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First-release paper · 2026-10-07

We Found No Magic in This Mighty Universe

Common-Source Generation and Classical–Quantum Correspondence in a Spin×SU(7) Theory

这浩瀚宇宙里，我们没找到魔法：Spin×SU(7) 理论的同源生成与经典—量子对应

Paper PDFSupplementarXiv versionDOI 10.5281/zenodo.23210292
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S
Beam: level means the two sides read the same currentLeft pan J by hand; right pan the state's two phasesS: read with the independent dual's exchangeTheorem 6.2 and Example 6.6. The left pan holds the classical current J = 4Nk·½ = 1.8590, computed from the source constants alone. The right pan holds the occupied state, whose upper and lower phases turn in opposite directions; it weighs 4Nk·⟨v, R(A) v⟩. With the independent dual's exchange S the beam is level at every time, with no counterweight to tune: the factor 4Nk is computed, not fitted. Slide S out and the reading becomes J·cos 2θ: level only at u = 0 and 2, and at the dark moment u = 1 the quantum side reads −J and the beam falls fully to the classical side.

Abstract

In the Spin+(1,3)×SU(7)\mathrm{Spin}^+(1,3)\times\mathrm{SU}(7) theory constructed here, none of gravity, gauge fields or matter is introduced separately: all three arise from one common source structure, and classical variation and quantum response are related by an exact identity whose coefficient is computed from the original action rather than fitted. A common action with an independent matter dual admits an explicit nine-field solution satisfying every Euler–Lagrange equation. For this solution's matter field ψ\psi, independent linear dual χ\chi and every complex-linear operator AA on the 252-dimensional matter space, χ(Aψ)=4k⟨v,R(A)v⟩\chi(A\psi)=4k\langle v,R(A)v\rangle. Here vv is a normalized eight-dimensional state, R(A)R(A) is determined by the original action and dual, and k=2k=\sqrt2. The identity recovers, term by term, the gauge current and the sixteen kinetic loads; standard eight-mode fermionic Fock lifting preserves its one-particle matrix elements.

Read the full abstract

The same original action carries quantization all the way through. The complete 252-dimensional matter and its independent dual form a 504-mode CAR which, together with the scalar CCR, carries the common Hamiltonian H=H0+YH=H_0+Y; its action core is recovered exactly from the original action, and its coupling is a configuration function generated by the original scalar Gram rather than a supplied constant. The original four time constraints generate the quantum clock order by order, and the whole energy tail generates one fixed self-adjoint remainder RR, whose closed-factor form plus RR reads back the complete Weyl energy exactly; for every precision, one source point carries all preparation fields at once—physical unit, near spectrum, Yukawa charge and eight external legs among them—and the near-spectral and full-Yukawa cutoff residuals tend to zero together as the precision is refined. Along the full field curve of a genuinely varying measure, the prepared responses and curvature readings, with their first and second derivatives, commute with the limit from cutoff to uncut. The gauge current above thereby becomes a charge–current Ward identity on the complete CAR: the one-particle sector carries no quartic pair current, and the two-propagator response is read by the same prepared state. The current then returns to the field: the mother action's second variation is the same 289-dimensional Jacobi matrix the Green function uses; the real current returns through the complete positive half-axis and source-generated two-sided inverses to the 289 field directions, with spectrum on the imaginary axis; in the static limit the uncleared field leaves a pole residue determined by constraint source number 114, and the field equation holds if and only if the nine null-direction cosources vanish.

The common-source result reaches beyond the physical world of this paper. On the original admission interface, every admitted world state over any relation network, vocabulary and authority root, every complete inquiry and every complete evolving process is formed from the same source's finite-program image via pointwise completion, with full recovery of its states, inquiry and action rules, and histories at every finite depth; an inquiry is a registered readout question about a state, answered in the original physical process by the field readings. That source is the original occurrence source of the physical construction, whose occurrence history is generated by the raw event structure; any authority root proposed as another source falls under the same quantifier and is itself formed by it. Every formed world also satisfies total reality: the difference between any two distinct visits is located at their registered occurrences, so no real difference is left internally unlocated — there is no magic. The theorem directly preserves the original physical process's field readings and actual evolution.

The action also yields exact signed auxiliary elimination and nonzero gravitational feedback. On fixed coframe and Cartan-spin backgrounds, every real impulse generates a unique all-real-time coupled orbit whose Legendre energy is recovered from quantum time derivatives. Coherence and Bell probabilities give analytic predictions, among them a 32-cell prediction reaching 222\sqrt2 constructed by the same source with no empirical input. The empirical verdicts are separated by object: the frozen ideal joint model is rejected by superconducting-circuit Bell data; the named nominal model of NIST 2015 still deviates from the five documented settings after the efficiency-unit correction, while the complete optical source domain generated from the public counts is nonempty under the joint 95% contract with every accepted source's CH strictly positive; for the Munich atomic experiment, the complete readout domain is compatible over all 20,403 prefixes, the ideal readout surface is rejected, and within the regular range all readout parameters of the same probability law are exactly one family of reciprocal scales — the hardware inverse requires independently prepared probe inputs.

Keywords: Spin×SU(7); gravity and gauge fields; classical–quantum correspondence; common-source generation; BF action; independent dual; common quantum Hamiltonian; Ward identity; fermionic Fock space; formal verification

Claims and proofs

Every claim is registered in the claim map. Open one to see its statement, where it appears in the paper, and the Lean modules and replay programs that prove it. The English statements are translated from the registered Chinese.

  1. phys.P4The classical–quantum pairing identityFigureTheorem 6.2

    At every point and for every complex-linear A on the complete 252-dimensional mother matter carrier: χ(Aψ) = 4k⟨v, SPAE v⟩, k = √2.

    Location: Theorem 6.2

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  2. phys.P13Generated geometry enters the actual actionPropositions 2.3–2.4

    The Spin × SU7 total bundle, the parallel ODE and composition law, the actual gluing Ad(g)A − (dg)g⁻¹, matter descent, the unique potential minimum, the 35-coordinate stabilizer, local Spin preservation and the moving-frame law.

    Location: Propositions 2.3–2.4, 3.3

    Lean modules · 4

  3. phys.P3Early matter connects back to the actual fieldProposition 2.5

    At every point, for every mother element and spin: the early internal representation action equals the current complete matter action; the scalar, the complete mass map and the Fin 2 × Fin 2 mixing equal the early joint values exactly; likewise for next.

    Location: Proposition 2.5; Appendix A.3

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  4. phys.P14Exact signed elimination of auxiliary fieldsTheorem 3.2

    For any source and any nondegenerate complete field: B* = Kₑ⁻¹F and L(B) = L(B*) − ½W(B − B*, Kₑ(B − B*)); the nine fields are equivalent both ways to “constitutive center + B remainder”; native writes of any Nat order preserve this.

    Location: Theorem 3.2

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  5. phys.P1The whole chain actually generatedConstruction 4.1

    The fixed source constructs StageOneThroughTenClosure, carrying the Stage 10 closure, the complete Stage 8 credential, and the MatterRecovery of the current and the next configuration.

    Location: Construction 4.1; Theorem 8.3

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  6. phys.P2The complete classical world and its uniquenessTheorems 4.2–4.4

    There is a unique configuration satisfying both LawfulClassicalActual and the fixed source's ClassicalWorldAcceptance (smooth, nondegenerate at every point, Lorentz-legal, a joint zero fiber of the same action, scalar contact at the origin, all six sectors nonzero).

    Location: Theorems 4.2–4.4

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  7. phys.P19All-history, all-order compact-domain boundsTheorem 4.5

    ∀ m ∀ compact K ∃ C(K, m): over every index of the original complete history, the m-th derivatives at x ∈ K of all coordinates of all nine fields are ≤ C; every lawful weakly recovered actual shares the same bound.

    Location: Theorem 4.5

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  8. phys.P15Clock–B coupling and nonzero feedbackConstruction 5.1

    L = L₀ + κ(b² + 2ub + ub²), κ = 9N/5; the unique B minimum is b* = −u/(1+u); at u = σ = 1/2 the native writer changes the (3,0) component of the gravitational auxiliary field by −N/2.

    Location: Construction 5.1, Theorems 5.2–5.4

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  9. phys.P5Currents, kinetic loads, transport and exterior-power remaindersTheorem 6.3

    At every point and for every complete P286 variation: currentResponse = the original variational current; the 16 kineticLoad terms agree term by term; the mass is nonzero, the mixing nonzero, and the occupied Yukawa = 0; exp(tG) is unitary and ‖exp(tG) − (1+tG)‖ ≤ ‖G‖²t²; coordinate differences in every exterior-power degree are ≤ a source-generated scale · t²; moving-frame readings commute.

    Location: Theorem 6.3, Proposition 6.4

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  10. phys.P16Standard Fock preservationTheorem 6.5

    For any finite linearly ordered mode set and any complex matrix A: dΓ(A)I(v) = I(Av) and ⟨I(v), dΓ(A)I(w)⟩ = ⟨v, Aw⟩; the source's 8 modes and 256-dimensional Fock space preserve every reading; the dark-moment −1/2 counterexample.

    Location: Theorem 6.5, Example 6.6

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  11. phys.P26The complete quantum construction (Theorems 6.7–6.10)§6.7–§6.10

    Original action → common H = H₀ + Y (61 CCR pairs, a 504-mode CAR, a 100-dimensional configuration, the minimal closed graph, four-time Weyl; action-kernel identity (6.3), coupling 4W(q), W ≥ 1 source-generated) → all-order clocks, the fixed self-adjoint R = E_tail − C_src, the same 11-field preparation (both residuals tend to zero) → genuinely varying 289/36 field readings, nonlinear Laplace, cut → uncut 0/1/2-jet exchange, fixed measure fibers → the charge–current Ward identity P(k)Q_a = J_sp + J_pair (J_pair = 0 on the one-particle projection; the two-propagator response = the sum over channels; read out from the same preparation).

    Location: §6.7–§6.10 Theorems 6.7–6.10, end of §6.9; Figure 3

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    Replay programs and evidence · 18

  12. phys.P29The mother action recovers the same H289 and every Euler equation§6.11

    The actual nine-group field lift of the existing repaired original action, the independent dual and the one-jet density generate a genuine Fréchet Hessian; the original four-block source dictionary proves, for any four complex momenta, that its Fourier Hessian equals the same original H289; the original auxiliary graph, the full Number Legendre/quartic, the independent Noether momenta and all 289 holonomic Euler equations recover the original nine-group mother residuals; the same Green function, nine compatibilities and 36 curvatures are actually consumed.

    Location: §6.11 Theorem 6.11

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  13. phys.P27The original complete 289 Green function enters genuine finite-window field feedback§6.12

    The same spatial half-density and complete configuration integral → a common Field289 with genuine C² and a symmetric Hessian → a 1296-cell mixed response of the two 36s of the same preparation; the mother raw −4W·DH and the complete density contact → a five-term time derivative → the original 289 Green function (nine zero-direction residuals) → genuine physical finite-window field derivatives.

    Location: §6.12 Theorem 6.12(1)

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  14. phys.P30Complete-time payment over the original half-axis, the spectral axis and the actual varying background§6.12

    The whole-carrier evolution polynomial bound of the actual C + uncutRetainer gives the complete positive half-axis Re λ > 0, vanishing at the end and an explicit exponential tail; two-sided time generates two-sided inverses on both half-planes, the genuine spectral axis and the actual spectral points of zero transfer; the affine pencil of the common momentum carrier and the genuine Field289 inverse generate, for a given C¹ history, non-autonomous two-sided legs, genuine amplitude derivatives and the return to the original prepared Euler equations.

    Location: §6.12 Theorem 6.12(2)–(4)

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  15. phys.P33The original real current: half-axis operator, source-generated two-sided inverses and the uncleared static residue§6.12

    The complete Field289 real CLM of the same QC19 preparation has an operator-norm window → a half-axis price; the original two-quadrature real Fourier signal and its 0/1/2 time jets enter the actual ordered history, the mother Euler equations and causal feedback; the source-generated λ = 3 instance gives a nonempty open regular domain, two-sided inverses and a unique fixed point; the eight-dimensional moving pole, the same Gauss preparation and a nonzero pole defect return to the original H via Duhamel/dressing; five origins / 98 complementary spaces give the Schur complement over all four momenta and the κ⁻² coefficient of the uncleared field; the staticApproach residue limit for fixed forcing, the actual current point price and the Abel reading each keep their quantifiers; the N1 history/normal Ward identity is consumed from the same source.

    Location: §6.12 Theorem 6.12(5); §6.13 Theorem 6.13(3) fixed-forcing and actual-current residue, (5) weighted Ward form

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  16. phys.P36Same-source moving carrier, momentum continuity and the field pole under varying forcing§6.13

    The overlap U(p) from the complete moving-pole basis to the eight states at p = 0 is unitary, and the preparation/primal/creation/fiber/same-ε preparation expand layer by layer in U(p); the tensor M(p_L, p_R) = U_L† M₀[A] U_R keeps the whole Gauss operator A; actualC(p) = actualC(0) + v_F(p) (v_F real-linear and continuous), ‖C(p) − C(k)‖ ≤ ‖v_F‖‖p − k‖, and for non-real z the resolvent difference is ≤ |Im z|⁻² ‖v_F‖‖p − k‖; finiteRetainer and actualA agree across momenta, fulljoint R/time is continuous with time bound actualGrowth(0, F, |t|); every one of the 289 rawReader directions is continuous in momentum; all original currents and integration windows return exactly to the same 8-carrier U_L J U_R†; the −κ² limit of the uncleared field under varying forcing = staticResidue(actualCurrent), with coefficients (−9/125)√30·w and (−67/72)√30·w (w = originWeight); H field = current ⇔ axisNullCosource = 0; w = −cosource₁₁₄ = nativeContactWindow − deviationWindow = −(N1 Ward integral + covariant integral − (Q(T) − Q(0))); |w − nativeContact| ≤ ‖D₀F‖|T| / (|Im z||Im w|).

    Location: §6.13 Theorem 6.13(1)(2), (3) uncleared limit for varying forcing, (4) constraint compatibility, (5) contact–deviation split and price

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  17. phys.P34The all-frequency budget of the matched original Γ whole word, and the endpoint's common tail§6.14

    The same fullH₀ generates matched J3/R3 with a positive bulk and two Ritt profiles; ∀ μ > 0, the original g/k and both sharps, the common N/cofinal F pays the original whole-Γ budget inside the source (keeping normalization, CF/dF, and matter/vacuum/gauge/spatial and coframe contact); the signed middle term of secondGreen, the pole subtraction and the fixed-source jets give the absolute all-frequency L¹ common tail of renormalizedEndpoint; the same-volume PSD noise/diffusion crossed with the full carré gives the exact decomposition of R3.

    Location: §6.14 Theorem 6.14

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  18. phys.P7All-time gauge–Dirac orbitsTheorem 7.1

    Every real impulse generates a CompleteOrbit; every real time satisfies the original Hamilton derivative equations; the orbit of a given impulse is unique; the Euler terms vanish, energy is conserved, and Q varies for nonzero impulse.

    Location: Theorem 7.1

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  19. phys.P12The quantum time derivative recovers the orbit energyTheorem 7.2

    For any impulse, CompleteOrbit and real t: q = Re⟨Vψ, ψ′⟩/ω recovers r and p; the Legendre relative energy = p²/2m + c(r − r₀)² + a nonnegative term.

    Location: Theorem 7.2

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  20. phys.P8Analytic predictions and the Bell probability familyTheorem 7.3

    The coherent reading is cos²(ω·x₀), with ω² = 972/3125; the five points 1, 1/2, 0, 1/2, 1 against the exclusive path's constant 1/2; the Born probabilities of ticks 16/17 are equal, with marginals 1/2; a determinate color-X preparation of Φ+; the six-radius rejection of the Storz joint model is kept.

    Location: Theorem 7.3, Proposition 7.4; §9.2; D.4

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  21. phys.P32Theoretical prediction, the atomic instrument domain and inverse reading of parameters§7.4

    The SpinPair source/current/next generates every lawful XZ family, a uniform Tsirelson bound and a zero-empirical-input 32-cell construction reaching 2√2; each of the two Munich runs has a lawful primitive witness, all 20,403 original-order prefixes pass the joint 1/20 contract, and the rejection of the April ideal surface is kept; the maximal quotient, all regular two-scale fibers, the near-sharp range and the whole confidence domain share eight response bounds.

    Location: §7.4; §9.2 Proposition 9.2(1)(2)(4)(5)

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  22. phys.P9Formation of an arbitrary physical source familyTheorem 8.1

    ∃ law ∀ source : SmoothUnifiedSource ∀ state ∀ center: the mother evaluation recovers the complete input and outputs p286CartanStateNext; the existence law, prior to Material/current, gives the native compile/nextCurrent with target = the original writer; every lawful occurrence of any given law generates a successor.

    Location: Theorem 8.1

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  23. phys.P10Complete classical–quantum realization of any sourceTheorem 8.1

    For every SmoothUnifiedSource the same materialField generates a smooth, nondegenerate, Lorentz-legal nine-channel JointZero with scalar contact; CWA ⇔ physicalPhaseAmplitude ≠ 0; the writer, nine fields, actions and quantum response of any center/epoch/point/matter action are consumed together.

    Location: Theorem 8.1

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  24. phys.P11Complete source paths and autonomous programsTheorem 8.2

    ① Every finite list of (SmoothUnifiedSource × 195 real remainders) has a lawful finite event path in one mother history; ② every finite list of discrete materials/260 rational coordinates is actually formed and executed in one autonomous history.

    Location: Theorem 8.2

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  25. phys.P6Complete representation, all events and the macro successorTheorem 8.3

    The Pointwise and Compact descriptions have a unique comparison that preserves and reflects every relation and operation; the complete history of any length n recovers visit n; the 10th event recovers the original writer, projections, whole ledger, fields and any matter response; the macro process keeps the living law for every index.

    Location: Theorem 8.3

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  26. phys.P22Complete realization by the fixed mother sourceTheorem 8.4

    The original Type 0: ∀ N, V, authoritative root and lawful world state ∃ origin (formation, recovery, total reality ⇒ no magic bit); ∀ N, V and complete inquiry state ∃ origin; ∀ original SourceNativeInquiryEngineProcess ∃ origin whose restrict equals the original complete process and keeps the sealed activation, the whole activation law and every finite-depth history of any runtime.

    Location: Theorem 8.4, Corollary 8.5; Appendix C.9

    Lean modules · 2

  27. phys.P24NIST 2015 nominal replay (correct units)§9.2

    r0003 is frozen before execution at the published ±0.3% (probability half-width 0.003); the center and the 16 corner points agree across two implementations; all five documented values lie outside the pre-declared optimal band; center (r, θ₀, θ₁) = (0.315463895, 4.954737358°, −27.232869633°); readiness actually consumes the negative result.

    Location: §9.2 NIST nominal-replay paragraph; Appendix D.4.6

    Replay programs and evidence · 2

  28. phys.P25A conditional source member from public counts (BL8)§9.2

    Shalm 2015 Table S-II, 5-pulse window, N = 177358351: a conditional complete-Fock source member trained on 00/01/11 with 10 held out, whose 12 envelopes lie inside the po0003 domain.

    Location: §9.2 Table S-II conditional-member paragraph

    Replay programs and evidence · 3

  29. phys.P28Observation-generated complete source slice and strict update over the whole box§9.2

    The five training centers and the joint11 original intervals generate a complete lawful source slice and predict two whole held-out cells; 69 segments on two paths keep both boundaries; on the whole ±0.05° angle box a finite update Bcommon −0.01° has a strict raw CH gain consistent on both paths and an independent Fock endpoint.

    Location: §9.2 observation-generated slice and Bob two-angle update paragraph

    Lean modules · 1

  30. phys.P31The complete optical source domain and the strictly positive CH of the public joint 95%§9.2

    Full single-count error intervals and a common phase produce by themselves a complete optical source; Pol ⊗ Env gives effects for all n and matched infinite Born; a complete multi-window source domain; the joint 95% domain consumes the actual setting exposures and the complete outcomes, has 8 Γ/Fock members and a continuous outer cover, and every accepted source has CH_N5 > 1.3790180504 × 10⁻⁶.

    Location: §9.2 Proposition 9.1

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  31. phys.P35Hardware inverse, the pulse-realizable image and the original post-measurement history§9.2

    The same whole-parent domain produces a joint cap across four gains; on the regular range of the identified complete law, two source-known signed probes and a nonzero identification determinant give the unique inverse of the complete effect; the detector micro-fiber gives the full (d, k) conditions, a unique inverseAtom and a pulse-area cap; the original 12-state GKSL matrix, natural/ion jumps and two implementations give the actual atomic response, and detector rates are generated inside the complete realizable image of Spectrum; six strictly different atomic responses give the same joint probabilities and all prefix factors; the complete original source/visit 10/tick 16→17 history is kept; the nine fields of the 41,673 public local records, the 867 unpaired entries and the successor gaps are recovered completely.

    Location: §9.2 Proposition 9.2(3), Proposition 9.3

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  32. phys.P17Complete matter actions formed from mother materialAppendix C.5

    A 252-complex-dimensional matter basis; for every A ∈ End_ℂ there is a unique completed value v with operator(v) = A; the finite operatorAt reads only past samples.

    Location: Appendix C.5 Theorem C.1

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  33. phys.P18The complete joint carrier and nonzero feedbackAppendix C.6

    Joint is the integer span of the Ω-orbit of jointInput; two mother laws and a common law exist prior to values; ∀ parent ∀ value ∃ query such that compile returns (query, some v, some nativeLift v); every query keeps its own answer.

    Location: Appendix C.6 Proposition C.2

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  34. phys.P20Mother-law completion and continuous process representationAppendix C.7

    ∀ f : Stream → Stream ∃! law; likewise for every Input → Stream; the original Dynamics on a complete separable metric space with continuous emit/update embeds closedly and recovers every state and event.

    Location: Appendix C.7 Proposition C.3

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