Paper Citation Record · LEDGER

Angle of Null Energy Condition Lines in Critical Spacetimes

As of 13 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 1 inbound Pith citation observation for arXiv:2411.09233.

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

pith.paper-citation-record.v1
2411.09233 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T21:02:02.721004Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T21:02:02.536226Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-12T21:02:03.271240Z

Reference resolution

39 of 39 outbound references displayed

verified exact2
verified fuzzy11
unresolved26
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 26e4e4c1-a639-4167-b995-aced298ce1cf · outbound

This paper cites Constructing the critical solution is akin to solving critical collapse.

Angle of Null Energy Condition Lines in Critical Spacetimes Constructing the critical solution is akin to solving critical collapse

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.479322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3e42e7db-cccb-460e-a853-1f2c0e31787f · outbound

This paper cites The recipro- cal of the eigenvalue of the unstable mode is the Choptuik parameter γ [7].

Angle of Null Energy Condition Lines in Critical Spacetimes The recipro- cal of the eigenvalue of the unstable mode is the Choptuik parameter γ [7]

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.461020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 41d3a4a3-90b1-4177-b356-73f9d93211f5 · outbound

This paper cites In 4D, Choptuik found γ ≈ 0.37 and ∆ ≈ 3.44.

Angle of Null Energy Condition Lines in Critical Spacetimes In 4D, Choptuik found γ ≈ 0.37 and ∆ ≈ 3.44

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.495898Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a26490d8-87c8-4e43-a895-b25a9a08fba1 · outbound

This paper cites Angle of Null Energy Condition Lines in Critical Spacetimes.

Angle of Null Energy Condition Lines in Critical Spacetimes Angle of Null Energy Condition Lines in Critical Spacetimes

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-12T21:02:03.277187Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a46087fa-4967-4767-8277-09e14cdf1033 · outbound

This paper cites Chrusciel, Geometry of Black Holes.

Angle of Null Energy Condition Lines in Critical Spacetimes Chrusciel, Geometry of Black Holes

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.444885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation a2775fa2-01d9-4bd5-a060-cc5f46d353f1 · outbound

This paper cites Grumiller and M.

Angle of Null Energy Condition Lines in Critical Spacetimes Grumiller and M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.427147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8a6b2967-5cf1-445d-a287-22240df93e24 · outbound

This paper cites Universality and scaling in gravitational collapse of a massless scalar field,.

Angle of Null Energy Condition Lines in Critical Spacetimes Universality and scaling in gravitational collapse of a massless scalar field,

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.410155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bd616f46-a2bb-42bc-8b8c-31ff0cd81db3 · outbound

This paper cites The problem of a selfgravitating scalar field,.

Angle of Null Energy Condition Lines in Critical Spacetimes The problem of a selfgravitating scalar field,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.387029Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f1b54c5d-5d65-4be0-8474-d2283d0197ee · outbound

This paper cites Critical phenomena in gravitational collapse (Physics Reports).

Angle of Null Energy Condition Lines in Critical Spacetimes Critical phenomena in gravitational collapse (Physics Reports)

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.563172Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b01665e1-c9b3-43ee-a340-c0bd47f8020d · outbound

This paper cites Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---.

Angle of Null Energy Condition Lines in Critical Spacetimes Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.568675Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0968118f-6320-4146-adb0-7dddd8f91135 · outbound

This paper cites The Choptuik spacetime as an eigenvalue problem.

Angle of Null Energy Condition Lines in Critical Spacetimes The Choptuik spacetime as an eigenvalue problem

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.574507Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5df37a87-bc84-4a7d-8971-21e748a60b60 · outbound

This paper cites Prethermalization.

Angle of Null Energy Condition Lines in Critical Spacetimes Prethermalization

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.579822Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c01ced4b-7e45-438e-b9e2-59705d3b54b7 · outbound

This paper cites Prethermalization and universal dynamics in near-integrable quantum systems.

Angle of Null Energy Condition Lines in Critical Spacetimes Prethermalization and universal dynamics in near-integrable quantum systems

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.585028Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 884dd57a-0dea-45e9-9f49-38e333f766c0 · outbound

This paper cites QCD thermalization: Ab initio approaches and interdisciplinary connections.

Angle of Null Energy Condition Lines in Critical Spacetimes QCD thermalization: Ab initio approaches and interdisciplinary connections

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.590315Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e54d8b8-1a10-4cca-bf73-50eb1a61d880 · outbound

This paper cites Understanding critical collapse of a scalar field.

Angle of Null Energy Condition Lines in Critical Spacetimes Understanding critical collapse of a scalar field

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.595465Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 464163a0-05f6-424b-ae66-394fca4761ad · outbound

This paper cites On Choptuik's scaling in higher dimensions.

Angle of Null Energy Condition Lines in Critical Spacetimes On Choptuik's scaling in higher dimensions

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.600812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdb9a800-c4c9-4a49-acad-200da9239b6f · outbound

This paper cites Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse.

Angle of Null Energy Condition Lines in Critical Spacetimes Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.606018Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 127ae6a0-99ed-466e-8787-fee4838e899f · outbound

This paper cites Global structure of Choptuik's critical solution in scalar field collapse.

Angle of Null Energy Condition Lines in Critical Spacetimes Global structure of Choptuik's critical solution in scalar field collapse

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.611339Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3d5b7ee-36f7-4b0c-863a-fca1360a05a1 · outbound

This paper cites Ecker, F.

Angle of Null Energy Condition Lines in Critical Spacetimes Ecker, F

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.368520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 547239a8-3c07-4797-9573-af872fdd32f3 · outbound

This paper cites However, we have no proof of Taylor-expandability around x = 0 for arbitrary D >3.

Angle of Null Energy Condition Lines in Critical Spacetimes However, we have no proof of Taylor-expandability around x = 0 for arbitrary D >3

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.349205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 208aa7de-579d-4634-bb78-30476a125721 · outbound

This paper cites an unresolved cited work.

Angle of Null Energy Condition Lines in Critical Spacetimes Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T21:02:03.330731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0e669c5e-6a02-4e28-a549-cee9a4d87bbb · outbound

This paper cites However, unlike in critical spacetimes, a NEC vertex is not guaranteed, and when it does exist, it lacks a geometric interpretation in terms of zero-curvature contours.

Angle of Null Energy Condition Lines in Critical Spacetimes However, unlike in critical spacetimes, a NEC vertex is not guaranteed, and when it does exist, it lacks a geometric interpretation in terms of zero-curvature contours

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.311438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7367500e-a371-4f0a-a994-68079cf3532e · outbound

This paper cites Dilaton Gravity in Two Dimensions.

Angle of Null Energy Condition Lines in Critical Spacetimes Dilaton Gravity in Two Dimensions

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.636746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3b019a7-ac62-435c-83dc-51c67f590d32 · outbound

This paper cites Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity.

Angle of Null Energy Condition Lines in Critical Spacetimes Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.641970Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39e55b35-2330-48cf-a2a2-fec030a08c76 · outbound

This paper cites Universality and Scaling at the Onset of Quantum Black Hole Formation.

Angle of Null Energy Condition Lines in Critical Spacetimes Universality and Scaling at the Onset of Quantum Black Hole Formation

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.646613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e4f9652-cb4d-4df8-a24d-5d2b1fd1cd93 · outbound

This paper cites Surprises in the Evaporation of 2-Dimensional Black Holes.

Angle of Null Energy Condition Lines in Critical Spacetimes Surprises in the Evaporation of 2-Dimensional Black Holes

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.651359Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6690c524-9d26-4df9-a02b-7aa9f5390acb · outbound

This paper cites The large D limit of General Relativity.

Angle of Null Energy Condition Lines in Critical Spacetimes The large D limit of General Relativity

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.656390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b024498b-59cc-4cf1-a9d5-6cdb94295d08 · outbound

This paper cites Large D gravity and low D strings.

Angle of Null Energy Condition Lines in Critical Spacetimes Large D gravity and low D strings

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.661145Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be504e84-a1f3-499e-9477-2ec608ce3fbb · outbound

This paper cites Gravitating Scalars and Critical Collapse in the Large $D$ Limit.

Angle of Null Energy Condition Lines in Critical Spacetimes Gravitating Scalars and Critical Collapse in the Large $D$ Limit

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.665891Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06023e41-e93d-4e88-a07c-e408113624e9 · outbound

This paper cites The Large D Limit of Einstein's Equations.

Angle of Null Energy Condition Lines in Critical Spacetimes The Large D Limit of Einstein's Equations

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.670636Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 08f1c106-71c8-4767-a7c1-b4814e279af8 · outbound

This paper cites Critical behavior and scaling in vacuum axisymmetric gravitational collapse,.

Angle of Null Energy Condition Lines in Critical Spacetimes Critical behavior and scaling in vacuum axisymmetric gravitational collapse,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T21:02:03.294691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8329b549-2664-4b4d-8335-01c55f732118 · outbound

This paper cites Critical Collapse of a Complex Scalar Field with Angular Momentum.

Angle of Null Energy Condition Lines in Critical Spacetimes Critical Collapse of a Complex Scalar Field with Angular Momentum

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.680935Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9e5fdb7e-0904-4c01-956b-8baf04292d97 · outbound

This paper cites Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid.

Angle of Null Energy Condition Lines in Critical Spacetimes Observation of critical phenomena and self-similarity in the gravitational collapse of radiation fluid

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.686580Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04d9d7c6-9f19-4ac1-b07c-624b932b961e · outbound

This paper cites Black Hole Criticality in the Brans-Dicke Model.

Angle of Null Energy Condition Lines in Critical Spacetimes Black Hole Criticality in the Brans-Dicke Model

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.692737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 98a7587e-d8f1-4ffa-ae3b-94be05e7eaad · outbound

This paper cites Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model.

Angle of Null Energy Condition Lines in Critical Spacetimes Type II Critical Collapse of a Self-Gravitating Nonlinear $\sigma$-Model

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-08-12T21:02:02.840445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e89cee6e-d0a2-4d84-84ac-096bf680ab9a · outbound

This paper cites Universality of curvature invariants in critical vacuum gravitational collapse.

Angle of Null Energy Condition Lines in Critical Spacetimes Universality of curvature invariants in critical vacuum gravitational collapse

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.704878Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 548de6fa-5fb6-4012-8312-b66da9974665 · outbound

This paper cites Critical phenomena in the collapse of gravitational waves.

Angle of Null Energy Condition Lines in Critical Spacetimes Critical phenomena in the collapse of gravitational waves

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.710519Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9003d067-008b-4357-9116-615ec9664dda · outbound

This paper cites Critical phenomena in the gravitational collapse of electromagnetic waves.

Angle of Null Energy Condition Lines in Critical Spacetimes Critical phenomena in the gravitational collapse of electromagnetic waves

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.716026Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ea23633d-79e0-4c21-822b-db32a509a66c · outbound

This paper cites Twist-free axisymmetric critical collapse of a complex scalar field.

Angle of Null Energy Condition Lines in Critical Spacetimes Twist-free axisymmetric critical collapse of a complex scalar field

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-12T21:02:02.721004Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation a26490d8-87c8-4e43-a895-b25a9a08fba1 · inbound