Exact charged-root action in the marked compiler frame. Does not identify geometric deck involution,CAR parity or gauging of a physical source.
Read the exact result, assumptions and evidence
Result
The marked Z4 glue character squared fixes grades0+2 with52+60=112 D8 roots and negates grades1+3 with64+64=128 spinor roots. At lattice level K union(K+2g)=D8. Thus the non-anomalous E8 to D8 Z2 action of standard fermionization is already in the original marked glue.
Required assumptions
Fixed marked glue and actual source D8 frame
Retain marked K=D5+A3 in E8 with E8/K=Z4, original O frame and existing M of the one-channel CAR fold. The actual even source frame is D8_F=M(D8_CAR); no fitted new Weyl rotation. Cartans,time vector d=Mdelta,cocycles and field words transport together.
Supplied full CAR and positive time; source U1 neutrality is neither the whole parity-even algebra nor physical EM/hypercharge identification. W1 remains global charged transport,not a claimed local individual element.
Read the exact result, assumptions and evidence
Result
For u=M_z,AdW1 preserves each original CAR interval. Exactly tau_t AdW1=gamma_t AdW1 tau_t; on the source U1 charge-zero net it commutes with given time. W1*QW1=Q+1,W1*HW1=H+Q+a,W1*J(f)W1=J(f)+fbar. Neutral current response and rank1 defect remain visible; old bounded Cartan four-word is not projected away.
Required assumptions
Full CAR image and same positive vacuum time as a conditional hypothesis
Conditional reduction: the FULL graded local CAR algebra including odd fields and adjoints belongs to the same OS vacuum representation; original time restricts to a(f)→a(exp(itK)f) for the same selfadjoint gapped one-particle K; H≥0 and HΩ=0. The P1 embedding/time identification is not established. Even CAR alone is insufficient.
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Longitudinal spin-reference core; actual transverse boundary-kernel selection and original per-sheet operator map are not inferred from the index sum.
Read the exact result, assumptions and evidence
Result
Exact unitary Fourier decomposition including H1 domains: B_cov=2(B1/4⊕B3/4),T_pi=diag(i,-i),u_cov=[[0,u_base],[I,0]],u_cov²=diag(u_base,u_base). SF is1 and2=1+1; compressed Toeplitz index is-1 and-2. Full NS reference circle a=1/2 suffices for the prior relative EM line factor without extra quarter selector. In the descended Pinor space scalar u_cov changes lift c to-c at fixed J_perp.
Required assumptions
Original A4 lift of the same Moebius identification
The order-four spin lift explicitly named by fullv21 A4 belongs to the same geometric Moebius Z2 identification. As a Pin lift it has r²=-I; the local spin-reference channel is examined. Extra flat U1 connection holonomy and physical OS time are not inferred.
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Local spin contribution in the original Moebius geometry; no choice of extra U1 Wilson holonomy,single quarter CAR channel or physical OS time. Not identity with separate P2 clock.
Read the exact result, assumptions and evidence
Result
A4 requires the order-four lift of the same Moebius identification. The double-cover core loop is its square,so spin holonomy r²=-I gives NS. Both Pin-minus lifts r,-r and the base sign twist have the same cover holonomy. Full combined cJ_perp gives spin-reference phases{1/4,3/4}. The tentative R twist on the cover preserved only thin A2/A3 and violated A4; it is not a countermodel to the full original.
Required assumptions
Original A4 lift of the same Moebius identification
The order-four spin lift explicitly named by fullv21 A4 belongs to the same geometric Moebius Z2 identification. As a Pin lift it has r²=-I; the local spin-reference channel is examined. Extra flat U1 connection holonomy and physical OS time are not inferred.
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Reuse of an existing exact source audit,not a new discovery or an all-TFPT/all-RG exclusion. A corrected original kernel needs at least integrability and actual moment preservation; no replacement kernel is chosen. Atlas navigation had exposed the old registered contract as pending rather than a curated conclusion.
Read the exact result, assumptions and evidence
Result
The original2026-10-13 audit already proves d(Tnu)/dt>=m*nu(total)/∫psi dnu>0,so output mass is infinite. Printed T is not an endomorphism of the asserted finite-measure cone and supplies no fixed point there. Current independent review confirms the same v42/tfpt45 wording. Positivity alone also does not preserve the moment slice.
Required assumptions
Printed positive RG kernel on finite half-line measures
Literal archived theorem contract: nonzero finite positive nu on[0,infty),0<∫psi dnu<infty and Tnu(dt)=(∫K(s,t)dnu/∫psi dnu)dt with0<m<=K(s,t)<=M on the entire infinite Lebesgue target half-line. No extra compact support,finite target reference or integrable envelope is introduced.
Targeted v21/31/32/42 source review,not absence across every future text. Spectral action,positive geometric marginal and full graded source remain typed. No mandatory separate eta source notation or universal exclusion of other bosonic contours. Actual full CAR/positive-time image already forces the free sea.
Read the exact result, assumptions and evidence
Result
fullv21 supplies the geometric one-particle circle; v31 closure assumes an RP CAR kernel and v42 has exp(W_k[J]) as a formal full parent integral. Existence under those hypotheses need not be rederived from B. Actual local mode map,time/reflection and the same coupled action/measure contract do not follow. The master functional already contains a separate eta asymmetry term; only its squared determinant alone is sign blind.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Original admissibility and graded-source interfaces
v42 defines P_adm through primitive seam/Cauchy,gap,color and determinant conditions; v31 closure assumes an RP CAR kernel without identifying it with the old circle. v42 exp(W_k[J]) is a formal parent integral; spectral action, positive geometric marginal and full graded source are not equated. The separate eta term of the master functional is retained. Seek an original local image, not global Hilbert equivalence.
Source-reviewed definitions and necessary image test,not a new proof of all original analytic reconstruction theorems. Failure of u* invariance for P+ excludes only an additional claim that u belongs to the same admissible star algebra; membership is not assumed. Odd fields and complete neutral response words remain distinct.
Read the exact result, assumptions and evidence
Result
Original later P_adm is primitive seam/Cauchy and gap selection with color and determinant upgrades. It is neither P+(B_a) nor the rank1 EM projector. Historical u=M_z is clutching,not already a local observable. Actual line membership is P_adm R0=R0; commutation alone is insufficient. An original local or reducing image isometry suffices; global Hilbert equivalence is unnecessary.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Original admissibility and graded-source interfaces
v42 defines P_adm through primitive seam/Cauchy,gap,color and determinant conditions; v31 closure assumes an RP CAR kernel without identifying it with the old circle. v42 exp(W_k[J]) is a formal parent integral; spectral action, positive geometric marginal and full graded source are not equated. The separate eta term of the master functional is retained. Seek an original local image, not global Hilbert equivalence.
No new identification J=E,Q,N or Q². No q_heat=q_EM needed on the direct defect route. Intended old pure relative reweighting is exact with fixed residual normalization. Positive diagnostic Zdef=e^-2alpha,Ztriv=e^-alpha shows only the omitted condition in the generally read lemma,not a TFPT countermodel. SF normalization and original positive orientation remain.
Read the exact result, assumptions and evidence
Result
fullv27/v28 already contain J=d SF and give q=delta_top e^-2alpha for d2,SF1 under their relative defect contract. For complete sectors q=e^-alpha*d*s R(alpha),R=Z_s^0/Z0^0 exactly. Fixed prefactor holds precisely for constant R, differentiably equivalent to partial_alpha logR=0 throughout the interval. With fixed measures this is the difference of residual action responses; moving measures add score terms.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Historical SF sector action and explicit relative normalization
fullv27/v28 set J1=SF,J=d SF,d2,SF1 in S_def(alpha)=S_def0+alpha J. Review concerns the intended defect-only relative reweighting and its extension to complete measure-compatible sectors Z_s=e^(-alpha d s)Z_s^0(alpha),Z0=Z0^0(alpha). Constancy of R=Z_s^0/Z0^0 is an explicit condition, not assumed from SF.
One-particle identity is exact on the given old representative. Fock statements need the actual full CAR/time image; then no free state choice. SOURCE W1 is reused, not novel. Pi and Fock density are related by explicit isometry Vf=c(f)*Omega, not identified. Neutral full words U*AU need no individually neutral U observable. Scalar matching proves no physical permission,locality or EM-response identity.
Read the exact result, assumptions and evidence
Result
On the old circle uP-u*-P-=Pi0 and [u,P-] has rank1. Under the same full CAR and positive time the existing SOURCE W1 is this mode shift: UOmega~c0*Omega with energy a. Directed relative Fredholm determinant det[(I-z(C+Pi))(I-zC)^-1]=1-z gives the exact minimal factor without a heat limit. Full finite-word responses follow from a rank1 update of existing Wick determinants.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Full CAR image and same positive vacuum time as a conditional hypothesis
Conditional reduction: the FULL graded local CAR algebra including odd fields and adjoints belongs to the same OS vacuum representation; original time restricts to a(f)→a(exp(itK)f) for the same selfadjoint gapped one-particle K; H≥0 and HΩ=0. The P1 embedding/time identification is not established. Even CAR alone is insufficient.
Analytic consequence on the supplied old circle, independently reviewed. Zero block outside P+H adds no trace norm or Fredholm contribution. P_adm=P+, EM parameter, exponent5/4, physical time and state identification are not derived by compression. Orders4 and6 concern different traces and are conditional diagnostics, not an alpha prediction.
Read the exact result, assumptions and evidence
Result
For canonical P+=1_(0,infinity)(B_a), exp(ta)P+exp(-t|B_a|)P+ on P+H has eigenvalues1,s,s²,...,s=e^-t. For every0<a<1 its limit is exactly the Toeplitz defect Pi with trace-norm error s/(1-s). At a1/4 D_full=D_+D_- with exponents1 and3 modulo4. Opening qD_+^(-5/4) first differs by5q^6/4 from the single-mode form; the full q^4 term comes from the negative q^3 mode.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Historical source audit of a best-effort PDF extraction, not a new derivation or numerical change of P1. First geometry choiceY7/forms, n1 selection and c3 parametrization remain explicit. Local factor3 modulo derivative is not a global c3 correction; global patch data and da0 special case are separate.
Read the exact result, assumptions and evidence
Result
V1.06 chooses M4×Y7 with integral forms, quantizes g_top=n/(8pi²) under printed period/flux conventions, then defines g_top=8c3². n1 and positive root yield1/(8pi). Canonical fields instead give coefficient n g4²/(8pi² F_a), before trace/embedding factors; the kinetic integrals are not supplied there. For dynamical a, dC also contains da∧omega3 and local CS reduction has mixed terms.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
P1/P2 remain declared starting axioms
This program checks which additional source, state, event, and observable structures follow from accepted TFPT principles; it does not revoke or replace P1/P2.
Recovered formal definition, not an existence proof of an infinite mixed measure. Full moments, symmetric positive time and uniform OS growth remain actual requirements; no specific source notation is mandatory.
Read the exact result, assumptions and evidence
Result
v42 defines exp(W_k[J]) as a regulated functional integral and gives the Hessian propagator. Formal full moments follow by differentiating exp(W_k[J]-W_k[0]); no new general Z template is required. STr permits collective graded field/source notation, so missing separate eta symbols do not prove exclusion. Concrete graded action/measure, seam map and joint RP are not established there. Direct OS use of expressly truncated cumulants still needs correction.
Required assumptions
Historical concrete circle, heat-transfer and source-functional passages
Historical audit contract: fullv21 contains D_Gamma=i partial_theta, u=exp(i theta) and twisted H1 domains; v31/32/42 write P_adm exp(-ell|B_Sigma|)P_adm; v42 has exp(W_k[J]) as a formal functional integral with STr. V1.06 contains the 11D C3 mode ansatz and n=1,g_top=8c3². The actual scope is audited, without assuming equality of old/new operators, physical times, traces or parameters.
Original seam operators and explicit moment definition in the OS passage
Source basis: the original boundary core supplies selfadjoint tangential B_Sigma; the seam has winding and stated spectral flow one. EM later names an allegedly selected rank-one line. QFT defines S_n^T as log-Z derivatives and uses them as the OS family. These statements and operator identifications are audited at the originals, not assumed proved.