TFPT scientific source excerpt Original repository path: experiments/theory-contracts/tfpt-unified-source-derivation-20261029/aps_source_review/ORIGINAL-PRIMITIVE-WEDGE-CONSUMER-HARDY-REVIEW.txt Original file SHA-256: f830ec1e84b614b175918fd7aad5659121c3f53d9f12693ab0bed602e4d4f87c Inclusive original lines: 1-123 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 | THE ORIGINAL PRIMITIVE WEDGE CONSUMER READS THE NEW HARDY COEFFICIENT 000002 | Independent targeted source/operator continuation, 30 October 2026. 000003 | No original edits, Atlas writes, new tangent, fixed-point law or source/state. 000004 | 000005 | CORRECTION AND POSITIVE RESULT 000006 | The original carrier theorem ALREADY contains the concrete weak Clifford 000007 | consumer at the primitive Yukawa level. The last broad statement that no 000008 | inspected original rule applies a weak exterior creator needs this precise 000009 | qualification. The original primitive wedge contraction IS that creator 000010 | followed by the fixed exterior-volume pairing. Its execution on the actual 000011 | whole-96 dictionary is nonzero for the proven Hardy coefficient. 000012 | What remains to identify is its FAMILY COEFFICIENT SOURCE: the original 000013 | branch formula reads Hol(nabla_F*) K_f^str, while the new coefficient is the 000014 | actual finite Hardy Bmu response. No new weak matrix unit needs inventing. 000015 | This does not assert that the Hardy contribution must be the entire Y_br. 000016 | 000017 | 1. Exact original formula, context and registered anchors 000018 | Original file: 000019 | documents/archive--tfpt-45--source_extracts--02_carrier_source/sections/ 000020 | 008-source.tex 000021 | source_id paper-source:dde605e44a40ce9601149525 000022 | SHA256 aa2731355579b961ea9de47532cb0a4cb3db6e1c29e0f18965b517d1280d8d85 000023 | Read113-152,155-245,277-310. Lines167-169 name Y_br as the branch tensor 000024 | induced by the canonical transport kernel and rigid family holonomy. 000025 | Its primitive component at185-188 is explicitly the map 000026 | (E3 tensorE2) tensorLambda2(E3) tensorE2 000027 | -> Lambda3(E3) tensorLambda2(E2)=detE=C. 000028 | The proof at237-242 uses the actual canonical exterior contraction. 000029 | This is more information than the one-dimensional invariant-space count. 000030 | For s_Q in E3 tensorE2, s_uc in Lambda2(E3), H in E2, its explicit 000031 | realization in the already oriented P2 carrier is 000032 | C_prim(s_Q,s_uc,H)=vol_E(s_Q wedge s_uc wedge H) 000033 | =vol_E(s_Q wedge c_H s_uc), (1) 000034 | c_H s=H wedge s. 000035 | The last equality uses the even degree2 of s_uc. Thus the weak Clifford 000036 | creator is an existing expression of this original map. Equation(1) 000037 | does not invent the neutral-to-odd commutator as a printed P1 rule. 000038 | 000039 | 2. Execute the actual primitive channel on the new coefficient 000040 | Use the fixed exterior order (c0,c1,c2,w1,w2), and let 000041 | s_Q=c0 wedge w1, s_uc=c1 wedge c2, H=w2. 000042 | The original map has 000043 | C_prim(s_Q,s_uc,w2)=+1, 000044 | because moving w1 past c1,c2 uses two transpositions. Charges are 000045 | Y(s_Q)=1/6, Y(s_uc)=-2/3, Y(w2)=1/2, 000046 | whose sum is0; both fermionic exterior inputs have even carrier degree. 000047 | Insert the actually evaluated family contribution kappa E02. Its 000048 | corresponding directed primitive coefficient is EXACTLY +kappa, not zero. 000049 | This is a contribution in a fixed original trilinear channel, not a claim 000050 | that the full branch tensor or all four Yukawa matrices equal this block. 000051 | 000052 | The SAME statement was replayed directly using the existing whole-96 000053 | signed dictionary and actual v252 grading, without its suite or run(). 000054 | Take Q=particle u_L,color0,G0 and uc=antiparticle u_R,color0,G2. 000055 | The existing normalized block A=[X_w2,E02 P_gamma,+] maps the latter 000056 | exterior mask6 in family2 to mask22 in family0. The actual compact 000057 | conjugation includes the fixed complement-reversal sign: 000058 | C_comp(s_Q)=-c1 wedge c2 wedge w2. 000059 | Hence its KO Hilbert pairing is 000060 | =-1, 000061 | =-kappa. (2) 000062 | The +kappa in the original wedge and -kappa in(2) are the determined 000063 | exterior/compact-conjugation convention, not a new adjustable phase. 000064 | The positive KO6 and four-sector completion already proved in the two 000065 | HARDY-BMU reports is retained, including rank64 and D_KO^2; it is not 000066 | rederived or silently replaced by a naive adjoint completion. 000067 | Durable replay: workspace outputs/multi-model-source-search-20261029/ 000068 | ORIGINAL-WEDGE-HARDY-CONSUMER-CHECK.json. 000069 | 000070 | 3. The actual original alternative coefficient source must be preserved 000071 | Original file: 000072 | documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/ 000073 | 004-source.tex 000074 | source_id paper-source:7268c6c6db6ca8a62299c024 000075 | SHA256 107d525221eb816043dbf4fb1a3c7e8244d3e24a5a5bcbfe1c2c34d8ee192f4a 000076 | Read180-197 and219-244. The actual prescribed input to that branch tensor is 000077 | (Y_f)_ij=, 000078 | with the printed hard-holonomy/length reduction on the corresponding branch. 000079 | Thus the strongest original route DOES supply a carrier trilinear consumer 000080 | and a specific family-kernel consumer, not merely arbitrary v252 inputs. 000081 | The newly proved Hardy coefficient has not yet been shown to be that 000082 | matrix element, its actual source variation, or one of its path summands. 000083 | These are different comparisons; no requirement that this one Hardy 000084 | rank-one contribution equal the whole original transport matrix is imposed. 000085 | 000086 | For this exact up-type channel, a proposed common-source identification 000087 | can now be tested as the concrete coefficient equality 000088 | =kappa, 000089 | IF it claims equality of the full entries. If the original source rule 000090 | instead makes Hardy Bmu a tangent or a summand, compare that tangent or 000091 | summand, retaining its basis, endpoint and variation terms. No new source 000092 | map is supplied just by naming this equality. The carrier side (1)-(2) 000093 | is already executable and does not need another weak-creator selection. 000094 | 000095 | 4. Other original paths and the exact remaining first application 000096 | The primitive handoff001:274-287 defines finite polarization; it does not 000097 | execute(1) on a computed Bmu coefficient. The C6 transport definition 000098 | em003:100-118 is D_y,delta=yI-delta U6, with its positive structural kernel; 000099 | em005:42-55 permits a gap-stable V_adm without identifying it with Bmu. 000100 | The original fullv21 unit seam matching is a scalar U_Gamma=e^(i theta) 000101 | matching and spectral-flow rule; it remains distinct from the coefficient 000102 | assignment above. The original spacetime covariant derivative and its 000103 | Clifford symbol are not the internal creator c_H; equation(1) gives the 000104 | correct INTERNAL carrier operation directly. 000105 | The targeted v479 quiver check constructs the Kronheimer/McKay geometric 000106 | bridge and marks; its actual run() does not evaluate a neutral response 000107 | into this Yukawa trilinear. It is not a competing hidden coupling formula. 000108 | 000109 | The existing Lean BoundaryYukawaKernelInterface.lean:18-40,46-57,86-93 000110 | explicitly calls itself a typed target for this source derivation. It takes 000111 | omega, contraction injectivity/surjectivity as fields; it does not claim 000112 | a boundary-to-form operator computation. This is consistent with the 000113 | precise positive separation found here, not an additional missing gate. 000114 | 000115 | FINAL SCOPE 000116 | An original weak Clifford/wedge CONSUMER is present and has now been 000117 | executed on the newly nonzero coefficient with its actual charge/KO sign. 000118 | The next provenance question is the common-source coefficient operation 000119 | relating the Hardy matrix moment to the SPECIFIC original HolK branch 000120 | formula (or its actual variation/summand). It is not an absent carrier map, 000121 | new state/time/normalization requirement, or a demand that Hardy replace 000122 | every other original source route. All native clock, signed-deck, whole 000123 | products, reflection and original state/time structures stay retained.