OpenAI · 362-01 · 2026-09-23 · Partial differential equations
Global classical solutions of the three-dimensional relativistic Vlasov–Maxwell system
preprints/Global-classical-solutions-of-the-three-dimensional-relativistic-Vlasov-Maxwell-system-September-23-2026
Family 362. Global smoothness for relativistic Vlasov–Maxwell.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Emergence. This language is not spacetime emergence and not a derivation of a metric. Oai276-A's one-use Holevo certificate does not derive a metric. Oai279-A's finite factoring circuit does not derive a metric. Oai227-A's finite SK certificate does not derive a metric. Oai119-A's finite Hellinger certificate does not derive a metric. Oai211-A, Oai290-A, Oai265-A, and Oai265-B do not supply that derivation. Oai280-A does not supply a metric derivation. Oai280-B does not supply a gravitational surface. Oai280-C does not supply a gravitational dictionary. Oai282-A does not supply Einstein dynamics. Oai282-B does not supply Einstein dynamics. Oai069-A does not supply a gravitational dictionary. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Oai119-A · Oai227-A · Oai279-A · Oai276-A · Oai069-A · Oai282-B · Oai282-A · Oai280-C · Oai280-B · Oai280-A · Oai211-A · Oai290-A · Oai265-B · Oai265-A · En07-C · En07-B · En07-A · En06-B · En05-C · En06-A · En05-B · En05-A · En04-A · III · VI · XVII-A · En02-A
Proves large-data global existence and uniqueness for the three-dimensional, one-species relativistic Vlasov–Maxwell system. Smooth admissible initial data may be arbitrary provided the particle density is compactly supported and the electromagnetic fields have finite energy and bounded derivatives of every order; the solution remains smooth on every finite time interval.
We prove global existence and uniqueness for arbitrary smooth admissible initial data in the three-dimensional, one-species relativistic Vlasov–Maxwell system. The particle density is initially compactly supported, and the electromagnetic fields have finite energy and bounded derivatives of all orders. The solution remains smooth on every finite time interval. This resolves the large-data global classical regularity problem for this model, without size or symmetry restrictions on the data.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 362: Global smoothness for relativistic Vlasov–Maxwell. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.
VlasovMaxwell.lean · VlasovMaxwell.lean
Emergence
Vlasov–Maxwell smoothness is not Einstein dynamics
Family 362 records large-data smoothness for relativistic Vlasov–Maxwell. That kinetic statement is not a derivation of a metric, not Einstein dynamics, and not spacetime emergence. Oai282-A prop:einstein says symmetry, conservation, and zero trace do not imply the Einstein equation. Oai282-B prop:einstein keeps that separation for the constructed free tensor. Oai211-A's metric scaling record, Oai290-A's typed certificate, Oai265-A's area-law separation, and Oai265-B's memory certificate are not a derivation of a metric. The authors are OpenAI. The companion does not verify those proofs. O.1 stays NOT_CLOSED.
EmergenceOai282-B free Ward actionOai282-A local Ward certificateOai211-A path-sum certificateOai290-A typed recoveryOai265-B memory certificateOai265-A area-law separationEn07-C Hawking comparisonEn07-B endpoint certificateEn07-A complete residualEn06-B finite transportEn05-C tensor-free comparisonEn06-A layer accountEn05-B isotropic limitEn05-A exact coneEn04-A residual responseIII gravitational equationsVI descent