TFPT scientific source excerpt Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/ACTION-TYPE.txt Original file SHA-256: bea1f96bfb16206f6fb177be2fe489d09072d7825e86d3c4302d9eaadf4f8d41 Inclusive original lines: 201-302 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. 000201 | 000202 | Only if the actual weights obey w_A/w_R=exp(-DeltaS) on that SAME basis may 000203 | one write (1) as omega_R(exp(-DeltaS+J.fields)). It is not legitimate to set 000204 | DeltaS=S_prim-S_ref automatically: S_prim already contains a reference 000205 | subtraction, while Z_ref is a separately displayed fixed denominator. 000206 | Nor is a fixed operator D_ref by itself a complete reference field-density 000207 | w_R on the same integration-coordinate space. 000208 | 000209 | The precise equation to locate in the original is the weight/reference 000210 | identification, not a second free measure choice. Joint_origin is following 000211 | its actual nu/blocking producer; this report does not invent one. 000212 | 000213 | 6. SMALLEST EXACT REFERENCE-TYPING TEST 000214 | 000215 | The following is an algebraic check on the actual displayed types, not an 000216 | auxiliary physical model. Under a common constant shift of two ABSOLUTE 000217 | input actions S_A->S_A+c, S_R->S_R+c, 000218 | Z_A/Z_R is invariant, and exp(-(S_A-S_R)) is invariant. 000219 | If one first uses that ALREADY RELATIVE density on the same bare basis and 000220 | then divides by the same shifted Z_R once again, the result gains exp(c). 000221 | It has counted the reference at two different levels. 000222 | 000223 | Three exact symbolic invariance checks were run in this work directory; 000224 | action-type-identities.json records them. This proves the extra substitution 000225 | would be wrong. It does NOT prove the original performs it: the original 000226 | would have to assert the same weight/reference equality first. The report 000227 | therefore records the first unsupported identification rather than declaring 000228 | a contradiction from a shared word 'relative'. 000229 | 000230 | 7. WHAT A FULL GIVEN omega ALREADY FIXES 000231 | 000232 | A conditional CAR state at fixed bosonic b forgets its own unnormalized 000233 | scalar. The FULL original joint state does not generally forget a factor 000234 | q(b). When b belongs to the actual integrated/observable commutative bosonic 000235 | field algebra and the positive marginal is mu, multiplying its full weight 000236 | by q(b)>0 gives 000237 | dmu'=q(b)dmu/E_mu q. 000238 | Equality on ALL bounded bosonic observables implies mu'=mu and hence 000239 | q=E_mu q almost everywhere. A nonconstant radial/geometric reweighting 000240 | cannot leave that full joint source unchanged. Full mixed words further fix 000241 | the conditional correlations. If another bare contribution is adjusted by 000242 | the inverse factor so the total weight stays the same, that is a different 000243 | factorization of the same source, not a physical source ambiguity. 000244 | 000245 | This is an important correction to our repeated conditional-reader scalar 000246 | comparison. A missing scalar in a selected CAR marginal is not automatically 000247 | a missing scalar in the already given whole P1 source. 000248 | 000249 | The actual input/field distinction still matters. If g is held as an EXTERNAL 000250 | background and only omega_g is normalized separately for each g, multiplying 000251 | Z_g by an independent c(g) is invisible to those fixed-background normalized 000252 | words. Its geometric derivative must come from the original action/reference 000253 | normalization. If g is itself integrated and observed, a nonconstant factor 000254 | in g changes the joint source. The abstract symbol varphi in W_k is not by 000255 | itself proof of which of these two actual calls is intended. This is exactly 000256 | the original field/source map to read, not a new general measure axiom. 000257 | 000258 | FINAL ACTION JUDGMENT 000259 | 000260 | No: the reviewed original does not already identify its primitive spectral 000261 | S with evaluated -log Z. Yes: once its actual structured whole source and 000262 | reference are supplied, there is no second free state/scalar to choose for 000263 | that SAME source. Its relative scalar follows from the actual full weight 000264 | quotient, and its normalized full joint moments already constrain every 000265 | integrated background reweighting. 000266 | 000267 | The first unjustified shortcut would be any of: 000268 | S_adm=S_prim=-log Z_rel=Gamma_ren=M, 000269 | a spectral reference subtraction equals the same reference partition ratio, 000270 | or a conditional CAR scalar equals the entire original boson/geometry weight. 000271 | The original named objects are distinct. Resolve their actual density/field 000272 | mapping once and preserve it through integration and derivatives. Further 000273 | partial-reader reconstruction cannot substitute for this whole-source call. 000274 | 000275 | EXACT SOURCES READ / PINNED 000276 | 000277 | Boundary001:302–350, paper-source:8027564739689dd02e02f11c, 000278 | SHA7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79. 000279 | Boundary002 operational Seed:100–249, paper-source:92324c2bfff42fe248080ffe, 000280 | SHA1de90a4a7379bef804cc7815d72c0f86bb398a5771e9b00997c4bb15e8815f9e. 000281 | Boundary003:1–25, paper-source:b89bdb8852963f5e5386ea87, 000282 | SHAd1136b33055198aedd6d1322912672977374f13f30e65dd073312ed272df0858. 000283 | QFT002:256–270, paper-source:35c4c41ef6cded2368b36527, 000284 | SHA61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c. 000285 | QFT005:144–214, paper-source:972de2429406831890ef4161, 000286 | SHA8bf0a37157505ca12b90154dbe41a29c49a503686a8493dffd63945f205e0af6. 000287 | QFT007:1–200, paper-source:f588a78cad85dd5237213db3, 000288 | SHA9c1c587cbd61fc4034649d778d16f1ee0e8c1e1189885babb3d8148a6fe72d7c. 000289 | v42 primitivecompletion027:229–381, paper-source:2e7a7e8683a7d25b990bcfed, 000290 | SHA59f89c232f7636919ee049f25e066f2ba7937a0e636333b9c4eab2fef17c5d42. 000291 | Researchcontract017:153–185, paper-source:1b8338240b1064ce2b8145a6, 000292 | SHA492599a0d20043a5589ca610ce7e1ebceffb8de043eae8eb406e4469d3e4be83. 000293 | ActiveSM010:270–318 and verification/v259 full file, direct known-source read. 000294 | DYNAMICAL-HIGGS-SOURCE-PROOF and FULL-SOURCE-REGULATOR-PROOF existing typed 000295 | integration results are reused, no new source construction claimed. 000296 | 000297 | Primary technical context checked: Chamseddine/Connes/Marcolli, 000298 | hep-th/0610241, equation1.3 and theorem4.3/equation4.8 distinguish the spectral 000299 | trace and the fermionic bilinear action; the latter yields its Pfaffian upon 000300 | Grassmann integration. https://arxiv.org/pdf/hep-th/0610241 . This supports 000301 | keeping those action/integration levels separate; it does not supply a new 000302 | TFPT reference density or identify the original full Z by citation alone.