Paper Citation Record · LEDGER

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations

As of 18 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2608.00477.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2608.00477 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:27:44.914006Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

24 of 24 outbound references displayed

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verified fuzzy18
unresolved6
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External citation measurements

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Outbound references

Observation 22c83fd6-14df-4d53-b871-9686eee039ec · outbound

This paper cites The cubic Dirac equation: small initial data inH1(R3).

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations The cubic Dirac equation: small initial data inH1(R3)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.092448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 94f33cdc-dd74-4358-aba0-04259d0e62e5 · outbound

This paper cites Global well-posedness for the massless cubic Dirac equation.International Mathematics Research Notices, 2016(22):6735–6828, 2016.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global well-posedness for the massless cubic Dirac equation.International Mathematics Research Notices, 2016(22):6735–6828, 2016

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.085455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6d6b370c-e9cc-42c6-ad5d-44875b84cad3 · outbound

This paper cites Coifman, Pierre-Louis Lions, Yves Meyer, and Stephen Semmes.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Coifman, Pierre-Louis Lions, Yves Meyer, and Stephen Semmes

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.078415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 96403783-7a0c-4ea5-b671-ca9708ca6f70 · outbound

This paper cites Null structure and almost optimal local regularity for the Dirac–Klein–Gordon system.Journal of the European Mathematical Society, 9(4):877–899, 2007.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Null structure and almost optimal local regularity for the Dirac–Klein–Gordon system.Journal of the European Mathematical Society, 9(4):877–899, 2007

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.071452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c4ab6327-4c23-4a3c-8a95-468bd4e141e3 · outbound

This paper cites Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II).

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations (II)

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T15:27:44.865411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78e31b15-db76-4ac0-b96b-7bd2c4259a0d · outbound

This paper cites Global existence for quadratically perturbed massless Dirac equations under the null condition.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global existence for quadratically perturbed massless Dirac equations under the null condition

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.064423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5341fa91-0ea8-437d-aa10-5105a7a59490 · outbound

This paper cites Space-time estimates for null forms and the local existence theorem.Communications on Pure and Applied Mathematics, 46(9):1221–1268, 1993.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Space-time estimates for null forms and the local existence theorem.Communications on Pure and Applied Mathematics, 46(9):1221–1268, 1993

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.057491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7096aefe-a47d-4b40-9a5b-bd33d7843e19 · outbound

This paper cites A physical space approach to wave equation bilinear estimates.Journal d’Analyse Mathématique, 87:299–336, 2002.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations A physical space approach to wave equation bilinear estimates.Journal d’Analyse Mathématique, 87:299–336, 2002

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.050427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6eec1063-b347-42c6-a6d1-2e2c562bc20b · outbound

This paper cites Global well-posedness in the critical Besov space of the skew mean curvature flow in $\mathbb{R}^d: d\ge 5$.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global well-posedness in the critical Besov space of the skew mean curvature flow in $\mathbb{R}^d: d\ge 5$

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T15:27:44.875857Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d59d349-6c51-4e08-b09c-74ca2a591fae · outbound

This paper cites Asymptotic properties of the spinor field and the application to nonlinear Dirac models.International Mathematics Research Notices, 2021(13):9609–9647, 2021.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Asymptotic properties of the spinor field and the application to nonlinear Dirac models.International Mathematics Research Notices, 2021(13):9609–9647, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.043579Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 51950bca-93a6-437d-b0a2-566d40559d7f · outbound

This paper cites A vector field method for some nonlinear Dirac models in Minkowski spacetime.Journal of Differential Equations, 273:58–82, 2021.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations A vector field method for some nonlinear Dirac models in Minkowski spacetime.Journal of Differential Equations, 273:58–82, 2021

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.036760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 77bede6d-cb1e-4752-95e1-109ce8879b83 · outbound

This paper cites Compacité par compensation.Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 5(3):489–507, 1978.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Compacité par compensation.Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 5(3):489–507, 1978

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.029550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 15165080-f954-4bc9-b276-511f92baf110 · outbound

This paper cites Local well-posedness for the quasilinear schrödinger equations via the generalized energy method.Calculus of Variations and Partial Differential Equations, 65:67, 2026.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Local well-posedness for the quasilinear schrödinger equations via the generalized energy method.Calculus of Variations and Partial Differential Equations, 65:67, 2026

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.022637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f6070bd5-f633-4862-aa3b-7a8fafff361e · outbound

This paper cites Classical, stable, nonlinear spinor field with positive rest energy.Physical Review D, 1(10):2766–2769, 1970.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Classical, stable, nonlinear spinor field with positive rest energy.Physical Review D, 1(10):2766–2769, 1970

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.015402Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 23171d6b-39d8-4982-bd95-a6e7a9db3a1e · outbound

This paper cites an unresolved cited work.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:27:45.008429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5fec737f-a1e1-4ba7-b187-a09828d9f100 · outbound

This paper cites Thirring.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Thirring

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:45.001322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d75bcff4-1878-4b21-8f3a-e481458da8be · outbound

This paper cites Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Physical Space Proof of Bilinear Estimates and Applications to Nonlinear Dispersive Equations

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T15:27:44.895295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35cc941e-2052-47ab-b037-ffb0729516b8 · outbound

This paper cites Periodic Schr\"odinger map flow on K\"ahler manifolds.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Periodic Schr\"odinger map flow on K\"ahler manifolds

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T15:27:44.898270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a77dfd4-712e-49fd-b258-a2872cd475a7 · outbound

This paper cites Physical space approach to wave equation bilinear estimates revisit.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Physical space approach to wave equation bilinear estimates revisit

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:44.994509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d585a300-75de-422e-a6f4-5736dbd218e3 · outbound

This paper cites Global well-posedness for radial extremal hypersurface equation in (1 + 3)-dimensional minkowski space-time in critical sobolev space.Annals of PDE, 12(1):1, 2026.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global well-posedness for radial extremal hypersurface equation in (1 + 3)-dimensional minkowski space-time in critical sobolev space.Annals of PDE, 12(1):1, 2026

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:44.988141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 75991136-d4e4-43a6-a6e3-f38eb3d1aa66 · outbound

This paper cites On global existence of 3D charge critical Dirac–Klein–Gordon system.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations On global existence of 3D charge critical Dirac–Klein–Gordon system

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:44.981725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ab703fbc-9fb3-49af-9e24-9cb8147a14b2 · outbound

This paper cites Global well-posedness for incompressible hookean elastodynamics in the critical besov spaces.Calculus of Variations and Partial Differential Equations, 64(7):206, 2025.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global well-posedness for incompressible hookean elastodynamics in the critical besov spaces.Calculus of Variations and Partial Differential Equations, 64(7):206, 2025

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:44.975509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 50fb5bc8-09ef-44d6-90ee-311ec89183d6 · outbound

This paper cites Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations Global well-posedness of non-integrable hyperbolic-ellptic Ishimori system in the critical Sobolev space

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T15:27:44.911184Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5b2793f-0bd0-4ebb-8bff-e37bf3e4bf24 · outbound

This paper cites (1+2)-dimensional radially symmetric wave maps revisit.Chinese Annals of Mathe- matics, Series B, 43(5):785–796, 2022.

Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations (1+2)-dimensional radially symmetric wave maps revisit.Chinese Annals of Mathe- matics, Series B, 43(5):785–796, 2022

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:27:44.967806Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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