TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/ORIGINAL-MIRROR-EMBEDDING-SEARCH.txt
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000001 | R108. Original mirror embedding: old-source recovery and decisive type test
000002 | 3 November 2026. Entry plan94 / Atlas d89da18237c9f54dd12391b4.
000003 | 
000004 | VERDICT
000005 | The requested primitive field embedding and H_adm[F,0] are NOT derived.
000006 | This report does not rename any given DET parent as the original source.
000007 | Two genuinely different old source routes were examined and actual native
000008 | functions executed. One proposed whole-algebra identification is excluded
000009 | under its stated action; a positive explicit wall smearing is recovered
000010 | within the original four-flavor QWZ analogue. Neither is promoted to P1.
000011 | 
000012 | LIVE ATLAS RECONCILIATION BEFORE PERSISTENCE
000013 | Concurrent L20261103K was published during this work, plan95 / Atlas
000014 | 923b6826d0d1905a1d420d18. Its FIELD-PROJECTOR-MAP.txt:1-150 and
000015 | K-URTEIL.txt:1-120 were read. The original v474 internal Splus and native
000016 | v1002 sixteen-label Clifford actions are NOW exactly intertwined by
000017 |  W e_I=(-1)^(|I|(|I|-1)/2)|sum_(k in I)2^(5-k)>.
000018 | K's actual comparison gives all ten Clifford/45 generator defects0 and
000019 | detW=+1, so Gamma(W) transports complete CAR without a new phase.
000020 | That positive internal component dictionary is preserved, not reopened.
000021 | It does not identify the vector Majorana FIELD operators of section1
000022 | with spinor field operators, or choose the source spacetime smear/time.
000023 | K's complete source-kernel reader, reducing-net result and scoped
000024 | same-local-Weyl/scalar-rest exclusion are retained independently; they
000025 | are not overwritten or counted as new R108 results.
000026 | 
000027 | 1. THE OLD SIXTEEN ARE REAL VECTOR MAJORANAS
000028 | 
000029 | v113_quasifree_kernel.py:11-17,25-31,150-158 explicitly uses16 REAL
000030 | Majoranas: (10,1)+(1,6) under Spin10 x Spin6, with complex polarization
000031 | rank8. At one finite mode block this is eight complex modes and Fock
000032 | dimension256. Native v1002 instead has sixteen COMPLEX annihilators
000033 | transforming in a Spin10 half-spinor, and Fock dimension65536.
000034 | The Splus states of the first Clifford representation must not be
000035 | confused with spinor-transformed annihilator OPERATORS of a second CAR.
000036 | v173_pfaffian_cp_car.py:46-77 uses n8,dim16 coefficient matrices for its
000037 | declared finite Pfaffian model; it constructs no missing spinor field map.
000038 | 
000039 | There IS an old actual CAR partner double, not merely a guessed second
000040 | source: two_face_source_20261029/PROOF.txt:38-59 gives the full source
000041 | graph P, its cross covariance and the normal HS operators
000042 |  a_R=L_a, a_L=-Gamma R_a, a_L*=Gamma R_(a*).
000043 | The two CAR families are algebraically independent and source-correlated.
000044 | Their null/sewing equations and old source/reflection/time results remain.
000045 | This particular partner is not automatically the second physical P1 face.
000046 | Historical source-boundary wording in that file is not used to erase the
000047 | subsequent complete S/Z or G/H/I/J source results.
000048 | 
000049 | It is tempting to use this double as32 real ->16 complex -> native CAR16.
000050 | For a finite8-mode source its HS dimension also equals65536. Even when
000051 | the abstract CAR dimensions match, their ACTUAL GROUP ACTION must match.
000052 | 
000053 | 2. ALL-WORD EXCLUSION FOR THIS PARTICULAR VECTOR/PARTNER ROUTE
000054 | 
000055 | Assume exactly the original (10,1)+(1,6) vector action and its covariant
000056 | canonical partner action, with no extra charged/disorder field sectors.
000057 | Let g=-1 in Spin10 be its central element z^2, represented by a2pi
000058 | rotation in ONE INTERNAL Spin10 plane. This is NOT a spacetime rotation.
000059 | It projects to the identity in SO10, so its automorphism alpha_g fixes
000060 | every old vector Majorana. It also fixes their canonical partners.
000061 | 
000062 | Let A_vec,2 be the unital * algebra these actual fields generate.
000063 | Multiplicativity and adjunction give alpha_g(A)=A for EVERY word and
000064 | finite linear combination. Isometry extends this to its C* norm closure.
000065 | For a covariant representation with normal automorphism, sigma-weak
000066 | continuity gives the same identity on the generated W* closure.
000067 | No bound on word length or number of AI candidates is involved.
000068 | 
000069 | On the native Spin10 half-spinor, rho_Splus(g)=-I16; its dual also has
000070 | sign minus. Therefore its annihilator generators transform as
000071 |  beta_g(c_i)=-c_i.
000072 | Suppose iota:CAR(Splus)->A_vec,2 were a unital equivariant * embedding.
000073 | Then iota(c_i)=alpha_g(iota(c_i))=iota(beta_g(c_i))=-iota(c_i),
000074 | so iota(c_i)=0. But {c_i,c_i*}=1 implies {0,0}=iota(1)=1,
000075 | a contradiction. Thus no such FULL charged-field embedding exists.
000076 | 
000077 | Native exact check: v1002.spin10_vector_weights_doubled gives the ten
000078 | integer-vector weights (doubled coordinates even); add the six original
000079 | Spin10-singlet weights from v113. Their2pi character is+1 on all16.
000080 | v1002.spin10_chiral_weights_doubled gives16 half-integral weights with
000081 | odd doubled coordinates, all character-1. With the canonical partner,
000082 | the candidate16x32 linear intertwiner has512 complex entries and its
000083 | central constraint is simply -2 times every entry, hence kernel0.
000084 | This finite check verifies the load-bearing source signs. The stronger
000085 | all-word/closure statement follows from the algebraic proof above.
000086 | 
000087 | The implementer on STATES is not its conjugation automorphism on FIELDS.
000088 | A spinorial phase on a Clifford state does not turn a vector operator
000089 | into a spinor operator; a central implementer can lie in the commutant.
000090 | Replacing this particular central action with source fermion parity
000091 | would change the proposed equivariance map, not solve the original one.
000092 | 
000093 | STRICT LIMITS: This excludes only the stated vector/canonical-partner
000094 | algebra as a fully Spin10-equivariant source of the individual spinor
000095 | CAR fields. It does NOT exclude an even observable map or DET16 itself:
000096 | an even product of spinors, including sixteen, is g-even. It does NOT
000097 | set a determinant coefficient to0. Genuine charged Ramond/DHR/disorder
000098 | extensions are outside A_vec,2; their possible field maps are not killed.
000099 | Nor does it assert that the complete original S/Z is only this algebra.
000100 | 
000101 | 2b. THE MINIMAL FINITE PACKET ALSO FAILS UNDER THE ACTUAL COLOR GROUP
000102 | 
000103 | Full Spin10 equivariance is not a new universal physical requirement:
000104 | the original physical carrier stabilizer is S(U3 x U2), as explicitly
000105 | stated in Source45 Carrier002:70-91. Thus section2 alone must not be
000106 | advertised as an obstruction under only the physical gauge group.
000107 | 
000108 | There is an independent decisive test within that SMALLER actual group.
000109 | Consider the proposed SAME minimal finite double packet: two equivalent
000110 | real16 vector copies with canonical partner covariance, paired by the
000111 | invariant polarization c_a=(gamma_R,a+i gamma_L,a)/2. Its sixteen complex
000112 | modes carry the complexified10+6 vector representation. No further rest,
000113 | spatial or charged Hilbert factors are included in this packet comparison.
000114 | Both full CAR algebras are M_65536; no time-autonomy premise is used.
000115 | 
000116 | Take g=diag(omega,omega,omega,1,1) in the ACTUAL SU3 color subgroup,
000117 | omega^3=1. The source one-particle charge multiplicities modulo3 are
000118 | (10,3,3); those of native Spin10 spinor16 restricted to color are(4,6,6).
000119 | These numbers follow from the original doubled weights by
000120 |  q=(w2[0]+w2[1]-2w2[2])/2 modulo3,
000121 | using a traceless logarithm of g. No fictitious global Spin10 gauge group
000122 | or guessed hypercharge convention is needed for this element.
000123 | 
000124 | Exact exterior Fock recursion (each mode either empty or occupied) gives
000125 |  source charge-sector counts=(22528,21504,21504),
000126 |  target charge-sector counts=(21856,21840,21840).
000127 | Both sum to65536, but their implementer trace magnitudes are1024 and16.
000128 | Every unital * embedding M_65536->M_65536 is an isomorphism. Equivariance
000129 | would make the two inner group implementers unitarily conjugate up to a
000130 | scalar phase, which preserves the ABSOLUTE trace. Hence no such same-
000131 | packet equivariant embedding exists, even for this physical color element.
000132 | Indeed a nonzero * homomorphism between these same full matrix algebras
000133 | is already unital: its finite-dimensional representation multiplicity
000134 | must be1. Dropping the word unital supplies no smaller same-size escape.
000135 | Equivalently the adjoint fixed-algebra dimensions are
000136 |  source22528^2+2*21504^2=1432354816,
000137 |  target21856^2+2*21840^2=1431655936.
000138 | An equivariant isomorphism would preserve these dimensions as well.
000139 | 
000140 | Root executed that exact integer recursion from the ORIGINAL v1002
000141 | weight functions. This is a finite representation-class exclusion;
000142 | unlike section2 it does not extend to arbitrary larger field algebras
000143 | or rest factors. Another spatial packet, a larger source, a different
000144 | actual partner action or a genuine charged extension changes the premise.
000145 | An even-only observable map and the primitive DET coefficient are NOT
000146 | decided by this full-CAR packet test. No new zero coefficient follows.
000147 | 
000148 | 3. EXISTING E8 SPINOR SOURCE IS RETAINED, NOT FORGOTTEN
000149 | 
000150 | v983_simple_current_generator.py:9-35 has the actual original
000151 | lambda=(omega_s,omega_f), ||omega_s||^2=5/4,||omega_f||^2=3/4,
000152 | lambda^2=2,h=1, and (16,4)+(bar16,bar4) source sectors.
000153 | The existing mixed-current review:88-140 carries their actual cocycle,
000154 | adjoint, family OPE, charged carry and source H_exc=8(L0+d.h0).
000155 | This charged E8 extension is OUTSIDE the vector algebra in section2.
000156 | Its existence and existing192 mixed/64 diagonal source answers remain.
000157 | No unchanged root/OPE census was rerun.
000158 | 
000159 | The given weight1 local E8 current is even/bosonic; the native c_i is
000160 | odd/fermionic. A grading-preserving direct identification is impossible.
000161 | The four-component family factor cannot simply be dropped, either.
000162 | This is not a proof against a correctly constructed dressed fermionic
000163 | source. The old source_origin_audit.txt:73-109 supplies D_I=X_flux tensor
000164 | U_arc in an enlarged flux space, not an actual bare-matter/P1 mirror map.
000165 | Adding an unproved Klein/disorder factor is not an original derivation.
000166 | 
000167 | 4. ACTUAL POSITIVE WALL PROFILE RECOVERED AND EXECUTED
000168 | 
000169 | Native v1008_master_assembly_scaffold.py:229-256 fixes LY8,MASS1,
000170 | FLAVORS4 and computes the nullspace of its original QWZ strip at k0.
000171 | Its localized position basis gives, up to phase,
000172 |  v_phys(y)=delta_y0(1,-1)/sqrt2,
000173 |  v_mir(y)=delta_y7(1,1)/sqrt2.
000174 | Root called the actual original functions. Profile projector entry
000175 | errors are1.3401183557113164e-18 and0; cross overlap0.
000176 | In the corresponding canonical QWZ field algebra the actual mode formula
000177 | is c_mir,a(k0)=(Psi_k0,7,1,a+Psi_k0,7,2,a)/sqrt2, a=1..4.
000178 | Orthonormal smearing gives canonical CAR and physical/mirror anticommutation.
000179 | This is a genuine explicit profile of an EXISTING analogue, not a new model.
000180 |