Pharmacophoric-ODE fragmenting, merging, and recording: Biogenetoligandorol AI-heuristic algorithm.
The patterns of this Biogenetoligandorol fragmentation Scheme are sorted into the working inputs of the Galilean transformation by examining the ―extended‖ Galilean transformation based on a set of heuristically determined descriptors moving with relative acceleration to a rigid system to a nonrotating geometric observer having an arbitrary time-dependent acceleration (20,21,27,28). (25,29) These descriptors as an applied nonconcurrent to both translate and rotatecan be, for example, the number of atoms describing the pattern of a force system which can both translate and rotate and be determined by the substitution as a polynomial in ip (r, t) = eiJ{rt) (p (r’, t). (equation2) V’ip = (V’ip + iV ’f) eif, (equation3) ρ¯sQFI≈∑i=01Re (ρi12) 2 (1ρi11+1ρi22) + (ρi11−ρi22) 2ρi11+ρi22, (equation4) ρ1ij=〈υi 〈1 ρs (equation5) υj〉 1〉 (equation6) ρ0ij=〈υi 〈0 ρs (0) υj〉 0〉 0〉1〉 (equation7) H1=γB0⋅Sˆ1Re (ρi12) ρi12ρs (0) ρ¯s (equation8) S〉=12 (〉− 01〉) 30%ρs (equation9) ρ¯s=H⊗m (equation10) V’2ip = {V’2ip + 2iV’f-V’ (p+ (pV’2f+ W ←S (I ⊗H) (equation11) M1; <p (V’f) (equation12) eφf,i>= 〈Φ|MT (I3−NT) −2 (ρ ⊗I2) |Φ〉 (f) + if<p) (equation13) eif,and the Schrödinger equation becomes n 2 2 m (V,z (p + 2 iV’f-V’ (p+ i (pV f - M = {M0,M1} (equation14) (V ’fY <p) = ifi I3 ←E (m2) (equation15) (*m2-dimensional identity*) ((<p + if (p) -g. (V ’ (p + i (pv’ f)) through the example of two coupled Chern-Simons Topology driven anti-de Sitter harmonic black-hole oscillators and brane spacetimes where p+2 are the the number of bonds predicted or the number of double bonds. (20,25) The complete pharmacophoric fragmentation Scheme was analyzed to compare similar series of chemical patterns that are contained in the chemical phase structures as exctraced from within the selected 10 hit compounds of the Colchicine, Raltegravir, Hexacosanol, Benzoxazolinon, Carboxy-Pentaric acid, Ursane, Antheraxanthin, RA-XIII, Crotonate and Byrsonima coccolobifolia. (Table 1/), (20,35) Whenever searching for a specific pattern, if the group has such a parent pattern, the parent pattern is searched first eliminate the terms in V’ (p, which gives f = — %-r’+ g (t) (equation16). Then one can choose n g{t) such as to eliminate the purely time-dependent terms, and one finally arrives at, = (2mV ’2 (p + mf; ■ r’ (p = ih (p,ipir, t) =— ea h J (pir’,t) (equation17). (20,25,26) of the strong equivalence principle in quantum theory. After that, the child pharmacophoric pattern is searched in an inertial repeated merged system S asip = % (ml5 r, t) + ip2im2, r, t (equation18). (25,26,37) Then assume that one fragmented pharrmacophore can describe the same superposition in an accelerating to a larger ligand-receptor system S’ that obeys (20), with § = £ (r) (equation19), £ (0) = £ (7) (equation20), so that the system S’ performs a closed quantum circuit and coincides with the chemical structure system the S at times t = 0 and t=T, such that r ‗ iT) = r (7) (equation21). (25-34,37) To avoid q { h q; } qreg q (3) ; creg c (3) ; reset q (0) ; reset q (1) ; reset q (2) ; h q (0) ; u2 (pi/2,pi/2) q (1) ; incomplete (1Z) ‐2‐ { ((2S,3S,5R) ‐5‐ (2‐amino‐6‐oxo‐ 6,9‐dihydro‐ 3H‐purin‐9‐yl) ‐3‐hydroxyoxolan‐2‐yl) methylidene} ‐2‐cyano‐ 1‐({ ((2S,4R,5R) ‐2 group assignments, through two hydrogen-bonding interactions whenever a part into the S2 subsite of the structure relative to the complex between the 2‐ ({[fluoro ({[ (2E) ‐5‐oxabicyclo [2.1.0] pentan‐2‐ylidene] cyano‐lambda6‐sulfanyl}) methyl]phosphorylidene} amino) ‐4,6‐dihydro‐1H‐purin‐6‐onecyano‐1‐ ({ ((2S,4R,5R) ‐2‐methyl‐ 2‐ (methylamino) ‐ 1,6‐diazabicyclo with heptan‐4‐yl) oxy} imino) ‐1lambda5,2 lambda5‐azaphosphiridin‐1‐ylium chemical groups of the cyclohexyl methyl is already recored and fragmented, the subsequent carbonyl oxygen matches have to be adjacent to the from the main-interacting chain amide of the residue Glu166 amino acid already occupied the space normally by the canonical S4- cyano‐1‐ ({ ((2S,4R,5R) ‐2‐methyl‐2‐2‐ ({[fluoro ({[ (2E) ‐5‐ oxabicyclo [2.1.0] pentan‐ 2‐ylidene]cyano‐lambda6‐sulfanyl}) methyl]phosphorylidene} amino) ‐4,6‐dihydro‐1H‐purin‐6‐one (methylamino) ‐1,6‐diazabicyclo (3.2.0) heptan‐4‐yl) (1S,2R,3S) ‐2‐ ({[ (1S,2S,4S,5R) ‐4‐ethenyl‐4‐ sulfonylbicyclo[3.2.0]heptan‐2‐yl] oxy} amino) ‐3‐ 2‐ ({[fluoro ({[ (2E) ‐5‐oxabicyclo [2.1.0] pentan‐2‐ylidene]cyano‐lambda6‐sulfanyl}) methyl]phosphorylidene} amino) ‐4,6‐dihydro‐1H‐purin‐6‐one[ (2R,5R) ‐5‐ (2‐methyl‐6‐methylidene‐6,9‐ dihydro‐3H‐purin‐9‐yl) ‐3‐methylideneoxolan‐2‐yl]phosphirane‐1‐carbonitrile-oxy} imino) ‐1lambda5, 2lambda5‐azaphosphiridin‐1‐ylium binding site of the PDB:6LU7 main protease. (26,31-39) As a first step, our Chern-Simons oriented fragmentation algorithm performs a quick fragmentation Scheme search for extracting different chemical groups formed by the nucleophilic attack of the catalytic domains of the target proteases onto the α-carbon of my new Roccustyrna small molecule by applying the heuristic quantum phases for group prioritization when performing parent-child group prioritization as described above. (29,32-39) This topology geometric for pharmacophoric search and design indicating the canonical binding pockets moieties of a new small-sized prototype that goes sequentially through a sorted fragmentation Scheme, adding groups that are found in its active conformation phases and do not overlap with the 2‐ ({[fluoro ({[ (2E) ‐5‐oxabicyclo [2.1.0] pentan‐2‐ylidene] cyano‐lambda6‐ sulfanyl}) methyl]phosphorylidene} amino) ‐4,6‐dihydro‐1H‐ purin‐6‐onecyano‐1‐ ({ ((2S,4R,5R) ‐2‐methyl‐2‐ (methylamino) ‐1,6‐diazabicyclo (3.2.0) heptan‐4‐yl) oxy} imino) ‐ 1lambda5,2lambda5‐ azaphosphiridin‐1‐ylium chemical groups that were already screened. In case it successfully estimates a valid fragmentation, Scheme this is taken as the phase solution relating to how one clustered pharmacophoric element occupies the space normally filled by the protease‗s substrate‗s interacting main chain; would describe the same phase in an alternative XYZ coordinate smile system. (33,35-42) This Lindenbaum-Tarski algebraic algorithm was implemented as a recursive algorithm that leads to enhancement of my novel small molecule‗s catalytic activity against the 3C protease–like domains I and II and performs a complete decision tree search of all possible combinations of fragmentation, merging, and pharmacophoric re-coring systems targeting in the in SARS-CoV Mpro. (12,13,28-39) Therefore, from a mathematical perspective, a TQFT that recovers the above AI-Quantum Hilbert symmetric spaces may be called ―Chern–Simon’s theory. We present here potential condensed eigenvalues applications for the positive spectrum and finite-dimensional eigenspaces: S=14π∫M3 (a+ℓ) ta+ℓ {1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧dAk+13 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧[A∧A]k (mod2π) 1→U (1) →LG∼ →LG→1 (equation22) of the free loop group LG = (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1 (S1, G) (equation23) is a functional of G bundles with connections over compact 3 manifolds. Here, A is the connection form, (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1∧ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1F) 2zEGk: 2zEG ⊗ 2zEG → ℝ (equation24) is a certain metric constructed and the integral from the level, is taken over a global section of the principal bundle. ‡ δ ¯ υ−γμ¯ǫDμ ¯σ − ¯σσ¯ǫ −i_f (ϑ) ¯σ¯ǫ + i ¯ Fǫ (equation25), δF = (−γμDμυ + συ + λσ) +i (2_− 1) 2f (ϑ) ǫυ (equation26), δ ¯ F = ¯ǫ (−γμDμ ¯ υ + ¯ υσ − ¯σ¯ λ) +i (2_ − 1) 2f (ϑ) ¯ǫ ¯ υ, (equation27) We hybridized then every level k ∈ H4 (BG, ℤ) that yields the quantum field theory with those levels k that satisfy the following positivity condition: Chern-Simons theory equation of the: (∫tr (+23).S=k4π∫Mtr) (3d N = 2CSA∧dA+23A∧A∧A) (equation28). A (equation 1), (ie. considering S as a functional of A). associated to a connected Lie group ας a simple current Roccustryna XYZ chemical extension of the tensor product of the d/dx (33833 y^n×1152N^2 x^2 k^4) =3d N 2 CS 77951232 k^4 N^2 x y^n (equation29) associated to an even lattice and 38975616 k^4 N^2 x^2 y^n = sum_ (ν=0) ^∞ (n^ν 38975616 {x sin^ (-1) (sqrt (3)) x sin^ (-1) (sqrt (779) sqrt (θ^3)) x sin^ (-1) (2 sqrt (114109)) (sqrt (1 - sqrt (456457) sqrt (x)) x^ (1/4) (2 sqrt (456457) sqrt (x) + 3)) / (8 456457^ (3/4)) + (x - 3/3651656) sin^ (-1) (456457^ (1/4) x^ (1/4)) 1/2 sqrt (x/456456754 - x^2) + (x - 1/912913508) sin^ (-1) (sqrt (456456754) sqrt (x)) x sin^ (2^ (3/4) 57057^ (1/4)) x sin^ (-1) (sqrt (sum 444546 θ)) x sin^ (-1) (2^ (3/4) 431683182057^ (1/4) sqrt (sqrt (θ) / (sin^ (-1) (44545545)) )) } + constant (k^4 N^2 x^2 log^ν (y)) ) / (ν!) (equations2,3,4,5,6,7,8,910,11,12,13,14,15,16,17,18,19,20-30) associated to a simply connected Lie group classical equations of motion obtained via i and ii are known to be equivalent by combining the works of Finkelberg obtained in this way are: =0k2πF=03d N = 2 CS (equation31) also known as Connes fusion or every connected group G and level k≥0. It is given byγμǫDμ_ + ǫ (ρ · σ) _ +i_f (ϑ) ǫ_ = Mǫ_, (equation32) where M is the eigenvalue given by M = Mm,n=ρ· σ + i_mb + nb−1+Q2 m n 2 Z_0 (equation33), Q = b + b−1 (equation34). The product of the eigenvalues roughly gives ―denominator‖ of the one-loop determinant, where the right action on H uses the isomorphism induced by reflection along the horizontal axis. (41) For every simple simply connected Lie group G with the quantum Hilbert space CSG,k (S1 and every level k ≥ 0, a tensor category A∧A,k whose Drinfel‗d center Z (dA,A) associated to a Riemann surface Σ can and has been defined at a mathematical level of precision and is equivalent to the the VectkG[G] Vectk[G]) CSG,k (pt) d/dx (33833 y^n×1152 N^2 x^2 k^4) = 77951232 k^4 N^2 x y^n (equation33) categories of the sin (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1Vectk ((a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } +Fǫexp(iℏpˆ2A2mA+−1+(a+ℓ) ta+ℓ{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1∧ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1F) k^4 x^4 y^n sin^ (-1) (n) ^33833 5429 N^2 (newtons
squared) - 1/3 x^6 (k^4 y^n sin^ (-1) (n) ^33833 5429 N^2 (newtons squared)) + 2/45 k^4 x^8 y^n sin^ (-1) (n) canonical quantization, it is the geometric quantization of LocG (Σ) with respect tothe natural symplectic Roccustyrna structure coming from the Chern–Simons Lagrangian. We explain below that, at leastalong the direction θ is defined by SθP (g) = Z1eiθ0dt e− tg BP (t) (equation35), (1) where BP (t) is analytic continuation of the formal Borel transformation P1ℓ=0cℓ (a+ℓ) ta+ℓ-{1/12+ (∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′ (t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1.whenG 432 π k^4N^2 x^2 sin^ (-1) (n) ^33833 (2 x- sin (2x)) y^ (Λn) for Vectk[G] dCSG,k (pt) (equation36) is simply canonically connected with the the Reshetikhin– Turaev TQFT quantizations as associated to the modular tensor category Repk (LG) of positive energy representations of the loop group at level k has that property 14π∫M3 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧dA 2zEG Zcl (σ) = exphXnp= 1isgn (kp) gptr (σ (p)) 2i (equation37), Z1loop (σ) =Qα2root+4 sinh (πbα · σ) sinh (πb−1α · σ) QaQρa2Rasb_ρa · σ − iQ (1−_a) 2_) equation38), sb (z) =1 (equation39), Ym=01 (equation40), n=0mb + nb−1 + Q/2 − izmb + nb−1 + Q/2 + izk+13 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧[A∧A] (equation41) the coordinate (x1, x2, x3, x4) = (cos ϑ cosϕ, cos ϑ sin ϕ, sin ϑ cos τ, sin ϑ sin τ) and f (ϑ) =pb−2 sin2 ϑb2 cos2 ϑ.k (mod2π) [1]+sin (a+ℓ) ta+ℓ{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩ CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1Vectk ((a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1+ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1∧ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1F) 1 4π∫M3 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧dA 2zEG k+13 (a+ℓ) ta+ℓ-{1/12+ (∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧[A∧A]2zEG k (mod2π) [1]∧sin (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1Vectk ((a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1+ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩ B+∣α2′(t) ⟩ CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1∧ (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1F) 14π∫M3 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2 A2mA +−1A∧ dA 2zEG k+13 (a+ℓ) ta+ℓ-{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧[A∧A]2zEG k (mod2π) (equation42), F= dA+A∧A Repk (dA+A∧A AGA) (equation43) by [28]Fμν = 0, σ = const, D = −σf (ϑ), λ = ¯λ = 0. (4) Repss (Fq 2zEG ) [or Repk (AF2zEG ) ] and Rep (Dk (ℂ[G])) =Repf ((a+ℓ) ta+ℓ 1) where xˆAψ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α 2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩ B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). = exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 Πˆ2B2MB+Πˆ2C2MC EXP(IℏPˆ2A2MA(QˆC−ΠˆCMDΠCDΠ2|∇|2 −ΔKΣ(DT− ASIN2ΘDΦ ) IFŜBPˆAMAŜ†B+IF√(∣∣Α1′(T) ⟩CQ1T∣Φ(T) ⟩B+∣Α2′(T) ⟩CQ2T∣Φ(T) ⟩B) (P) -G.(V‘(P I(PV’ F)) if√(∣∣α 1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆC−πˆCmdπCdπ2|∇|2 −ΔKΣ(dt− asin2θdϕ) IfŜbpˆAmAŜ†b+if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) where the function X(t) =X0, with X0 being a constant, and takes the form XˆAΨ1CMDΠCDΠ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) − 1 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where xˆAψ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) − 1 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B +∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt− asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where 1 = exp(iℏpˆ2A2m A(qˆC− πˆCmdπCdπ2 |∇ |2 and 3 =if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2 A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′ (t) ⟩C Q1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). = exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 Πˆ2B2MB+Πˆ2C2MC EXP(IℏPˆ2A2MA(QˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(DT−ASIN2ΘDΦ) IFŜBPˆAMAŜ†B+ IF√(∣∣Α1′(T) ⟩CQ1T∣Φ(T) ⟩B+∣Α2′(T) ⟩CQ2T∣Φ(T) ⟩B) (P) - G.(V ‘(P + I(PV’ F)) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). (t) =eiℏpˆ2A 2mAτxˆAψ1CmdπCdπ2 |∇ |2 = { 2 −1 if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _11 = 2 where if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) (1 −) − 1. e−iℏpˆ2A2mAτ, (Equation2) and the full operator Ŝ is ŜT=exp(−iℏπˆ2 C2mC(t−τ)) ˆ(x) ACexp(iℏxˆAψ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) g. (V‘(p+i(pv’f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩ B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). pˆB) exp(iℏpˆ2A2mA(t−τ)) (Equation3), where ˆ(x) AC= ˆAC(Equation4) in (Equation1) and we have introduced the term exp(−iℏπˆ2C2mC(t−τ)) to ensure that the position of the system A at time τ tranforms into the symmetric position of the system C, ŜT(xˆAψ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). −pˆAmA(t−τ)) Ŝ†T=−(qˆCif −πˆCmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ 1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _11 = 2 where y2 = exp(iℏpˆ2A2 mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) (1 −) −1. C(t−τ)) (Equation5). Notice that for t = τ the operator ŜT in (Equation2) is precisely the operator Ŝx in (Equation3) a generalization of the simplest non-static Schwarzschild metric, and is expressed in Eddington coordinates (u,r,θ,ϕ), as follows ds2=−(1−2m(u) r) du2+2ϵdudr+dΩ2,(ϵ=±1) (Equation6) where dΩ2=dθ2+sin2θdϕ2. ϵ=+1 (Equation7) represents the ―advanced‖ or ―ingoing‖ Vaidya metric, while ϵ=−1 represents the ―retarded‖ or ―outgoing‖ Vaidya metric (31). Therefore, we can interpret Ŝx as the operator which performs the translation to a quantum reference frame when the dynamics is ―frozen‖ at time τ. The transformation implemented by ŜT is ŜTxˆAψ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A 2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θ dϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A 2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ 1t∣ϕ(t) ⟩B+∣α 2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt− asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2m A(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+ ∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B +∣πˆ2B2mB+ πˆ2C2mC exp(iℏpˆ2A2m A(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α 1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). Ŝ†T=−qˆC+πˆCmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). C(t−τ) −πˆB+ πˆCmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where Fǫexp(iℏpˆ2A2 mAπˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩ B+∣πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) A(t−τ) ; ŜTpˆAŜ†T=−(πˆB+πˆC) ; (Equation8) ŜTxˆBŜ† T=qˆB −qˆC+πˆCmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 where if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 πˆ2B2mB+πˆ2C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g. (V ‘(p + i(pv’ f)) if√(∣∣α1′(t) ⟩ CQ1t∣ϕ(t) ⟩B+∣πˆ2B2mB+πˆ2 C2mC exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t ) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f) ). C(t−τ) ; ŜTpˆBŜ†T=πˆB (Equation9) implies that the position at time t of pharmacophoric system of ((2S,5R,6R) ‐ 6‐((2S) ‐2‐amino‐2‐ phenylacetamido) ‐3,3‐ dimethyl‐7‐oxo‐ 4‐thia‐1‐ azabicyclo (3.2.0) heptane‐2‐ carbonyloxy) ({((2‐amino‐6‐oxo‐ 6,9‐dihydro‐3H‐purin‐9‐yl) oxy) (hydroxy) phosphoryl} oxy) phosphinic acid B: ŜT is ŜTxˆAυ1CmdπCdπ2 |∇ |2 = { if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 from the point of view of C is mapped into the relative position between system B and the position of A: 1 if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B|∇ |2 −ΔKΣ(dt−asin2θdϕ) 1 ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if√(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) (p) - g.(V ‘(p + i(pv’ f)) ≠ exp(iℏpˆ2A2mA(qˆCif −πˆCmdπCdπ2 |∇ |2 −ΔKΣ(dt−asin2θdϕ) IfŜbpˆAmAŜ†b+ if(p) - g.(V ‘(p + i(pv’ f)) + 2 2 _1 1 = 2 at time τ, while the momentum of B remains unchanged. In addition, this transformation is a symmetry of the free particle according to the definition given in (Equation6), because the Hamiltonian Ĥ(C) AB is mapped through (Equation5) to Ĥ(A) BC=πˆ2B2mB+πˆ2C2mC. Kerr metric in Boyer– Lindquist coordinates can be expressed as follows: ds2=−ΔKΣ(dt−asin2θdϕ) 2+ΣΔK+Σdθ2 +sin2θΣ((r2+a2) dϕ− adt) 2(Equation10), (31) where Σ=r2+a2cos2θ, ΔK=r2−2Mr+a2 (31). Therefore, the transformation ŜT in (Equation3) constitutes a generalisation of the Galilean translations to quantum reference frames. The simplest example of dynamical conserved quantities, in this case, are the two momenta Ĉ(C) 1=pˆA and Ĉ(C) 2=pˆB(Equation11). It is immediate from (Equation4) and (5) to see that the choice Ĉ(A) 1=ŜTĈ(C) 2Ŝ†T=πˆB (Equation12) and Ĉ(A) 2=−ŜTĈ(C) 1Ŝ†T−ŜTĈ(C) 2Ŝ†T=πˆC (Equation13) leads to the corresponding conserved quantities in the reference frame A. A similar procedure holds when we consider the extended set of conserved quantities composed of translations pˆi and Galilean boosts Ĝi=pˆit−mixˆi, i=A, B(Equation14). Notice that this construction of the ŜT operator satisfies the transitive property, meaning that changing the reference frame from C to A directly has the same effect as changing the reference frame first from C to B and then from B to A, i.e. Ŝ(C→A) T=Ŝ(B→A) TŜ(C→B) T (Equation15) static axisymmetric solutions, one may start from a Minkowski spacetime, expressed in Cartesian form as ds2=−dt2+dx2+dy2+dz2 (Equation16). (31) We then applied the following ellipsoid coordinate transformations to (Equation3) as follows x→(r2+a2) 1/2sinθcosϕ, y→ (r2+a2) 1/2 sinθsinϕ,z→rcosθ,t→t. (Equation17).{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1G,k) (equation43) are equivalent as balanced tensor category Repk (dA+A∧AAGA) of positive energy representations of the loop group at the:
INPUT: (432 k^4 N^2 π t^2 y^ (n Λ) {θ sin^ (-1) (sqrt (3) ), θ sin^ (-1) (sqrt (779)  sqrt (θ^3)) - 3/5 sqrt (779) θ sqrt (θ^3) 2F1 (1/2, 5/6, 11/6, 779 θ^3), 1/6 sqrt (1/49394 - 9 θ) sqrt (θ) + (θ - 1/889092) sin^ (-1) (3 sqrt (49394) sqrt (θ) ), θ sin^ (-1) (sqrt (sin^ (-(44545545)) ) } + constant sin^ (-1) (n) ^33833 sum g x^4 + O ((1/x) ^6)) + sin (2 x) (-216 (k^4 N^2 π t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g) x^3 + O ((1/x) ^6)) + e^ (-x^2/2) sin (2 x) (-108 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (- 1) (n) ^33833 sum g) x^2 + O ((1/x) ^6)) + e^ (-x^2/2) sin (2 x) (108 k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ ((n) ^33833 sum g x^2 - 108 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (- 1) (n) ^33833 sum g) + (324 k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g) /x^2 - (1620 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g)) /x^4 + O ((1/x) ^6)) + e^ (-x^2/2) (216 k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g x^3 + O ((1/x) ^6)) + e^ (-x^2/2) (-216 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (- 1) (n) ^33833 sum g) x^3 + 216 k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g x - (648 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ ((n) ^33833 sum g)) /x + (3240 k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-(n) ^33833 sum g) /x^3 - (22680 (k^4 N^2 sqrt (2 π) t^2 y^ (n Λ) sin^ (-1) (n) ^33833 sum g)) /x^5 + O ((1/x) ^6)) (equations34,35,36,37,38,39,40-43)
In this Scheme we see two subkeys k1 and k2 along the axes of the graph. The choices for them are both ordered by probability. In the x-y plane each square uniquely represents a key k (j) 1|k (i) 2, which is the concatenation of two subkeys. For this figure we include on the z-axis the probability of each key to illustrate the gradual differences of probabilities in the space. The blue key represents the key k used in the implementation that was attacked. The green keys are those with a higher probability than k∗, the red those with a lower probability. In the graphical representation this would mean starting at the top-left square and using the corresponding key to decipher a ciphertext (or some equivalent check that verifies the key). If this does not yield the desired results, then we try squares one by one, in order of their probabilities until one corresponding key does work.
OUTPUT: = (7aR) ‐5‐amino‐N‐*(S) ‐2‐*(S) ‐*(E) ‐(aminomethylidene) amino+(cyano) methyl+hydrazin‐1‐
yl(aziridin‐1‐yl) phosphoryl+‐1‐*(2E) ‐2‐*(fluoromethanimidoyl) imino+acetyl+‐7‐oxo‐7aH‐pyrazolo*4,3‐d+pyrimidine‐3‐carboxamide; 3‐(2‐amino‐5‐sulfanylidene‐1,2,4‐triazolidin‐3‐ yl) oxaziridin‐2‐yl(3‐ sulfany lidene‐1,2,4,6‐tetraazabicyclo*3.1.0+hexan‐6‐yl) phosphoroso 1‐(3,4,5‐trifluorooxolan‐2‐yl) ‐1,2,4‐triazole‐3‐carboxylate; N‐*(2‐amino‐6‐oxo‐1H‐purin‐9‐yl) amino(,1‐*5‐(,*cyano(,1‐[(diaminomethylidene) amino]ethenyl}) amino+oxy-methyl) ‐3,4‐dihydroxyoxolan‐2‐yl+‐1,2,4‐triazol‐3‐yl-formamido) phosphoryl +‐6‐fluoro‐3,4‐dihydropyrazine‐2‐carboxamide (7aR) ‐5‐amino‐N‐ *(S) ‐,2‐*(S) ‐*(E) ‐(aminomethy lidene) amino+(cyano) methyl+ hydrazin‐1‐yl-(aziridin‐1‐yl) phosphoryl+‐1‐*(2E) ‐2‐* (fluoromethanimidoyl) imino+ acetyl+‐7‐oxo‐1H,7H,7aH‐pyrazolo*4,3‐d+pyrimidine‐3‐carboxamide; N‐,*(2‐amino‐6‐oxo‐6,9‐ dihydro‐1H‐purin‐9‐yl) amino+(,1‐*5‐ (,*cyano(,1‐*(diaminomethylidene) amino+ethenyl-) amino+oxy-methyl) ‐3,4‐dihydroxyoxolan‐2‐yl+‐1H‐1,2,4‐triazol‐3‐yl-formamido) phosphoryl-‐6‐fluoro‐3,4‐ dihydropyrazine‐2‐carboxamide; *3‐(2‐amino‐5‐sulfanylidene‐ 1,2,4‐triazolidin‐3‐ yl) oxaziridin‐2 ‐yl+(,3‐sulfanylidene‐1,2,4,6‐tetraazabicyclo*3.1.0+hexan‐6‐yl-) phosphoroso 1‐(3,4,5‐ trifluorooxolan‐ 2‐yl) ‐1H‐1,2,4‐triazole‐3‐carboxylate
(22,27,28,35) This InSilico approach keeps track of the solutions already found of the selected group of the selected hit candidates which were fragmented, re-cored, and superposed in a non-relativistic quantum mechanics environment and finally led us to the complete Roccustyrna chemical structure. (Table 1/), (20,28,29,30) If several chemical space solutions were found in the phase end, the combined theory has a sequence of similar such function spaces of finite but arbitrarily large selected dimension, where the partition dimension increases with the finite resolution of relative knot space measurements to the first dihydro‐3H‐purin‐9‐yl) ‐ system when extracted from the 10 hit selected small molecules as the possible chemical bimodules over a hyperfinite 1-factor solutions which were sorted by the number of different SARS-CoV Mpro, PDB entry 6lu7 receptor patterns. This small molecule prototype was obtained directly from the solution of the D[- (k^ (-4 - k^4 n^33835 N^2) n^33834 N^213) /33834432, n] LocG (S1) CSG (equation47), k (S1) = TrigToExp[ArcSin[x[τ] x’[22 τ]^244 y’[τ]^ArcSin [242424222242424 Sin[X] x[τ]^22]]] (equation48), VectkG[G]= Rep (Dk (C[G])) Z (Vectk[G]) (equation 49) into the (k^ (-8 - k^4 n^33835 N^2) N^211) / (1144788006720 Log[3d N = 2 CS k]) (50) by a procedure akin to geometric quantization as derived by a first phase solution was taken as the 13 (a+ℓ) 3dN=2CSta+ℓ{1/12+(∣∣α1′(t) ⟩CQ1t∣ϕ(t) ⟩B+∣α2′(t) ⟩CQ2t∣ϕ(t) ⟩B) } + Fǫexp(iℏpˆ2A2mA +−1A∧[A∧A] 2zEG k (mod2π), (equation51) determined fragmentation. (36,37,39) and larger groups are prioritized over smaller chemical patterns with potential antiviral properties of GisitorviffirnaTM, Roccustyrna_gs1_TM, and Roccustyrna_fr1_TM small molecules of Preferred IUPAC Names of (7aR) ‐5‐ amino‐N‐ [(S) ‐{2‐ [(S) ‐ [(E) ‐ (aminomethylidene) amino](cyano) methyl]hydrazin‐1‐ yl} (aziridin‐ 1‐yl) phosphoryl]‐ 1‐[(2E) ‐2‐ [(fluoromethanimidoyl) imino]acetyl]‐7‐oxo‐1H,7H,7aH‐pyrazolo[4,3‐d]pyrimidine ‐3‐carboxamide; N‐{[(2‐amino‐6‐oxo‐ 6,9‐dihydro‐ 1H‐purin‐9‐yl) amino]({1‐[5‐({[cyano({1‐[(diaminomethylidene) amino]e thenyl}) amino]oxy} methyl) ‐ 3,4‐dihydroxyoxolan‐2‐yl]‐1H‐1,2,4‐triazol‐3‐yl} formamido) phosphoryl} ‐6‐fluoro‐3,4‐dihydro pyrazine‐2‐carboxamide; [3‐(2‐amino‐5‐sulfanylidene‐1,2,4‐triazolidin‐3‐yl) oxaziridin‐2‐yl]({3‐sulfanylidene‐1,2,4,6‐ tetraazabicyclo [3.1.0]hexan‐6‐yl}) phosphoroso 1‐(3,4,5‐trifluorooxolan‐2‐yl) ‐1H‐1,2,4‐triazole‐3‐carboxylate PDB generated (Figure 1///) patterns.