Overview Kernel-Native Upstream Continuation is Module C of the post–structural-unification continuation of the gravity–quantum unification ARC. The preceding modules establish two essential common structures: Module A constructs the operational source and lawfully attaches it to the Einstein metric projection. Module B derives gravitational and inertial mass from one conserved source-generated Poincaré Casimir. Module C addresses the next constructive obligation: Can the gravitational and quantum developments be obtained as compatible projections of one standing-bearing upstream continuation, rather than merely aligned as separate histories after the fact? Within the manuscript’s frozen regular local comparison class, the answer is affirmative. Module C constructs a common upstream history object, defines its gravitational and quantum projection maps, and proves the required projection intertwinings, overlap compatibility, reference preservation, and quotient stability. The result converts common origin from a static structural claim into a dynamically realized continuation architecture. Central Result The manuscript constructs a common upstream continuation of the form Hup⟶ΠGHG,Hup⟶ΠQHQ,\mathfrak H_{\mathrm{up}} \overset{\Pi_G}{\longrightarrow} \mathfrak H_G, \qquad \mathfrak H_{\mathrm{up}} \overset{\Pi_Q}{\longrightarrow} \mathfrak H_Q,Hup⟶ΠGHG,Hup⟶ΠQHQ, where: Hup\mathfrak H_{\mathrm{up}}Hup is the standing-bearing common history object; HG\mathfrak H_GHG is the gravitational or Einstein history; HQ\mathfrak H_QHQ is the quantum or Schrödinger history; ΠG\Pi_GΠG and ΠQ\Pi_QΠQ are lawful projection maps preserving the relevant source, mass, reference, and continuation data. For admissible upstream evolution UupU_{\mathrm{up}}Uup, the projections satisfy the appropriate intertwining relations: ΠG∘Uup=UG∘ΠG,\Pi_G\circ U_{\mathrm{up}} = U_G\circ\Pi_G,ΠG∘Uup=UG∘ΠG, and ΠQ∘Uup=UQ∘ΠQ,\Pi_Q\circ U_{\mathrm{up}} = U_Q\circ\Pi_Q,ΠQ∘Uup=UQ∘ΠQ, on the manuscript’s declared domains and regular local charts. Thus, projecting after common continuation agrees with continuing after projection. The gravitational and quantum histories are not independently evolved objects subsequently declared compatible; they are lawful images of one prior continuation-bearing carrier. Principal Contributions Imports the common-interior architecture established by Structural Unification of Einstein and Schrödinger Dynamics. Imports the operationally attached source constructed in Module A. Imports the common mass reference established in Module B. Constructs a common upstream history object independently of the downstream Einstein and Schrödinger evolutions. Defines the gravitational and quantum projection maps on the declared regular local domains. Proves that each projection preserves the standing-bearing data appropriate to its target. Establishes source preservation across upstream continuation and gravitational projection. Establishes preservation of the common Casimir mass reference across both projections. Proves the gravitational projection intertwining with Einstein first-response continuation. Proves the quantum projection intertwining with Schrödinger Hamiltonian continuation. Establishes overlap compatibility between local continuation charts. Shows that changes of representative do not alter the descended physical histories. Distinguishes continuation-bearing tensor structure from coordinate, gauge, phase, normalization, and chart skin. Prevents either downstream projection from manufacturing or repairing the common upstream history. Supplies the continuation coordinates required by Module D’s exact certificate-fibre exhaustion. Provides the dynamically integrated carrier used by the final FEP-1.0 realization certificate. The Upstream Continuation Problem Structural unification establishes that Einstein and Schrödinger dynamics descend from one admissible physical interior. That result alone does not yet construct a single history whose projections reproduce both developments. Without an explicit common continuation, one could still have: a gravitational history and quantum history formed independently; a numerical correspondence between selected parameters; a retrospective pairing of states at matching labels; a projection-specific repair used to force compatibility; an unproved assumption that the two evolutions belong to one physical process. Module C closes this gap by constructing the continuation-bearing upstream object itself. A genuine common-history theorem must establish: formation of the upstream carrier independently of its projections; lawful gravitational and quantum projection maps; preservation of identity and reference through continuation; compatibility of source and mass data across both branches; commutation or intertwining of projection with the relevant evolution; overlap consistency across local charts; quotient invariance under nonphysical changes of representative; absence of downstream backflow into upstream formation. These obligations are discharged within the fixed target and regularity assumptions of the manuscript. Independent Formation of the Upstream Carrier The common history cannot be defined merely as an ordered pair of independently completed Einstein and Schrödinger solutions. Such a pairing would encode coexistence but would not prove common physical origin. The manuscript instead follows the dependency order common admissible interior⟶source- and mass-locked upstream data⟶Hup⟶{HG,HQ.\text{common admissible interior} \longrightarrow \text{source- and mass-locked upstream data} \longrightarrow \mathfrak H_{\mathrm{up}} \longrightarrow \begin{cases} \mathfrak H_G,\\ \mathfrak H_Q. \end{cases}common admissible interior⟶source- and mass-locked upstream data⟶Hup⟶{HG,HQ. The upstream carrier is formed before either projection is granted completed standing. Its admissibility does not depend on whether a desired Einstein or Schrödinger trajectory can later be recovered. This independence blocks circular constructions in which downstream solutions are chosen first and an alleged common origin is manufactured retrospectively to fit them. Projection Intertwining The decisive dynamical requirement is not simply that maps ΠG\Pi_GΠG and ΠQ\Pi_QΠQ exist. They must preserve continuation. For the gravitational branch, the manuscript proves the appropriate relation ΠG∘Uup=UG∘ΠG.\Pi_G\circ U_{\mathrm{up}} = U_G\circ\Pi_G.ΠG∘Uup=UG∘ΠG. For the quantum branch, it proves ΠQ∘Uup=UQ∘ΠQ.\Pi_Q\circ U_{\mathrm{up}} = U_Q\circ\Pi_Q.ΠQ∘Uup=UQ∘ΠQ. These relations certify that the projected histories are generated lawfully from the same upstream continuation. They also exclude a weaker construction in which: the same initial label is assigned to two unrelated evolutions; the endpoints happen to agree but intermediate continuation does not; a projection requires an additional hidden update; representative choices change the physical projected history; compatibility is imposed only after evolution has occurred. The intertwinings therefore provide the dynamical content of the common-origin claim. Source and Mass Preservation Module C inherits two locked structures from the preceding modules: the operational source attached in Module A; the common Casimir mass established in Module B. The upstream continuation must preserve both through the appropriate interfaces. Accordingly, the construction ensures that: the gravitational projection receives the same admissibly formed source throughout its declared continuation; the quantum projection retains the corresponding source and generator reference appropriate to its Hamiltonian development; the gravitational monopole and inertial coefficient remain projections of one common mass charge; neither branch introduces an independent mass-bearing coordinate; changes of chart or representative do not multiply source or mass standing. This prevents the common history from fragmenting into projection-specific source or calibration packages. Quotient and Skin Discipline The upstream history may admit multiple local or representative-level descriptions. These do not automatically correspond to distinct physical continuations. Module C therefore separates: standing-bearing continuation data; source- and mass-bearing tensor structure; admissible projection relations; chart, gauge, phase, normalization, and labeling skin. Representative multiplicity is quotiented whenever it changes no admitted physical continuation or projection predicate. Conversely, a difference that alters source attachment, mass reference, continuation, projection compatibility, or endpoint standing cannot be dismissed as skin. The common history is consequently defined by its lawful standing-bearing structure, not by the raw cardinality of its presentations. No-Backflow and No-Repair Discipline The lawful construction has the direction Hup⟶HG,HQ.\mathfrak H_{\mathrm{up}} \longrightarrow \mathfrak H_G,\mathfrak H_Q.Hup⟶HG,HQ. It does not permit either downstream history to create, select, or repair the upstream carrier that is supposed to generate it. The module excludes: Gravitational backflow: using a desired Einstein history to define the common upstream continuation. Quantum backflow: using a desired Schrödinger trajectory to supply missing upstream standing. Cross-projection laundering: transferring data from one projection to the other without mediation by the common carrier. Endpoint-only matching: identifying histories because selected endpoints agree while their continuation maps fail to intertwine. Representative inflation: treating multiple charts, phases, gauges, or labels as distinct physical histories. Hidden scope expansion: introducing new dynamical structure without registering it as part of a richer target. This ensures that common continuation is genuinely constructed rather than retrospectively declared. Place in the Completed Unification ARC The domain-general AASC kernel and Unus Solus Possibilis Est remain upstream machinery used across the wider research program. The gravity–quantum sequence proceeds as follows: Gravity as Structural Necessity — establishes the necessary physical constraint role; Einstein Dynamics — derives the unique minimal first-response metric projection; Schrödinger Dynamics — derives the corresponding minimal Hamiltonian quantum projection; Structural Unification — proves that the gravitational and quantum descriptions are projections of one admissible physical interior; Module A — completes operational metric–source attachment. Module B — proves common mass–charge matching. Module C — constructs common upstream continuation and projection intertwining. Module D — establishes exact certificate-fibre exhaustion and unique lawful role occupancy. Complete Certificate Closure — integrates the full FEP-1.0 gravity–quantum realization certificate. Module C therefore transforms the structural and charge-level unity established upstream into an explicit common continuation. Relation to Modules B and D The division of labor is precise: Module B fixes the common source-generated mass reference that both projected histories must preserve. Module C constructs the upstream history and proves that its projections reproduce the required gravitational and quantum continuations. Module D classifies and exhausts the remaining target certificate fibres, proving that every required role is lawfully occupied and that no inequivalent admissible assignment survives within the frozen target. Module C cannot complete its task without Module B, because a common continuation carrying independently normalized mass coordinates would not preserve the required shared reference. Module D, in turn, depends on Module C because exact certificate closure requires an actually constructed continuation-bearing carrier, not merely static source and mass correspondences. Scope and Nonclaims The manuscript does not claim: an independent derivation of the universal AASC kernel; a new derivation of the Einstein or Schrödinger equations; that every gravitational history admits a compatible quantum projection; that every quantum history admits a compatible gravitational projection; common continuation outside the frozen target and declared regular local comparison class; a unique global spacetime topology or quantum state; a universal preferred time parameter; elimination of all gauge or chart freedom; construction of a Wheeler–DeWitt equation; primitive quantization of the Einstein metric; a nonzero interacting quantum-gravity field theory; resolution of every global constraint, singularity, or boundary problem; unique realization across different source, sector, boundary, or calibration packages; completion of exact certificate-fibre exhaustion within this module alone. Those matters are either outside the fixed target or belong to Module D and the integrated capstone. Conceptual Significance Module C converts the claim of a common physical interior into a common dynamical construction. The Einstein and Schrödinger histories are not merely compatible descriptions placed beside one another. Nor are they independently complete evolutions linked by a shared parameter after the fact. They are projections of one prior continuation-bearing object, and the projection intertwinings certify that their lawful developments remain coordinated. The resulting architecture is: one source⟶one common mass charge⟶one upstream continuation⟶{Einstein history,Schro¨dinger history.\text{one source} \longrightarrow \text{one common mass charge} \longrightarrow \text{one upstream continuation} \longrightarrow \begin{cases} \text{Einstein history},\\ \text{Schrödinger history}. \end{cases}one source⟶one common mass charge⟶one upstream continuation⟶{Einstein history,Schro¨dinger history. This is the dynamical realization of common-origin unification. It supplies the last major constructive carrier required before the ARC can proceed to exact certificate-fibre exhaustion and final integrated closure.