TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/original-local-source-variable-background-20261102/PADM-ACTUAL-ACTION.txt
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Inclusive original lines: 1-153
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This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | ACTUAL ORIGINAL Padm ACTION AND THE REGISTER/Gauss SOURCE
000002 | 3 November 2026. origin_topology. No canonical edit, new projector or run.
000003 | 
000004 | FILE PRESERVATION
000005 | My full independent zero-free proof, including the three-mode even-parity
000006 | counterexample, is preserved as ZERO-FREE-ORIGIN.txt,124lines,
000007 | SHA0d5c234139fdf89283d68643c176a5d66579b6463b228bfca5b393ab1323d99f.
000008 | ZERO-FREE-REVIEW.txt was only read/copied and is not changed again.
000009 | 
000010 | VERDICT ON THE ACTUAL QUESTION
000011 | 
000012 | The reviewed original defines Padm on the original seam/color/determinant/
000013 | gap representation. It does NOT bind those operators to a concrete parity,
000014 | C4-charge, or Spin10-singlet projector on the Fock space of the GIVEN
000015 | quasi-free Clifford heat caller. Thus no actual projected heat trace has
000016 | been proved zero-free, or proved to have zeros, by identifying Padm in that
000017 | caller. The unprojected zero-free theorem remains scoped to its true source.
000018 | One must not set Padm=I to call it physical, nor choose an alternative
000019 | Fock projector by matching its name to an original factor.
000020 | 
000021 | This is a concrete operator/type determination, not absence from a search:
000022 | 
000023 | 1. WHAT THE ORIGINAL SEAM SELECTOR ACTUALLY DOES
000024 | 
000025 | Boundary001:112-169 defines iota_C=2P_C-I ON THE CAUCHY-DATA Hilbert space;
000026 | its +/- eigenspaces are the solution/antisolution reflection spaces of the
000027 | original boundary problem. P_Sigma,+ is that geometric Cauchy selector.
000028 | It is not defined there as second-quantized total matter parity or as a
000029 | number-modulo-four condition. Boundary001:173-180 explicitly separates the
000030 | geometric deck reflection, boundary polarization, and its finite carrier
000031 | restriction. Their transport/restriction maps are specified; literal
000032 | identification is forbidden by the original corollary.
000033 | 
000034 | The primitive projector adds the declared spectral gap selector from the
000035 | relative/admissible Dirac operator. QFT002:94-97 makes this a HIGH spectral
000036 | projector above epsilon_adm^2/4, not a low-energy Fock vacuum projector.
000037 | The operator Dadm in this formula has its original sector/domain role;
000038 | it is not thereby the positive excitation Hamiltonian H_free. Substituting
000039 | the latter would be an unproved operator map.
000040 | 
000041 | Sources freshly read:
000042 | paper-source:2c00b99902dffffff710a671:57-205,
000043 | SHA7d6e673d99c29d950dc601283cd51c1cc0b113567eeb79c8396fec9c82a02c79;
000044 | paper-source:35c4c41ef6cded2368b36527:1-118,
000045 | SHA61ecee7727bdec47936bbffc028d3dbac5260a025b6dbcce30124a60d635fc9c.
000046 | 
000047 | 2. ACTUAL COLOR AND DETERMINANT ACTIONS
000048 | 
000049 | QFT002:14-29 fixes the factor roles H_Sigma tensor H_c tensor H_Theta
000050 | tensor H_t. The color selector is the ACTUAL Z3 color-centre average.
000051 | Q_Theta is a selfadjoint involution on the determinant sector. The printed
000052 | definition fixes Q_Theta^2=I and its sector role; it supplies no equation
000053 | Q_Theta=(-1)^N_matter and no occupation-basis matrix on Fock(Splus16).
000054 | The compact bosonic index fixes a weak Higgs doublet/determinant class,
000055 | not a displayed parity action on quantized matter states. Carrier009:
000056 | 304-337 refers to the fixed determinant class; it adds no such Fock action.
000057 | 
000058 | There is a concrete discriminator against replacing COLOR/G_SM Gauss by
000059 | total fermion parity. The ACTUAL v252 representation contains nu_R, a
000060 | color and physical G_SM singlet. The color centre acts as identity on
000061 | its component. In the full physical gauge lift
000062 |  U(u)=pi(u) J_F pi(u) J_F^-1,
000063 | the particle nu_R factor lambda cancels the conjugate antiparticle lambda,
000064 | giving U(u)nu_R=nu_R. Raw pi(u) alone is NOT that physical lift.
000065 | Consequently the canonical induced gauge action commutes with the odd
000066 | nu_R field; matter fermion parity instead changes that field's sign.
000067 | These are distinct actual actions. This comparison uses no chosen mode
000068 | or new gauge projector. It does not determine what the SEPARATE full
000069 | Q_Theta or gap factor does after a valid whole-source embedding.
000070 | 
000071 | The carrier Splus=Lambda_even(E3+E2) has16 internal species. Its exterior
000072 | evenness is not parity on Lambda(Splus), the65536-state CAR16 cluster.
000073 | Likewise the four auxiliary eta ghosts in QFT002 are not the physical
000074 | four-state register or the matter Fock parity. These distinctions are
000075 | necessary before claiming a concrete physical Padm image.
000076 | 
000077 | Sources:
000078 | source:0efcd98bb98cc5888eb1:119-168,
000079 | verification/v252_full_finite_triple.py,
000080 | SHA820254440e178430422e50605067775656236602996307f67c9e69124ba5d163;
000081 | paper-source:4b1606c7f13b67cb4ff57b0f:166-207,
000082 | SHAcf801a467465db8d72e4eb3f8e32eea2e23393bf42232a225116c34ed093f761;
000083 | paper-source:53863c09a4de7cc562018991:304-337,
000084 | SHA27114e2ce775346dac11c53ecb77871453f3ecf226fe40951f8b3099bdea6b05.
000085 | 
000086 | 3. THE EXISTING NONLINEAR C4 REGISTER MAP IS REAL AND NOT A Padm SELECTION
000087 | 
000088 | The complete Sept20 charged-register source was read, not dismissed as a
000089 | missing field/time map. It explicitly assumes C4 tensor Fock(V) and uses
000090 | the UNCHANGED source blocks
000091 |  h_r=b+i^r a+i^-r a^*, H_R=sum_r Pi_r tensor dGamma(h_r).
000092 | Its exact correlated maps satisfy
000093 |  F_j=S tensor c_j, C=Z tensor i^N,
000094 |  J_s|psi_N>=|s-N mod4> tensor |psi_N>,
000095 |  F_j J_s=J_s c_j, H_R J_s=J_s H_s.
000096 | All FOUR orthogonal J_s images exhaust the original register/Fock space.
000097 | This is a simultaneous whole-field/state/SAMEtime theorem.
000098 | 
000099 | The actual sharp-arc source has the corrected nonlinear fields
000100 |  F_j^u=D(Z^-q_j tensor c_j),
000101 | and the original D obeys D J_s^u=J_(s+1)^u. Thus the whole source algebra
000102 | does not superselect a single C eigenspace. Keeping only one s would lose
000103 | that actual original D word; no source rule in this theorem selects it.
000104 | The original explicitly retains every s and labels the Fock lift, state
000105 | and physical source identification conditional. Its firewall states no
000106 | paper/ledger promotion or physical gate closure. This has not been
000107 | identified with the original QFT002 Padm by this source.
000108 | 
000109 | The WHOLE register Hamiltonian is a direct sum of controlled free branches,
000110 | not a single additive dGamma(h). The encoded H_s is number-dependent.
000111 | Hence the zero-free product premise must not simply be assigned to this
000112 | different whole caller. Its positive nonlinear CAR/time result is preserved
000113 | in precisely that scope, without declaring it the actual physical Padm.
000114 | 
000115 | Source: source:64b926c9dcc254233ac7:1-127, full README,
000116 | experiments/theory-contracts/source-charged-register-20260920/README.md,
000117 | SHA9b30008b4b3f49adacf9708b5ef49730284cf276a7c1f1a2a98d02faeaf8dd5e.
000118 | The existing source-driven/carry and pair-transfer proofs remain its
000119 | registered antecedents; their algebra was not rerun or replaced.
000120 | 
000121 | 4. LATER PARITY Gauss COMPLETION EXPLICITLY ANSWERS THE PROMOTION QUESTION
000122 | 
000123 | The Oct14 original supplies a genuine all-size, full-state isometry E
000124 | onto the local Gauss space for
000125 |  G_x=(-1)^n_x tau_(x-1)^x tau_x^x,
000126 | with H_new E=E H_old, all transported words, and unchanged original time.
000127 | It is not just a dimension count or low-state embedding. It retains the
000128 | full EVEN register source; its old local Z becomes a global Wilson loop.
000129 | 
000130 | Crucially the SAME original calls this the NEW LOCAL GAUSS PREMISE
000131 | (:112-118), states the new local-net assignment changes the physical net
000132 | (:177-183), and says the original primitive source provides neither these
000133 | G_x nor an identification of its Padm with this Gauss sector (:185-190).
000134 | This is explicit original provenance, stronger than a failed search.
000135 | The result is a valid conditional source-preserving Gauss completion,
000136 | not a proof that the original admissibility projector equals that rule.
000137 | 
000138 | Source: research-source:0bbdaa9c57c61e2955a69da0:112-235,
000139 | REGISTER-GRADE-LIMITS-GAUSS-AND-DIRAC.txt,
000140 | SHA94dc3fe2f4b612b2a6f081db8339165f6b7beadfb764f4e3ae143b922d9aa8dd.
000141 | 
000142 | CONSEQUENCE
000143 | 
000144 | The actual original Padm has not been turned into a concrete Fock projector
000145 | in the unprojected positive Clifford heat caller by any of these reviewed
000146 | maps. The conditional register and local Gauss completions are positive
000147 | existing alternatives, but their sources explicitly do not assert that
000148 | identification. Therefore the zero-free theorem cannot be used to rule out
000149 | the ORIGINAL physical projected source, and a parity/C4 choice cannot be
000150 | silently inserted to rescue or falsify its premise. The next projected
000151 | spectral calculation has a precise input: the image of the ORIGINAL Padm
000152 | under the actual whole field/quantization/positive-time map. No new physical
000153 | projector is chosen in this report, and no generic formulas are run again.