exact return form/block identity;long trajectories are finite Galerkin tests. Profile/epsilon are diagnostic inputs,not P1-derived. Second responses are forms,no unproved higher domain powers. No Fock implementer or3+1D/P2 closure claimed.
Read the exact result, assumptions and evidence
Result
deltaD[h]=-(hD0+D0h)/2 gives exactly ||Q deltaD psi_k||²=k²Var(h)+<h_prime²>/4 for every smooth real even normal profile,zero precisely for constant h. Full Fourier/zeta check yields4k²/45+1/3 for h=w². Actual bounded U=exp(i dt D_e)gives memory(P0 U Q)(Q U Q)^j(Q U P0),without resets. For the same collar-preserving probe,400 steps agree with full257-mode evolution to2.11e-13;129/257 curve difference<3e-10. Wrong adjoint feedback differs by.02084. Normal/-OO byte-identical.
Required assumptions
Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
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.
Controlled conformal normal geometry of the given Pin Dirac source
For the authorized source study,the same given Dirac comparison D0 on its fixed(c,b)Pin/boundary domain is varied by smooth real even profiles h:g_e=exp(2e h)g0,D_e=exp(-e h/2)D0 exp(-e h/2)after unitary density transport. Profiles/amplitude are explicitly chosen diagnostic interventions,not a P1-selected history. Original pure D0 sea remains initial state;thermal Green quantization stays separate.
Given pure D sea,correct b orientation and actual domains. P0 is normal zero branch,not native five. No full P1 locality/admissibility identification or equality with thermal C.
Read the exact result, assumptions and evidence
Result
Vf=(1,b)f/2 is isometric on the original Pin fundamental region and obeys D0V=V b(-i partial_x),q=cb. Spectral projections,all quasifree CAR words and Theta_x transport. This explicitly composes the known zero branch. For every uniform a>0,QD_aP0=0. Exact nonlocality witness ||Q M_w phi0||²=1/3 shows P0 is not an automatic thin seam/collar projector.
Required assumptions
Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
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.
All-degree formal or finite-energy matrix-element identity;localized bounded bilocals use the separate net theorem. Unbounded native limits retain old core/smearing/affiliation hypotheses. No equality of dual net with full neutral CAR,no finite smooth pulse,new time flow,or original P1 net embedding proved. F_a to delta D_rel remains relevant to a claimed particular primitive interaction,but is not an extra existence requirement for an already neutral composite.
Read the exact result, assumptions and evidence
Result
In the original Q0 Maya/current dictionary,B(z,w)=w/(z-w) exp(sum(z^m-w^m)J_-m/m) exp(sum(w^-m-z^-m)J_m/m). CAR current commutators,infinite-sea vacuum contraction and cyclicity determine all finite-energy matrix elements. The actual quarter factor(z/w)^alpha follows from field powers. Independent exact checks test every matrix element through degree4/8 with12/67 states at two point pairs;normal and-OO are byte-identical. The connected current-net/fixed-point theorem places neutral interarc bilocals in a larger connected interval,and locality puts them in the complement-current commutant onQ0. The additive separate eight-arc net remains strictly too small. Substitution into actual A_a and unchanged point-split prescriptions reconstructs native currents and existing quartic/W8 composites without a new elementary coupling.
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.
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.
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.
Finitely tested modular one-particle response. No continuum reconstruction,pointwise quartic-field invariance,physical-time identification,or F_a to delta D_rel map.
Read the exact result, assumptions and evidence
Result
The actual source class was restricted on rings64 and128 for both quarter phases to eight equally spaced arcs. h=log((1-C)/C) has nonzero interarc transfers but numerically commutes with all four actual integrated native Cartan matrices. Removing interarc covariance removes the witness while changing the state. Normal and-OO produce byte-identical results.
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.
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.
Only identifying this finite crosscap state or its normal tree vacuum limit with the original quarter Hardy state under the claimed same time is excluded. No P1 no-go and no exclusion of actual open/closed sewing maps with appropriate state/time transport.
Read the exact result, assumptions and evidence
Result
In the declared flat Pin model,the crosscap Cauchy covariance on each lambda,−lambda pair is the graph with t=−c exp(−2Llambda). Its commutator with signed boundary B has norm lambda/cosh(2Llambda)>0. Fock energy variance is lambda²/cosh²(2Llambda),so the finite-L state is nonstationary. Further normal collars filter in trace norm to the tree NS vacuum,which loses c,b marks. The loop quarter operator still follows from cb=±i,but this limit supplies neither its Hardy state nor W8 source dictionary. Cauchy data remain free before imposing physical local b boundary conditions;imposing them would instead solve the different zero-kernel problem.
Required assumptions
Given flat Moebius Dirac boundary family and its full sea
The comparison fixes D=−i(sigma1 partial_x+sigma2 partial_w),Psi(x+1,−w)=c sigma1 Psi(x,w),c=±i,sigma1 Psi|boundary=b Psi|boundary,b=±1,and the canonical full two-dimensional negative D spectral polarization. This specified primary-literature family is not identified with all possible original P1 collars or covariances.
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.
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.
Raw flat spin pullbacks with explicit Clifford convention. Additional spin minimality requires genuine Spin/Pin bundle transport up to real central sign;an arbitrary projective U1 phase is another linearization. Do not identify Q,half translation,Pin operator and OS Real structure.
Read the exact result, assumptions and evidence
Result
For the untwisted NS NS line and raw complex-linear coefficient pullbacks,U_delta²=chi(1+i)=+I and U_rho U_delta=−U_delta U_rho,because universal lifts differ by the A cycle. The glide g=delta_E rho=−bar z+T has g²=z+i and U_g²=−I. With fixed sigma_s²=I,A=sigma_s U_g is Dirac covariant,A²=−I,and has c=±i spaces with involutive c^−1 A descent. Anti-linear Real j_g is distinct:(sigma_s j_g)²=+I and has no complex ±i eigenspaces. Q invariance allows only(+,+),(−,−);a genuine transported A4 Spin/Pin relation forces(−,−),without a separate no-zero-mode rule.
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 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 theorem only in the named h,Q,kappa subgroup and its eight-member anti coset. There the unordered OS annulus pair is canonical. Full already marked D4 lift has16 antiholomorphic members and an additional equatorial dividing pair;earlier unqualified full canonicity is narrowed by finding:full-marked-c2-lifts-distinguish-equatorial-and-os-real-slots. No square-modulus derivation or physical P1 cover identity. Free-deck uniqueness only among h,Q²,hQ².
Read the exact result, assumptions and evidence
Result
The complete affine census of eight h^a Q^b kappa has precisely two dividing members:hQkappa and hQ³kappa. With O=(0,i),T=(1+i)/2,Qz=iz,hz=−z+T,kappaz=−i bar z+T. Their halves have width1/2,circumference1 and Q exchanges them. Delta=hQ² is the unique free involution among h,Q²,hQ²;on the annulus it acts(t,s)->(1/2−t,s+1/2),with Moebius quotient. The earlier kappa-only nondividing statement is correctly scoped. v507 half-period origin,v510 free-deck/Fock class and v519 free RP are reused results.
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.
Existing marked cyclic cover tower and compact elliptic images
Use only existing C_n:u_n^n=x^4-1 with fixed x base,deck Delta_n and already forced compiler clock R12=Q12 Delta12^4=(ix,omega s),Q12=(ix,s). Compare compact algebraic curves over C and pullback function fields. A comparison of punctured local systems must retain its removed points,peripheral loops,spin and field transports.
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.
Finitely tested property of the expressly chosen learning rule. Frozen response is not the full Jacobian;no general attractor theorem,no identification with physical time or an original TFPT Clock.
Read the exact result, assumptions and evidence
Result
Nine prescribed beta/eta pairs around the original settings were executed5000 steps each. Three reach numerical rest,six retain motion. At beta=.25,changing eta=.15 to.075 changes frozen-response periods from11201/64540 to18551/106907 iterations. For all9 states,the observed frozen120x120 response reproduces the next1000 nonlinear steps with relative error<8e-14. Normal and-OO runs produce identical result bytes.
Required assumptions
Explicitly chosen recursive SOM rule on60 native signal cells
Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws.
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 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.