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The unitary extension of the specified dynamics

Original ledger classification: Open [O] + finite ladder complete [E]/[N] (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time; open = thermodynamic field limit only)

Recorded statement: THE UNITARY DILATION CONTRACT [O] (registered 2026-08-27; 'three meanings of dynamics' split, step (b)->(c)). The continuous semigroup e^{tQ} (DYN.MARKOV.EMBED.01) is irreversible statistical dynamics; fundamental quantum dynamics needs T…

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Paper context: Origin Theory

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DYN.UNITARY.DILATION.01

Original ledger classification: Open [O] + finite ladder complete [E]/[N] (discrete/kernel/field-free/interacting-classical/quantum-coupled/continuous-time; open = thermodynamic field limit only)

Original claim text

THE UNITARY DILATION CONTRACT [O] (registered 2026-08-27; 'three meanings of dynamics' split, step (b)->(c)). The continuous semigroup e^{tQ} (DYN.MARKOV.EMBED.01) is irreversible statistical dynamics; fundamental quantum dynamics needs T = e^{-aH} -> (OS) -> U(t) = e^{-itH} with H positive self-adjoint. DEMAND: (D1) a Stinespring/Hamiltonian dilation of the semigroup with (quasi-)local generator; (D2) size consistency (compatible with the thermodynamic limit -- no pathologically growing environment); (D3) a Lieb-Robinson bound (finite propagation speed of the dilated dynamics); (D4) the OS analytic continuation to a unitary one-parameter group on the reconstructed Hilbert space. KILL TESTS: every dilation of the seam semigroup is provably nonlocal; the Lieb-Robinson velocity diverges in the scaling limit; the OS continuation fails on the interacting algebra. RELATION: demand D2 of CCC.SEAM.CROSSOVER.01 (Stinespring isometry at field level) presupposes this contract -- named here as its prerequisite. NOTHING here is closed by the finite v971 result. [2026-08-27 lift-structure note (v976/v977, marker UNCHANGED): the dilation the corpus actually deploys (K_ij = sqrt(T_ij)|i><j|, the CCC Stinespring reading of the v221 kernel) is PROVABLY entanglement breaking (measure-and-prepare; quantum capacity 0; C_0 = 0) -- it cannot carry the coherent transport this contract demands, so any closing dilation must be a genuinely different object. The classical kernel admits the full lift trichotomy {EB dilation | random-permutation fibre with the hidden circulation parameter t (v976) | reversible unistochastic macro-gate with the hidden orientation bit sgn J = +-1/27 (v977)} -- the same classical data, three inequivalent quantum dynamics; and no fixed microstep unitary generates the relaxing sequence (Dirichlet recurrence witness), so repeated steps REQUIRE environment/dephasing between steps -- exactly the D1-D4 demand.] EXECUTED UPDATE (2026-08-28, v987): the OS/dilation LADDER is executed at kernel + free-field + interacting-kernel + quantum-coupled band level -- B = P1+(2/3)P2+(1/3)P3 > 0, H = -log B PSD (gap log(3/2)), T(t) semigroup inside the stochastic cone, U(t) = e^{-itH} with Wick anchor U(-in) = B^n (n=1..6); size-uniform free-band gap; congruence interacting family SPD; quantum SWAP coupling d(theta)~theta^2, CPTP, LR radius 1. MUST-FAIL: v971 negative kernel has no real half-step; one-sided mutant K B^(x L) is not symmetric. FIREWALL: continuous field-level OS reconstruction, thermodynamic-limit branch selection and any 3+1D reading stay [O]. Python-only / Wolfram mirror deferred. EXECUTED UPDATE (2026-08-29, review wave 4, v999): the finite ladder is now COMPLETE -- discrete / kernel / field-free / interacting-classical / quantum-coupled / CONTINUOUS-TIME. Weak-collision Hudson-Parthasarathy: generator extraction Richardson 1.098e-10, diag(L_GKSL)==Q=log B symbolic, e^Q=B exact, GNS splitting defect 0, locality 1.355e-20, strong-collision singularity contrast rank 9/81. Open = thermodynamic field limit only. Display stays [O]; no marker move.

Original classification detail

[E] (2026-08-28, v984): discrete collision/QCA-band dilation. [E] (2026-08-28, v987): kernel OS continuation exact + size-uniform free band + interacting congruence family + quantum SWAP coupling (d(theta)~theta^1.99, CPTP, LR radius 1). [O] continuous field-level OS reconstruction, thermodynamic-limit branch selection, any 3+1D reading; no marker move. | 2026-08-29 v999: finite ladder COMPLETE (incl. continuous-time weak-collision HP); open = thermodynamic field limit only. Display stays [O].

Dependencies as recorded

DYN.MARKOV.EMBED.01; CCC.SEAM.CROSSOVER.01 (D2); QFT4D.OS.RECON.01

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Registered verification modules

  • v984_markov_qca_dilation.pyRegistered verification module · frontier
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    DYN.UNITARY.DILATION.01 [O-Update: das DISKRETE Bein konstruktiv realisiert] (Externe Master-Objekt-Review Welle 2, 2026-08-28): **das exakte Kollisionsmodell — B^n als reduzierte Dynamik eines exakt unitaeren, strikt lokalen QCA-Bandes** — der Kollisionsschritt V = C (U_B (x) I) mit dem mod-3-Rekord C|j,k> = |j, j+k> ist unitaer auf System + Ancilla; die STINESPRING-IDENTITAET Phi(rho) = Tr_A[V (rho x |0><0|) V^dag] = sum_j P_j U_B rho U_B^dag P_j gilt als symbolische Operatoridentitaet (Kraus-Vollstaendigkeit sum K_j^dag K_j = I); diag Phi(diag p) = B p exakt mit verschwindenden Nebendiagonalen; SECHS frische Ancillas geben diag Phi^6 = B^6 p = T p exakt — das v977-Makro-Gate als reduzierte Dynamik eines Radius-1-Kollisionsbandes. MUST-FAIL FEUERT: der geschlossene Unitaer hat |U_B^2|^2 != B^2 (31/54 vs 0.2450) — die Dilatation ist notwendig. TYPISIERTE BEMERKUNG (Probenbefund GEGEN den Review-Text): eine WIEDERVERWENDETE mod-3-Addierer-Ancilla gibt diag = B^2 p weiterhin exakt (der Rekord j1+i bleibt unterscheidbar) — frische Ancillas braucht man fuer die Kohaerenzen, nicht fuer die Populationen. Der konjugierte Zweig V* dilatiert dasselbe B (sgn J = +-1/27 bleibt klassisch unsichtbar; Auswahl bleibt [O]). FIREWALL: nur das diskrete endliche Bein; quasi-lokale Hamilton-Dilatation, OS-Fortsetzung zu e^{-itH} und jede 3+1D-Lesart bleiben [O]; keine Marker-Bewegung.

  • v987_os_dilation_package.pyRegistered verification module · frontier
  • v999_weak_collision_hp.pyRegistered verification module · frontier
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    DYN.UNITARY.DILATION.01 [O-Update: endliche Leiter jetzt VOLLSTAENDIG -- diskret/Kernel/feld-frei/wechselwirkend-klassisch/quantum-gekoppelt/KONTINUIERLICHE ZEIT; offen = thermodynamisches Feldlimit] (Review-Welle 4, 2026-08-29): Schwache-Kollision/HP -- Richardson 1.098e-10, diag L=Q symbolisch, e^Q=B exakt, GNS-Splitting-Defekt 0, Lokalitaet 1.355e-20, starke Kollision Rang 9/81. Vertrag bleibt [O]. Python-only / Wolfram-Spiegel zurueckgestellt.

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