Outcome-dependent phase averaging before forgetting m,not one phase channel after coarsening. K4 is actual tested projective four-group,not automatically cyclic C4 clock. Proof in fixed event-label chart,without physical Bell10/Lambda²5 or SU5/native group identification. Classically merging20 outcomes does not restore lost coherences.
Read the exact result, assumptions and evidence
Result
For each of6 marks,old20 jump events group into5 blocks of4 with Hodge effectP_m/3 and same basis movement. Exactly R_l=D_l C_m onP_m;relative to baselineD0,H_l=D_lD0* form projective K4 with3 characters each multiplicity2. Psi_m=(1/4)sum Ad(H_lD0) after Phi_m. New/old Choi ranks peroutcome1/3,total5/15;superoperator ranks100/40. All60 ordered intersecting-duad coherences permark distinguish channels. No common10-label diagonal gauge for all5 baselines:complete finite test0 solutions permark.
Required assumptions
Given five-slot exterior source with retained complement index
V=C5 with given oriented unitary slot basis and volume form,H=Lambda²V. C_m[kl,ij]=epsilon(m,i,j,k,l) are five distinct linear maps to conjugate target;their coherent sum is a different operation. Inner products and CAR grading remain explicit. No physical record,coupling or time iteration assumed from exterior algebra alone.
Specified old J20 instrument in fixed six-mark duad chart
Actual twenty jump events U_l(I-D_l) per mark from compiler-correlated-event-clock-20260919/source_channel.py;J20 effect3I/5,normalized jump channel Psi=(5/3)J20. Retain common duad labels of ten basis states. Comparison chart does not provide linear SU5/native group identification of Bell10=Sym²C4 with Lambda²C5 or already selected P1 apparatus.
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.
New joint interpretation of existing clock shift and already known charge census. No rediscovery of old ground doublet or D8/E8 Coxeter grading claim. Q is source U1,not automatically electromagnetic charge. p* is an E7 root,not E7 singlet. No time generator changed.
Read the exact result, assumptions and evidence
Result
With rho_A7=(7,5,3,1,-1,-3,-5,-7)/2 and q=(1,...,1),exactly delta=-rho_A7/8+(2a-1)q/16 and H8=8L0-rho_A7.a0+(2a-1)Q/2. p*=(++++----)/2=omega4(A7) has norm²2,Q0,rho.p*=8 and is unique neutral E8 root of H8 grade0. The126 neutral roots form E7(q/2),exactly56 A7 roots plus70 Lambda^4C8 weights. All240 roots and reflection closure checked exactly.
Required assumptions
Four D8 source modules with fixed affine time
Mathematical parent of the four D8*/D8 modules 0,v,s,c with eight identical Heisenberg oscillators, source charge chart p and N≥0. H=8(N+|p|²/2+delta.p),delta_j=(j+a)/8−1/2,0<a<1,Q=sum p_j. Original quarter cases are a1/4,3/4. Conformal L0, individual Cartan charges and totalQ remain distinct. This mathematical completion does not assume a physical P1 realization of the Ramond space or a local field map.
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.
Implementation repair and exact finite recursion identities. v395 matrix comparisons themselves numerical; rational identity derived separately. E8 Cartan,P2 and scheduler remain given inputs;no quantum-field or physical-time origin. Paper sources and local website copy corrected;full publication audit failed on previously retired registry files,no published overall completion.
Read the exact result, assumptions and evidence
Result
Old _micro_step overwrote T_net@m during family update; old passing test never called it. Integrated fix computes T_net@m@M.T and checks all27 basis inputs through actual function. Existing v486/v487 M replaces incomplete v327 rule:spec M={1,2/3,1/3};O^T M^6 O=diag(1,64/729,1/729). One hand is N C^6=T_net tensor M^6,not (NC)^6. Normal and -OO6/6 with identical output;independently reviewed. McKay Doob transform with existing marks d gives P_ij=(A_ij+2delta_ij)d_j/(4d_i),reversible pi_i=d_i²/120.
Required assumptions
Specified Petersen shells and full finite family recursion
v808: ten two-element subsets of five marked slots, disjointness adjacency and radial P=[[0,1,0],[1/3,0,2/3],[0,1/3,2/3]] on H_pi with pi=(1,3,6)/10 and Y=diag(6,-4,1). v486/v487: M=[[1,0,0],[0,1/2,1/6],[0,1/6,1/2]], deck swap Delta of final two slots. v395: given affine E8 adjacency A,T_net=(A+2I)/4 and given 1:6 scheduler. These finite operators are compared without assuming identification with P1 fields,electromagnetic charge or physical time.
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.
Reuse even source structure and existing extension theorems. No global literature/P1 impossibility theorem and no promotion of finite controls to a derived continuum net. Missing is the actual local charged source operator or equivalent functorial gauging with marking and time. New refinement: old audit concerns full local spinor/GSO extension fromP1. On given even quotient net rho_s and smooth neutral transport now follow from existing current without spin sum. Neutral observable response requires neither individual-field membership nor fullQ-system; raw P1 locality and normalized response still need proof.
Read the exact result, assumptions and evidence
Result
Source audit v522: unique reflection-compatible two-torsion of tested NS clock tower is{1,(-1)^F}; stated finite even bondcut algebras pass RP controls,overall contract remains typed UNDECIDED. v490 counts four spin structures with mu_pre4;v469 supplies local holomorphic extension after choosing spinor current,not source selection. Reviewed operational seed,ordinary Haag duality and conditional holomorphic KMS theorem supply no spin-structure sum or Arf weight. Even projection and adding Ramond sectors remain different operations.
Required assumptions
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.
Two-object mathematical field closure preserves every given c0 linearization. Executable strict witness does not replace original J marking. No full G31 extension splitting,256 physical theories,single common local VOA or P1 source/time identification. Test deliberately uses T² different from1 and [T,beta0] different from1.
Read the exact result, assumptions and evidence
Result
For every given geometric faithful c0 and every unitary isometry lift T:V0->V1 set beta1=T beta0 T^-1,sigma1=T sigma0^-1 T^-1,alpha01=T,alpha10=beta0 T^-1. Then alpha²=diag(beta0,beta1),alpha^8=1 and alpha sigma alpha^-1=sigma^-1 hold on all lattice charges and finite-energy vertex fields. Both objects carry faithful C12 clocks. Standard cocycle depends only on Lambda/2Lambda; all256 classes and65536 pairs exhaust cocycle checks,while matrix relations separately hold exactly over Z. Character-gauge changes of T give equivalent groupoids. Optional strict C4×S3 census yields256 raw sign sections,but none with the zero-character J lift.
Required assumptions
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Completed theta frame with explicit primitive Gaussian integral normalization
Start with completed Wq=H0(Jac(C),O(2Theta)) tensor Nq^-1, beta=i, fixed Schrodinger frame e_x for x in F2², a unit norm-line trivialization and actual alpha=zeta8 V. The same-spin representative also retains odd B_O^-1 and its alpha sign. For affine d planes A and stabilizer phases phi in mu4 explicitly choose r(A,phi)=(1+i)^(2-d) sum(phi(x)e_x)/sqrt2. Gaussian integer numerators,norm squared2 and the central i orbit are the arithmetic construction. This is not deduced from complex dimensions and does not assert P1 selection,physical length normalization or uniqueness among all Heisenberg-stable lattices.
Two theta lattice VOAs with a given faithful geometric C12 lift
Lattices Lambda0 and Lambda1=zeta8 Lambda0 come from the explicitly normalized theta construction. Use their unitary lattice VOAs with standard cocycle. On object0 the existing faithful C12 lift c0 with geometric action i sigma is given; beta0=c0^9 lifts i and sigma0=c0^4 lifts sigma. T is any standard-cocycle VOA isomorphism lifting actual lattice isometry alpha01=zeta8 V. Branch-one marks are transported. No T²=1,[T,beta0]=1,full G31 splitting,common local VOA or physical P1 identification is assumed.
Equality of classified ungraded complex module class; not equality with fixed signed alpha or of super/Pfaffian sewing functors. Actual physical Cauchy space,action,state,reflection,local insertions remain to be identified. Two-cable ratio remains sufficient normalization, not necessary physical premise.
Read the exact result, assumptions and evidence
Result
Delta(E,M_z) tensor inverse Delta(E,M_1)=B(E)^(-1)=Nq^(-1) tensor B_O^(-1), using equivariantly trivial spin-relative Poincare norm. B_O has c=beta=1,Q=−1, changing only allowed alpha sign after forgetting grading. Full complex N64/clock class needs no separate unspun physical reference. Superline stays odd, index−3 versus0; two shifted cables give even relative parity. Original index−1 and three-cover index−3 are both odd.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
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.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
Seam shift versus identity on same spin space retaining grading
On original three-cover use E=S0 tensor P_spin with proved equivariant Nm_Dq(P_spin)=O. Compare M_z with M_1 on same half-form Hardy space in det kernel tensor inverse det cokernel convention, retaining determinant parity. Native complex module leaves global alpha sign free. This is a mathematical realization, not an assumed physical Cauchy/Calderon identity.
Complete complex N64/clock scope with retained markings; no inference of unique physical action from residue classes.
Read the exact result, assumptions and evidence
Result
Full finite relations for Wq,k require k=1 mod4. Adding four flips precisely the unresolved alpha sign; adding eight is canonically trivialized by the marked cotangent product and S0²=K. Fixed signed alpha distinguishes k1 and k5; existing projective spin-lift scope has one class. Finite relations do not determine integer winding.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
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.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
Complex four-dimensional module closure for explicitly constructed Wq including full central action. Physical source selection of one inverse Nq copy remains open. Does not derive integral Gaussian E8 lattice,physical metric,W8 dynamics,or state rule.
Read the exact result, assumptions and evidence
Result
Spin-rigidified theta space is identified as complete complex Heisenberg and clock module. For L=O(2Theta),N={g in G(L):g⁴=1} is canonical order64 group with mu4 center. Every symplectic Phi lifts to N≅N64;Stone-von Neumann identifies Wq=H0(L) tensor Nq^(-1) with native C4 module. c lift has no remaining Pauli shift because1−Sigma invertible. alpha gamma alpha^(-1)=gamma^(-1) and trace(Ad gamma)=1 force trace(gamma)=1,hence exactly gamma->sigma without cube-root phase. Same intertwiner sends alpha to fully classified joint Clifford conjugacy class.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Finite matrix construction with fixed central character. Geometric bridge for Wq is now separately proved by finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package. Conjugacy class is not automatically physical gauge;P1/P2 anchors,state and readout excluded.
Read the exact result, assumptions and evidence
Result
Joint clock relations have exactly one native Clifford gauge class. Under explicit module condition beta->J=iI,no matrix in any64-element G31 fiber over the9 admissible Q actions squares to+iI;in zeta8 G31 each fiber has8. Original relation alpha sigma alpha^(-1)=sigma^(-1) leaves exactly alpha and−alpha. Explicit alpha=zeta8(XI)U has alpha²=J,alpha⁴=−I,and joint group order24. Actual C_G31(sigma) has order72 and is transitive on all9 sign classes. Thus one gauge class remains for fixed sigma,J,Pauli system.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
This lemma covers exact symplectic bridge. Full central and four-dimensional bridge for Wq is closed in subsequent finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package. Older v784/v796 objects and exclusions retain scope.
Read the exact result, assumptions and evidence
Result
Source cubic matches native Pauli translations after correcting context target. v783 distinguishes code labels L/(1+i)L from P_nat=N64/mu4;full Sp4 modules admit no linear intertwiner. On P_nat original sigma is fixed-point-free with polynomial(x²+x+1)²,exactly as c on Jac(C)[2]. Phi with columns IY,YZ,ZY,YI is explicit symplectic intertwiner. Among35 planes exactly5 are sigma invariant,exactly2 symplectic and orthogonal,selecting same unordered triple pair natively. Exactly18 c-equivariant symplectic markings remain. Earlier0-versus2 fixed-space conflict concerns only wrong code/context target.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Native Pauli translations and frozen Gaussian phase class
Native theta-translation target is P_nat=N64/mu4 from v783 in frozen four-component frame,with actual sigma and J=iI. Code quotient L/(1+i)L is the distinct duality-twisted context module. G31 has center mu4;full Clifford matrix group has center mu8 and additional coset zeta8 G31. Retain these concrete actions and phases.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Spin bundle of actual genus2 source,not honest C2 linearization. Subsequent finding:spin-rigidified-theta-module-intertwines-full-native-heisenberg-clock-package closes complex module bridge for Wq. Physical choice of inverse point norm and state remains open.
Read the exact result, assumptions and evidence
Result
Original cubic and quarter select spin line and half-turn lift. S0=O(q0+q1+q2−K_C) is even,S0²=K_C,and equivalent to p definition. c has no nonzero fixed vector on Jac(C)[2],so S0 is unique c-invariant theta characteristic among16. Q preserves S0;at marked fixed point q0,Q*eta=i eta. Any compatible spin lift alpha has alpha^4=−I,order8. beta=alpha composed Q*alpha is order4 lift of h=Q²,independent of alpha->−alpha,with local phase+i. Previously open S0,beta selection is closed by existing data.
Required assumptions
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact finite source identities and reconstruction of known mathematical connections. No proof of universal computation,physical noise,clocks,couplings,Born rule,or simulation. Marginal information loss concerns this mixed-state pair,not all pure codewords. A fully Clifford-invariant Hermitian generator is scalar on5/30 only in that class. Literature links toHamming/E8,QCA,transfer convergence and sufficient statistics remain background theorems under their own premises. The historicalF_a->deltaD_rel question was later sharpened for merely defining composites by the existing current reconstruction.
Read the exact result, assumptions and evidence
Result
The initial exact original-source calculation is now archived in the repository and replayed normally,optimized,and at its archived location with byte-identical results. Pi_native=Q_Pauli Pi_sym4 holds in the unchanged frame;ranks16,35,5 remain distinct. All64 one-register matrix-unit conditions give the existing erasure property. The60 original source rays have frame potentials1/4,1/10,1/20,1/32;the fourth Haar value is1/35 and HS moment defect3/1120. For the already known pair Pi_native/5 andPi_sym4/35,relative entropylog7 and global distance6/7 disappear in all proper marginals. The external standard-gate control compresses to diag(0,0,i,i,i),leaking2directions. The original comparison and known Clifford-commutant literature retain all premises and the physical selection boundary.
Required assumptions
Actual native G31 event representation
Use the actual original Hamming/E8/J matrices and60 reflections, their four-dimensional action, characteristic P64=O2(G31), and existing S6 quotient. These are accepted mathematical core data, not a physical source derived from P1 in this round.
Symmetric quartic and actual erasure intertwiner
Use Sym^4 of the native four-representation, the actual five codeword sums, and the existing one-register erasure intertwiner. The symmetric tensor rule and its physical selection are not silently inferred from the full tensor product.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.