Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.
Seam, origin and declared inputs
The published foundation in this area
25 authored claim references lead into the original ledger and paper sections. This source record remains available even where no separate reviewed research packet is attached.
TFPT starts from the oriented seam normalization P1 (c3=1/(8π)) and the marked five-slot carrier P2. Integer anchors and later compiler readouts connect these inputs, but do not derive their physical origin or selection.
Starting structure in the Atlas orientation
P1 declares c3=1/(8π); P2 declares five carrier slots with a 3+2 marking. The (1,1,2) anchor organizes internal numerical relations.
Which connection is sought
The open work is a non-circular source for these inputs, the physical seam, and derivations of their markings and readout rules.
How it connects
The declared seeds feed E8, clock, flavor, α, and scale readouts. Shared seeds make those outputs correlated.
Finitely measured expressly chosen learning rule and same runtime environment;no general convergence,physical dimension or fundamental selection. Long measurement runs were not rerun during archiving. U35 and rate qualifications remain;no fresh UI-running claim.
Read the exact result, assumptions and evidence
Result
Six original10000-step controls are archived:baseline rank3.794/code.98067,no-feedback5/.99928,frozen-memory18.336/.63888,no-interaction1/.07348,magnitude-kernel1/.10458,no-initial-noise3.794/.98136.20starts of5000steps yield ranks3.458..4.99995 andcode.97952...98454. After perturbation.1,RMS falls from.09891 to.01182 after10steps and remains.01101 after5000. Stored states match measurements. Cold-load,identical random perturbation and continuation were reexecuted bit-identically during archiving.
Required assumptions
Explicitly chosen recursive SOM rule on60 native signal cells
Given solely for the authorized model study is the60x35 complex update of RECURSIVE-SOM-AUDIT.txt section1,with native K60,fixed neighbors,row normalization,Euclidean winners,batch means and chosen c,beta,eta. The code basis is readout only. This update and its initial alignment are not primitive TFPT laws.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Analytic finite saturation theorem plus separate all-mode theorem inside the explicit normal HS class. Finite checks do not prove all-mode saturation. The old interaction control is only an algebraic countercheck,not an admitted P1 coupling or new model study. No primitive law or physical odd-field/clock/reflection map is derived or freely chosen. For an actually nonlinear P1 half action,retain its operator contributions instead of forcing free saturation.
Read the exact result, assumptions and evidence
Result
For arbitrary faithful even rho,the actual canonical cross coherencemj=Tr(sqrt(rho)aj*sqrt(rho)aj) obeys0<=mj<=sqrt(cj(1−cj)). Equality holds exactly when sqrt(rho)aj=qj aj sqrt(rho),qj=sqrt((1−cj)/cj). On full finite CAR,saturation for all modes in a covariance eigenbasis is equivalent to a quasifree product density. On the existing normal all-mode HS carrier,actual all-mode saturation givesMij=qjCij,then full projection covariance and quasifreeness without uncontrolled density inverses. The already given H_int control has both deficits14745600/82945²>0 and half-modular factors2/32 and8/128 depending on spectator occupation. Positive standard doubling and its quarter clock remain,but projection coherence fails. The original property still to be tested is therefore a linear half-modular action on the actual odd fields,not merely existence of positive doubling.
Required assumptions
Normal even sea CAR source with canonical graded HS doubling
For the algebraic source test use the already given sea Fock/CAR carrier,with faithful even normalized traceclass density rho and its standard HS space,Omega=sqrt(rho),L_A X=AX,R_A X=XA,Gamma X=Pi X Pi. Gamma is the canonical GNS implementer of source parity fixing Omega. Partner fields are represented in the fixed mode-index chart by b_j=−Gamma R_aj;this assumes no physical second P1 boundary. The finite saturation theorem covers arbitrary faithful even finite densities;the separate all-mode route requires the actual normal HS carrier,a complete covariance eigenbasis and saturation in every mode. For the free elliptic connection,rho is the already derived original thermal density,not a newly chosen geometry or temperature. TomitaJ,OSTheta,classical doubling and physical time remain distinct until actually mapped.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact connection inside the already given free elliptic source and its faithful normal HS carrier. Its numerical cross kernel was not unknown;the previous cross gap still means its actual physical P1 operator/sewing identification. Geometric OSTheta is not presented as TomitaJ,nor the chiral scalar as a full Dirac vector. Domains/subtractions and previous state/time exclusions remain unchanged.
Read the exact result, assumptions and evidence
Result
The already given actual NS Green kernel gives S(W)=−S(−W)=(2cosh(WB))^-1=X_A,also as both reflected charge Grams at t=u=W/2. In the existing thermal HS GNS,aR=L_a and aL=−Gamma R_a with aL*=Gamma R_a* give full double CAR and crossMij=Tr(sqrt(rho)ai*sqrt(rho)aj). For the same free rho,M=X_A,hence complete covarianceP_A. The previous projection theorem gives all words;the cyclic isometry to the given graph-state GNS is ontoHS. No new physical state or particle carrier is introduced. Bare Euclidean evaluations a(W),a(0) are not independent CAR families:their cross anticommutator is exp(−Wlambda),not0. Using onlyL_Pi instead of canonical HS parity produces false spectator factors,detected already with2modes.
Required assumptions
Normal even sea CAR source with canonical graded HS doubling
For the algebraic source test use the already given sea Fock/CAR carrier,with faithful even normalized traceclass density rho and its standard HS space,Omega=sqrt(rho),L_A X=AX,R_A X=XA,Gamma X=Pi X Pi. Gamma is the canonical GNS implementer of source parity fixing Omega. Partner fields are represented in the fixed mode-index chart by b_j=−Gamma R_aj;this assumes no physical second P1 boundary. The finite saturation theorem covers arbitrary faithful even finite densities;the separate all-mode route requires the actual normal HS carrier,a complete covariance eigenbasis and saturation in every mode. For the free elliptic connection,rho is the already derived original thermal density,not a newly chosen geometry or temperature. TomitaJ,OSTheta,classical doubling and physical time remain distinct until actually mapped.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Free chiral Cauchy quantization of the canonical elliptic annulus
Treat the dividing half of the given square curve in its canonical flat conformal representative as a product collar. Compute the Cauchy graph of Dplus=partial_t+B_Sigma,B_Sigma=−i partial_s with NS boundary,then interpret it using the expressly free chiral CAR construction as a quasifree two-boundary state. The labelled second-face compression is the covariance;the other is complementary. This Gaussian interpretation does not derive the original relative spectral-action measure,P1 time or EM/Quillen response.
Original quarter CAR source with fixed fold and current dictionary
The already supplied single-channel CAR source with actual quarter domains alpha=1/4,3/4, negative-D sea, positive original excitation time, unitary eightfold F and actual channel diagonalization is fixed. M,O,U+ and the conformal NS point-splitting reference are the same original dictionary data; the single delta counterterm follows from the kernel difference. Even CAR current composites retain full arc correlations, charges, domains, all modes, original time and the existing subtraction prescription including finite derivative counterterms. No E8 root/spinor extension is assumed for this neutral current subalgebra. Identity with the original P1 net, Theta, collar and reference sector is not supplied. Real profiles and pulse strengths are intervention data.
Excludes only the bare gauge-ratio identification or explicitly described smooth zero-twist ansatz. Original relative factor1-q and T(q)=(1-q)^-5/4 remain intact. Does not exclude physical EM response,other originally derived couplings or completeTFPT.
Read the exact result, assumptions and evidence
Result
Exactly N(z+1)=N(z+i)=N(z),so a large-gauge full spectral norm ratio is1. The retained old NS circle still gives det_F[(I-q uCu*)(I-qC)^-1]=1-q. Forq nonzero these differently inserted operator comparisons cannot be identified. Additionally:an ansatz using only this norm,fixed multiplicity,constant reference and smooth z(alpha)withz(0)0 has first derivative0,while W_min_prime(0)=-(5/2)delta_top/(1-delta_top) is nonzero. Alpha0 still hasqdelta_top and is not a seam-free reference. A derived different background or additional actual insertions is not excluded.
Required assumptions
Given elliptic NS source with an explicit unit-charge flat unitary probe
On existing E=C/(Z+iZ) with original nontrivial NS/NS spin line and fixed H1_NSNS domain,calculate K_z=(-i partial_x+2pi v)+i(-i partial_y+2pi u),z=v+iu,as an explicit unit-charge probe. L_z=K_z*K_z,referencez0,gauge-periodic descent and positive theta-line convention are specified. Complex structure stays fixed;Q acts covariantly on external connection sources. This defines neither primitive P1 measure,physical hypercharge embedding,positive KMS state for every temporal twist,v472 Berry comparison map,nor z(alpha_EM). Parameter curvature and flat spacetime connection remain distinct.
Same original circle with trace-class changed polarization
For the mathematical continuation retain H,B_a psi_n=(n+a)psi_n,0<a<1,u psi_n=psi_(n+1),P=1_(B_a<0),uPu*=P+Pi. C is a positive contraction with trace-class C-P; actual functional-calculus C_beta=(I+exp(beta B_a))^-1,beta>0 belongs to this class. Physical KMS/OS/EM source identification is not presumed.
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.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Known Quillen torus calculation on the given mathematical carrier,with actual relative heat and line response. No new general theory of nature. Spacetime curvatureF_A0;parameter curvature/holonomy susceptibility is neither local4Da4 nor SMb1. No P1 law,joint positive CAR cross kernel,physical time or Berry-to-continuum limit.
Read the exact result, assumptions and evidence
Result
Actual free elliptic operator has L_z spectrum4pi²[(m+.5+v)²+(n+.5+u)²] and relative zeta determinant N(z)=exp(-2pi u²)|theta3(z|i)/theta3(0|i)|². Relative heat integration of the same spectrum independently checks the standard torus identity at three nonsingular60-digit probes. Positive theta line has A=2pi i u dv,degree+1 and holonomies exp(-2pi i u),exp(2pi i v),including endpoint descent. Null locusz(1+i)/2 is retained;no global nonvanishing section. At the original point Hess logN=-2piI,and the vectorlike doubled real action has HessGamma=2piI,the chiral modulus half. This supplies an explicit continuum object on this given carrier;physical P1 and v472 comparison remain open.
Required assumptions
Given elliptic NS source with an explicit unit-charge flat unitary probe
On existing E=C/(Z+iZ) with original nontrivial NS/NS spin line and fixed H1_NSNS domain,calculate K_z=(-i partial_x+2pi v)+i(-i partial_y+2pi u),z=v+iu,as an explicit unit-charge probe. L_z=K_z*K_z,referencez0,gauge-periodic descent and positive theta-line convention are specified. Complex structure stays fixed;Q acts covariantly on external connection sources. This defines neither primitive P1 measure,physical hypercharge embedding,positive KMS state for every temporal twist,v472 Berry comparison map,nor z(alpha_EM). Parameter curvature and flat spacetime connection remain distinct.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Minimal common holomorphic carrier of expressly given root coordinates and flat coefficient lines. No new physical worldsheet,CAR state or full compiler field map. Geometric clock here inverts deck generator;it is not separate commuting compiler order12 clock.
Read the exact result, assumptions and evidence
Result
For D:H¹²=f(z),w=H⁴,g=H³ and actual unramified V4 cover Yq/C,function fields are linearly disjoint over C. D/C is totally C4 ramified at four points and has no nontrivial unramified intermediate. X=Norm(D times_C Yq) has degree16 over C,degree48 over z,group C12 times_C3 A4 isomorphic A4 times C4,genus41. Minimality holds among all connected common covers:g and w determine H=w/g;trivializing three lines forces Yq. Common C3 quotient is identified once. Accepted quarter lifts combine diagonally with order4.
Required assumptions
Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
Ramified holomorphic half-form trace of the given C2 spin line
Retain actual E:y²=x⁴−1, its already supplied Q fixed nontrivial NS NS spin-line class alpha and normalized Szego kernel. Holomorphic trace includes sqrt(dz/dx), while ordinary flat coefficient p_*alpha remains separate. No extra Q linearization phase, positive equal-time CAR covariance or smooth circle domain is assumed.
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Equivariant flat coefficient lines of unchanged v117 source with actual clock direction. No selection of CAR field quantization or state,no identification of modularT with geometricQ,no new base inversion symmetry.
Read the exact result, assumptions and evidence
Result
Original geometric lift Q(z,w,eta)=(iz,w^-1,-i eta/w³) preserves q orbit and satisfies Q²=(−z,w,−eta). Kummer roots obey Q*h_a=epsilon_a omega/h_(-a-1),product epsilon_a=1. Actual local marked inertia t proportional s⁴ at q_0 forces epsilon_0/epsilon_2=−1 and epsilon_1=−1. The two inverse lifts are V4 frame-conjugate. Determinant-one coefficient representation fixes the remaining line with+1,square has two minus signs,spectrum1,i,−i. Explicit simultaneous basis change identifies U; positive quotient monodromy is contravariantly U^-1. C4 equivariance of existing coefficient lift is closed.
Required assumptions
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Only specified cyclic mu12 root cover as automatic sign or field completion. Older general C12 monodromy/intertwiner contract is unchanged. Does not exclude other common higher covers or actual transported field maps.
Read the exact result, assumptions and evidence
Result
Common cyclic fiber-product cover D:h¹²=(z²-1)/(z²+1) transports g=h³ and w=h⁴. Over C it is h⁴=w, totally ramified at two simple zeros and two simple poles of w. Its unique quadratic intermediate h² with square w is also ramified. Therefore D neither contains nor trivializes any of three nontrivial everywhere unramified actual v117 lines L_a. Geometric Q lift (z,h)->(iz,i/h) transports underlying curves but does not replace missing coefficients or a common field state.
Required assumptions
Existing C2 group with untwisted raw flat spin pullbacks
On the existing marked parity curve E:y²=x⁴−1,study h=(x,−y),Q=(ix,y),kappa=(bar x,bar y) and flat square-lattice spin characters. The explicit raw one-particle calculation uses the untwisted line alpha with chi(A)=chi(B)=−1. Complex-linear pullbacks U and anti-linear Real structures j are distinct;no fitted U1 phase. This is not the normal twist alpha tensor p*O1 with its two-dimensional kernel. An original P1 Spin/Pin or Calderon transport is not presumed.
Ramified holomorphic half-form trace of the given C2 spin line
Retain actual E:y²=x⁴−1, its already supplied Q fixed nontrivial NS NS spin-line class alpha and normalized Szego kernel. Holomorphic trace includes sqrt(dz/dx), while ordinary flat coefficient p_*alpha remains separate. No extra Q linearization phase, positive equal-time CAR covariance or smooth circle domain is assumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Excludes exactly these packets for fixed v117 clock and target marking. Does not refute their mathematical existence. Equal dimension,A4 group and genus5 alone do not identify a flat source map.
Read the exact result, assumptions and evidence
Result
Initial natural packet O(p_a-q_a) is nontrivial unramified V4 two-torsion on C, but v_a=z u_a gives V4 field over w sphere ramified at all six Weierstrass points, genus3. Actual target orders are4,3,4 rather than4,3,2. Positive triangle O(p_a-p_(a+1)) gives2,3,4 with fixed target marks. Both are different marked connections. Comparing imported T and B_k matrices would have been circular; actual function field and ramification test decide.
Required assumptions
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Exact flat coefficient lift with actual marked finite monodromy. No intertwiner of primitive CAR fields,state,positive time or support; no implicit selection of joint C2 NS field linearization. Older source already supplied curve and point intertwiner; line identification is separately proved here.
Read the exact result, assumptions and evidence
Result
On C:eta²=1-w⁶ the correct lines are L_a=O(q_a-q_(a+1)),q_a=-omega^a. Kummer roots h_a²=(w+omega^a)/(w+omega^(a+1)) multiply to1. V4 cover Zq of w sphere ramifies only at three q points and has genus0. Actual quotient coordinate t=((1+w³)/(1-w³))² gives degree24 with uniform ramification orders4,3,2 over0,1,infinity. Thus Zq is regular S4 triangle cover of same marked v117 class. Fiber product with z⁴=t has ordinary A4 image; intersection field is C(z²), since S4 has no C4 quotient. Over C this is exactly unramified genus5 V4 kernel cover. Hence pi*E_v117 decomposes into three expressly written unitary two-torsion lines. Equality follows from actual Kummer cover and target marks, not fitted target matrices.
Required assumptions
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Recovered genus2 cover with retained coefficients
Retain exactly the older three-sheet cover C:w³=(z²-1)/(z²+1), eta=z(1-w³), eta²=1-w⁶, six Weierstrass points p_a=omega^a,q_a=-omega^a, given z base and clock markings. Seek actual flat coefficient lines for existing v117 monodromy, not mere permutation equivalence or an assumed field intertwiner.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Only literal base inversion of unchanged A0* connection. Actual finite C4 monodromy is positively closed by old triangle proof. No exclusion of other base maps or other parabolic D4 objects. Same number or abstract group does not replace common clock marking.
Read the exact result, assumptions and evidence
Result
For A0* local exponent analysis forces every rational z->1/z lift into finite polynomial ansatz. Transformation equation G prime=A(z)G+z^-2G A(1/z) has only zero solution. Actual C4 quotient connection has isotropy orders4 and2 at0 and infinity, exchanged by base inversion. It is not marked D4 pullback with orders4 at both, despite abstract S4 generator pairs occurring.
Required assumptions
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.
Reused older analytic proof independently checked now. Closes ODE group identification incorrectly treated again as numerical-only. No new origin derivation selecting A0*, no complete field/state/time isomorphism. Physical gates remain open.
Read the exact result, assumptions and evidence
Result
The28Sept synthesis already contains analytic identification of unchanged v117 ODE: t=z⁴ and diag(1,z,z³) give three Fuchsian points of orders4,3,2; sole infinity resonance coefficient is exactly zero. Alternative frame diag(1,z,z^-1) gives semisimple exponents -1/2,0,-1/2 without resonance. Image is faithful S4 rotation representation; positive t0 meridian is U^-1. Marked pair is exactly v117 up to simultaneous basis change and remaining diagonal basis-sign convention. Diagonal0,-i/2,+i/2 follows analytically. Original four meridians have A4 image; U extends to S4. No new ODE fit needed.
Required assumptions
Original P2 order-three cusp class and stable bundle anchor
Target the original P2 Deligne class with cusp weights0,1/3,2/3 and holomorphic anchor O(-2)+O(-1)^2. Exact v117 M0_EXACT has polynomiallambda³−1,trace0,order3;its joint representation with U is irreducible. Keep these exact matrix properties distinct from the numerical ODE identification there. Test whether the natural scalar/spin pushforward of existing C2 realizes this actual connection;physical selection of the direct sum as flavor module is not presumed.
Unchanged A0* Fuchsian equation and actual C4 clock
Fix exactly v115 A0*, U=diag(1,i,-i), residues U^k A0* U^-k at i^k and regular base point z=0. Retain base rotation, positive meridian on t=z⁴ and simultaneous fiber basis change. No new Riemann Hilbert solution or D4 reflection lift is assumed.
Do not identify source types
Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.