TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/DET16-ORIGINAL-MAP.txt
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Inclusive original lines: 201-333
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000201 | as Haar projection onto the two Spin10 Fock singlets. The positive penalty
000202 | weights lambda_Theta etc. are input weights; they do not select the v1013
000203 | coefficient2. This is an actual difference of operator actions, not an
000204 | argument from absent annotations.
000205 | 
000206 | If an actual source intertwiner identified a Spin10 singlet subspace
000207 | span{|0>,|F>} AND Q_Theta with the phase exchange of its two vectors,
000208 | their joint projection would be P_phi. That is a precise sufficient
000209 | identification to verify. It is not established merely by the two labels
000210 | "singlet" and "determinant". No such equality is asserted by the exact
000211 | original definitions read here.
000212 | 
000213 | The original assembly probe also gives a positive, but scoped, coupling:
000214 | the order-four Psi is a charge-raising analogue of the v983 current, the
000215 | seam couples to PHYSICAL Q density, and the representative DET4 species
000216 | have centre-neutral total determinant. Its own head declares no full
000217 | Spin10, dynamical links or full spacetime seam field. Thus that concrete
000218 | coupling cannot silently supply the missing full DET16 gauge embedding.
000219 | 
000220 | Sources: research-source:75554c5535c27abac436633f:31-117,
000221 | old45 QFT002, SHA61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c.
000222 | research-source:89a4fe828234749ab2876220:26-35 and
000223 | research-source:727d131cbacfdadaff9db7df:66-73,
000224 | experiments/tfpt-discovery/tfpt2p1d_master_assembly_probe.py,
000225 | SHA2cb1d4dcc3d6a2e27503e8e6f812e05da966de3410fc793c7b62ee06cbed78eb.
000226 | Its actual physical_clock_hamiltonian:220-230 and
000227 | full_assembly_hamiltonian:233-244 were read through the code graph.
000228 | 
000229 | 5. NEW EXACT REDUCTION OF THE SAME PHYSICAL VACUUM PROBLEM
000230 | 
000231 | Assumptions are exactly the R104 factorized finite-volume Hamiltonian,
000232 | the actual Gauss projector P_G commuting with H, and gauge invariance of
000233 | each P_x. The latter holds for a canonical second-quantized determinant1
000234 | action on the stated modes; it must be checked for the actual source
000235 | representation. It is not inferred from the order of a centre element.
000236 | 
000237 | For S a subset of the mirror sites define the orthogonal projectors
000238 |  P_S=P_G product_{x notin S}P_x product_{x in S}Q_x.
000239 | They sum to P_G, commute with H_R, and on their ranges
000240 |  H=H_R+2|S|.
000241 | Consequently the COMPLETE Gauss-projected partition function satisfies
000242 |  Z_phys(beta)=sum_S exp(-2 beta |S|)
000243 |                  Tr_{Ran P_S} exp(-beta H_R),
000244 | and the physical ground energy is exactly
000245 |  E_phys=min_{S:P_S!=0}[inf Spec(H_R|Ran P_S)+2|S|].
000246 | The trace here includes the allowed residual mirror multiplicities. It
000247 | must not be replaced by a free rest trace unless the actual charge action
000248 | factorizes that trace. This is a direct orthogonal spectral decomposition,
000249 | not a model, approximation, beta prescription or numerical inference.
000250 | 
000251 | Thus an ambient ground state is already a rest ground state times all
000252 | DET ground lines. The SAME statement in the physical Gauss sector follows
000253 | if the S=empty value is strictly smaller than every S!=empty value.
000254 | Equality gives an actual ground degeneracy; a lower excited-sector value
000255 | gives a physical ground with charged mirror excitations compensating the
000256 | rest sector. Ground-state existence by itself does not fix this ordering.
000257 | 
000258 | This is also the precise check on taking beta->infinity in R104's group
000259 | sum. For one canonical actual action r(g) with det r=1,
000260 |  z_m(g)=a det(I+r(g))+b.
000261 | Its pointwise limit is1. In the whole projected trace, the leading rest
000262 | terms can cancel in the group average if that rest charge sector is not
000263 | physical. One cannot drop the exp(-2 beta) terms before comparing the
000264 | displayed charge-resolved energies. This retains the rest source and its
000265 | physical Gauss weight exactly. No gauge counterexample or new Hamiltonian
000266 | has been introduced.
000267 | 
000268 | For the literal v1013 factorized table, this finite list of sector energies
000269 | is the remaining concrete vacuum calculation after the actual gauge
000270 | representation is fixed. R104 solves its mirror traces, not H_R. The
000271 | reviewed v1013 theorem supplies a global finite-range interaction, a
000272 | thermodynamic local dynamics, and existence of ground/KMS states. Its
000273 | own source does not claim uniqueness, a mass gap, a selected beta or this
000274 | charge-resolved rest ground ordering.
000275 | 
000276 | 6. TIME, REFLECTION, REFERENCE AND THE WHOLE SOURCE
000277 | 
000278 | The finite DET Hamiltonian supplies its own Euclidean heat words and
000279 | Heisenberg time, and the v1013 theorem carries the frozen interaction's
000280 | local dynamics to the thermodynamic limit. These are concrete data.
000281 | The finite adjoint/graded reflected construction is not automatically the
000282 | original collar reflection simply because a CAR algebra is isomorphic.
000283 | A WHOLE unitary transport carries them by conjugation; all sources and
000284 | the reference must travel with it. G has already proved that statement
000285 | for its actual full, H-independent carrier chart and original S/Z.
000286 | The present review does not reopen that source equality or demand another
000287 | state after that source is given.
000288 | 
000289 | The first DET16-specific identity needed to use the v1013 row as the
000290 | ORIGINAL source is therefore an actual word/transfer intertwiner mapping
000291 | the original sixteen fields and gauge insertions to the stated c_i and
000292 | mapping the full original transfer generator, reflection and reference
000293 | to this H_R+2 sum Q. Its coefficient and full vertex fingerprint are in
000294 | section1. A rank match, covariance match, bare U_det rotation, or matching
000295 | one Omega response is insufficient. Conversely, integrating the original
000296 | Higgs field can induce higher fermion words, so failure to find a bare
000297 | 16-linear term is NOT an exclusion of such a whole-source identity.
000298 | 
000299 | 7. LATER POSITIVE CLOSURES PRESERVED; BOUNDED VERDICT
000300 | 
000301 | The active DET16 contract explicitly includes v1007's local stability and
000302 | small-hopping results and v1016's uniform small-coupling finite-group
000303 | open-chain gap theorem. v1023 is a separate derivative-filtered block,
000304 | not an interacting DET16 realization. v1027 closes the canonical local
000305 | field defect under its singlet premise. v1034 explicitly distinguishes
000306 | factorized, flat, additive and ordinary-hopping parents. None of these
000307 | is downgraded by this review. They are not evidence that one may change
000308 | the rest Hamiltonian while claiming the same original S/Z.
000309 | 
000310 | Original update: paper-source:1f0d0ad957501d87cf2096dd:304-366,
000311 | tfpt_research_contracts/sections/015-source.tex;
000312 | SHA2ec9c3ab6903e9d29823ee5a52ef588cf8504848df6c51c21f0412f31f9eb886.
000313 | source:a68081fd07f1bec4d887:1-125, v1016,
000314 | SHA99975c7c250401344bfa086e0d277d9e0a3d936ad73b0a0052ad2442c54210ab.
000315 | Current ledger source:615b42f3cb2f1a62a54b:746 and
000316 | source:ecb1bd75a58db5e3e89d:766,
000317 | SHA8723b921bdc50a6157acc6bee4342b40586eb89bec6d7dcc0abc3309562c78b4.
000318 | 
000319 | Review scope: the exact R104 proof/review, v1002 defining Fock functions,
000320 | v1013 original local table/theorem head, original assembly functions/head,
000321 | old45 admissibility definition, active DET16 contract and later v1007,
000322 | v1016, v1027, v1034 source updates. Atlas searches were navigation, not a
000323 | claim of exhaustive repository absence. No new code execution was needed.
000324 | 
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