Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T05:58:17.676460Z
Paper Citation Record · LEDGER
Competitive Facility Location with Market Expansion and Customer-centric Objective
As of 23 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2412.17021.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
21 of 21 outbound references displayed
- verified exact0
- verified fuzzy6
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 67fd566a-43e0-43c8-a806-fd27636b1568 · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.936909Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8f64b5c4-16e1-4afa-8c3d-71d34d98410d · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.925162Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 3ae9207c-86c5-4627-91a9-32837fb401fb · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.914332Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7e3e916a-e3b2-4270-bff2-568f99527dea · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.903375Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2b99ef9d-6185-4e66-82f3-d3f8e50d09db · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.893308Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 10778cb1-0c4c-44dc-b98c-749e1aac65ae · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.881841Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0f515ec7-0c23-49e6-9921-4e489db68334 · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.871448Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation a834c513-9519-4867-85f5-e7dc225b9a3c · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.860560Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2de761b5-e390-4de6-9f59-abf916dc0603 · outbound
This paper cites Combine this with the fact that Ψ ′ n(t) is (strictly) decreasing in t, we have ta 1 < ta.
Competitive Facility Location with Market Expansion and Customer-centric Objective Combine this with the fact that Ψ ′ n(t) is (strictly) decreasing in t, we have ta 1 < ta
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.849857Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4983914c-7ae4-4f4d-9534-f5fc053a1f4b · outbound
This paper cites t we get U ′(t) = Ψ′ n(t) − Ψ′ n(t) − Ψ ′′ n(t)(t − a) (b) > 0, ∀t > a where (b) is because Ψ ′′ n(t) < 0 (it is strictly concave in t).
Competitive Facility Location with Market Expansion and Customer-centric Objective t we get U ′(t) = Ψ′ n(t) − Ψ′ n(t) − Ψ ′′ n(t)(t − a) (b) > 0, ∀t > a where (b) is because Ψ ′′ n(t) < 0 (it is strictly concave in t)
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.838831Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 84a1f8df-3e8d-486f-b880-be547d1b3bec · outbound
This paper cites Inner-approximation.
Competitive Facility Location with Market Expansion and Customer-centric Objective Inner-approximation
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.827486Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 05337a52-e9b2-4eea-9b62-4431f0bde9d3 · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.816280Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0903f16d-0a58-43da-973d-e3881baa67db · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.805844Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 2d41f3e4-ce50-4261-a123-7baa5457490d · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.794559Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation bd355717-0f63-48d1-b760-7d1c43133cdb · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.782880Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation dda4431f-dde2-456f-a500-387f61fb82bf · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.770464Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation d47b6a98-ed10-4edb-9781-566456ecc55d · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.757851Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 650fec4e-1ad5-4849-ac27-fded6799bfff · outbound
This paper cites an unresolved cited work.
Competitive Facility Location with Market Expansion and Customer-centric Objective Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T05:58:17.746208Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0b228cdc-6fc0-4467-b3db-b20666219c85 · outbound
This paper cites Combine this with the fact that Ψ ′ n(t) is (strictly) increasing in t, we have ta 1 < ta.
Competitive Facility Location with Market Expansion and Customer-centric Objective Combine this with the fact that Ψ ′ n(t) is (strictly) increasing in t, we have ta 1 < ta
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.734392Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 60b96c5e-e4e3-4cce-8b55-527ea06dc9ae · outbound
This paper cites t we get U ′(t) = −Ψ′ n(t) + Ψ′ n(t) + Ψ ′′ n(t)(t − a) (b) > 0, ∀t > a where (b) is because Ψ ′′ n(t) > 0 (it is strictly convex in t).
Competitive Facility Location with Market Expansion and Customer-centric Objective t we get U ′(t) = −Ψ′ n(t) + Ψ′ n(t) + Ψ ′′ n(t)(t − a) (b) > 0, ∀t > a where (b) is because Ψ ′′ n(t) > 0 (it is strictly convex in t)
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.721913Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8ad3ce01-12c1-485b-9f72-045dfa835aea · outbound
This paper cites Thanks to the assertions in Lemma 3, we can derive the breakpoints cn 1 ,.
Competitive Facility Location with Market Expansion and Customer-centric Objective Thanks to the assertions in Lemma 3, we can derive the breakpoints cn 1 ,
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T05:58:17.709738Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.