TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/D8-NATIVE-K-AND-GLUE-ESCAPE-REVIEW.txt Original file SHA-256: e1990b88ef544c931bf52a338fe4623be0304e84be8da48db0e5feebbfa2fb0e Inclusive original lines: 1-190 Line numbers below refer to the original source. This bounded excerpt is source evidence; it is not a new proof/checker run. Conversation metadata and personal execution details are omitted where indicated. 000001 | D8 NATIVE K AND GLUE ESCAPE REVIEW 000002 | ================================== 000003 | 000004 | 30 October 2026. Independent exact source review. No Atlas, index, ledger 000005 | or pre-existing report was changed. 000006 | 000007 | Question 000008 | -------- 000009 | 000010 | The restricted original seed 000011 | 000012 | C_a, X_i,a and adjoints, a in F={1,2,3}, 000013 | 000014 | closes to a particular D8 with 112 roots. Does an operation already present 000015 | in the original P1/P2 and E8 glue chain cross its 128-root complement and 000016 | supply a missing C0, Xi,0 or the missing half of (10,6)? 000017 | 000018 | Verdict 000019 | ------- 000020 | 000021 | YES at the given P2 current algebra level, by an operation smaller than the 000022 | spinor seam extension. 000023 | 000024 | The original D5 current algebra contains twenty roots outside the restricted 000025 | D8. One such ordinary grade-zero D5 root current sends an already generated 000026 | (10,6) current to the missing carrier half in one bracket. The exact word is 000027 | 000028 | [ E_(-e0-e1), [ X_(1,3)^dag, C_2^dag ] ] . (1) 000029 | 000030 | In doubled current coordinates the two actual Chevalley brackets are 000031 | 000032 | [X_(1,3)^dag,C_2^dag] 000033 | = - E_(0,2,0,0,0,-2,0,0), 000034 | 000035 | [E_(-2,-2,0,0,0,0,0,0), 000036 | E_(0,2,0,0,0,-2,0,0)] 000037 | = + E_(-2,0,0,0,0,-2,0,0). (2) 000038 | 000039 | The last root is one of the thirty previously unreachable (10,6) roots. 000040 | Adding the full original D5 root action to the restricted seed gives the 000041 | exact closure 000042 | 000043 | 76 -> 172 -> 232 -> 240 roots. (3) 000044 | 000045 | Thus the old factor-two carrier gap is closed inside the already given 000046 | compact E8 current source. No O fermion and no freely inserted full 16 000047 | spinor input is needed. The input beyond the restricted three-family seed 000048 | is precisely the original D5 zero-mode action. 000049 | 000050 | This is more economical than the seam module switch for the carrier task. 000051 | It does not say that primitive P1 dynamics selects or executes this zero-mode 000052 | word. The mathematical P2 carrier and E8 current contracts provide the 000053 | operator action. A physical P1 pulse, response rule or preparation selecting 000054 | it is not derived here. 000055 | 000056 | 1. Why the native D5 word is an original operation 000057 | -------------------------------------------------- 000058 | 000059 | The original compiler starts with (D5)_1 times (A3)_1 before the mu4 000060 | extension. Therefore E_(-e0-e1) is a base current, not a newly chosen seam 000061 | field. Independently, v474 constructs the ten carrier Clifford generators 000062 | on Lambda* C5 and proves that their 45 bilinears span so(10), preserve the 000063 | even 16 dimensional carrier and act as the D5 algebra. The actual current 000064 | implementation then evaluates (1) with the original Chevalley table and its 000065 | fixed signs. 000066 | 000067 | The distinction from mere abstract covariance is therefore: 000068 | 000069 | * on the finite P2 carrier, the D5 action is an explicit matrix action; 000070 | * in the marked affine current source, the D5 roots are weight-one current 000071 | operators and their zero modes act through the checked Chevalley bracket; 000072 | * primitive P1 has not separately derived a source history which applies 000073 | this particular zero mode to the state. 000074 | 000075 | The first two bullets prove an available operator in the given P2/E8 source. 000076 | They do not imply the third. 000077 | 000078 | 2. Clock and cocycle do not need repair 000079 | --------------------------------------- 000080 | 000081 | Use the original internal glue grade 000082 | 000083 | gr(r) = -sum(r_5,r_6,r_7) mod 4. 000084 | 000085 | For the three roots in (2) the grades are 000086 | 000087 | gr(E_(-e0-e1))=0, gr(Y)=2, gr(output)=2. 000088 | 000089 | The D5 step is neutral under the original quarter clock and preserves the 000090 | grade exactly. Both bracket coefficients in (2) come from the actual compact 000091 | Chevalley table. Hence no new cocycle sign, Weyl dictionary or clock fit has 000092 | been introduced. 000093 | 000094 | The original mu4 grade is not the Z2 coset parity of the newly found D8. 000095 | Both the 112-root D8 and its 128-root complement contain grades 0,1,2,3. The 000096 | exact D8 grade census is 000097 | 000098 | D8: 26,28,30,28 for grades 0,1,2,3, 000099 | complement: 26,36,30,36 for grades 0,1,2,3. 000100 | 000101 | This prevents a false statement that the old quarter clock itself is the new 000102 | D8 module switch. 000103 | 000104 | 3. The old marked glue generator is also an exact escape 000105 | -------------------------------------------------------- 000106 | 000107 | The independent seam route is positive at its stated lattice and conformal 000108 | net scope. v983 fixes 000109 | 000110 | lambda=(omega_s,omega_f), 000111 | omega_s=(1/2)^5, 000112 | omega_f=(3/4,-1/4,-1/4,-1/4). 000113 | 000114 | The original A3 to D3 isometry maps omega_f to (1/2,1/2,1/2). Therefore in 000115 | the current table 000116 | 000117 | 2 lambda=(1,1,1,1,1,1,1,1)=root(C0^dag), (4) 000118 | 000119 | with the table using doubled coordinates. Its adjoint is exactly C0. Thus 000120 | the already marked glue vertex is not merely Weyl conjugate to a useful 000121 | escape. In this fixed chart it is the omitted minimal C0 pair itself. 000122 | 000123 | Relative to the new D8, lambda has integral pairing with every root. The 000124 | pairing numerators in doubled coordinates are -4,0,+4 with multiplicities 000125 | 28,56,28. Adding C0 and C0^dag to the closed D8 gives 000126 | 000127 | 114 -> 170 -> 240 roots. (5) 000128 | 000129 | The original quarter grades of lambda and its adjoint are 1 and 3. These are 000130 | retained rather than redefined. 000131 | 000132 | 4. What the D8 vacuum VOA cannot do 000133 | ----------------------------------- 000134 | 000135 | Let L be the root lattice of the new D8. Every state and every vertex mode 000136 | in V_L has momentum in L. Products add lattice momenta and oscillator modes 000137 | carry zero lattice momentum. Consequently arbitrary words and all modes of 000138 | the D8 vacuum VOA stay in L. They cannot produce e^lambda in the other coset 000139 | lambda+L. 000140 | 000141 | The E8 lattice VOA is the index-two extension 000142 | 000143 | V_E8 = V_L direct-sum V_(L+lambda). 000144 | 000145 | The vertex Y(e^lambda,z) is precisely the sector-changing operation. Once it 000146 | and its adjoint are admitted, D8 current modes generate the full 128-root 000147 | module and (5) recovers E8. v459 and the local Z2 crossed-product route 000148 | support this extension at lattice/net level. 000149 | 000150 | What remains open is narrower. The primitive one-channel P1 quarter source 000151 | has not been proved to produce Y(e^lambda,z) as a localized microscopic 000152 | operator with its GSO choice, cocycle, state and common time. The existing 000153 | source_spin_lift audit explicitly records that the formal quarter-field OPE 000154 | and the neutral eight-copy kernel do not prove this operator limit. This 000155 | open P1 realization does not undo the positive native D5 completion (1), 000156 | which only uses the already given P2/E8 current operation. 000157 | 000158 | Reproducible check 000159 | ------------------ 000160 | 000161 | aps_source_review/check_d8_native_k_and_glue_escape.py 000162 | aps_source_review/d8-native-k-and-glue-escape-results.json 000163 | 000164 | All 13 exact checks pass. Normal Python and python -OO produce byte-identical 000165 | JSON. 000166 | 000167 | Sources 000168 | ------- 000169 | 000170 | tfpt_explorer/current_block_geometry.py:92-125 000171 | actual phase-aligned C/X roots and original Chevalley coefficients 000172 | 000173 | verification/v474_entropic_hodge_carrier.py:9-19,91-126 000174 | explicit D5 Clifford and so(10) operator action on the P2 carrier 000175 | 000176 | verification/v1_e8_glue.py:1-145 000177 | original D5+A3 lattice and E8 glue certificate 000178 | 000179 | verification/v983_simple_current_generator.py:9-52,60-146 000180 | marked lambda, h=1, order four and the 128-root fusion powers 000181 | 000182 | tfpt_explorer/source_spin_lift.py:70-215,217-242 000183 | exact lambda chart, Chevalley closure, clock/cocycle scope and the still 000184 | missing microscopic P1 operator identification 000185 | 000186 | documents/tfpt_1_architecture_e8/sections/005-source.tex:55-70 000187 | the same glue on root lattices and chiral nets, with the local Z2 000188 | simple-current extension and its retained realization scope 000189 | 000190 | Exact source hashes are embedded in the result JSON.