Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T19:35:12.670195Z
Paper Citation Record · LEDGER
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions
As of 14 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2608.06857.
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 2026-08-14T06:32:32.682623+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
11 of 11 outbound references displayed
- verified exact2
- verified fuzzy8
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 3b0bd789-cf33-4921-8352-00a9bb040456 · outbound
This paper cites Kubo,Basicr-symmetric tropical polynomials, J.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Kubo,Basicr-symmetric tropical polynomials, J
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:13.039247Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 98d6145d-6614-433c-bd47-2c842fe44197 · outbound
This paper cites Stable complete coordinates for multisets of points via basic $r$-symmetric tropical polynomials.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Stable complete coordinates for multisets of points via basic $r$-symmetric tropical polynomials
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T19:35:12.889789Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 2b0e0cae-8b99-4c94-a81a-e0cb8d4c2068 · outbound
This paper cites Derksen,Tropical invariants for permutation group actions, arXiv:2512.13452 (2025).
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Derksen,Tropical invariants for permutation group actions, arXiv:2512.13452 (2025)
Reference 3
- Resolution
- verified exact
- raw_fallback, observed 2026-08-10T19:35:12.863077Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c6958502-d685-432c-a30e-d9a004e71b6d · outbound
This paper cites Cahill, J.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Cahill, J
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:13.023720Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 84d4ab34-fe9a-4eb0-a666-d549b504dd74 · outbound
This paper cites Rydh,A minimal set of generators for the ring of multisymmetric functions, Ann.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Rydh,A minimal set of generators for the ring of multisymmetric functions, Ann
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:13.006931Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 23c68acd-e561-45ca-a3da-56350e58d419 · outbound
This paper cites Lopatin and F.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Lopatin and F
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:12.989980Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e764dcd6-37a4-4d67-94f9-81a8f3d0062f · outbound
This paper cites Weyl,The Classical Groups, Princeton University Press, Princeton, 1939.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Weyl,The Classical Groups, Princeton University Press, Princeton, 1939
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:12.971953Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 67c5ee33-0d04-4345-9ad8-798e44bc3849 · outbound
This paper cites Ovchinnikov,Max-min representation of piecewise linear functions, Beitr¨ age Algebra Geom.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Ovchinnikov,Max-min representation of piecewise linear functions, Beitr¨ age Algebra Geom
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:12.947978Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 1b5d93cf-dab6-4ff6-bf09-95781569bae0 · outbound
This paper cites G-Invariant Representations using Coorbits: Bi-Lipschitz Properties.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions G-Invariant Representations using Coorbits: Bi-Lipschitz Properties
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-10T19:35:12.661345Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 813595dd-d1de-41dd-8728-62cf55bfad8f · outbound
This paper cites Vaccarino,The ring of multisymmetric functions, Ann.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Vaccarino,The ring of multisymmetric functions, Ann
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:12.927119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e6a07177-853d-4a3d-8208-b19509e4d750 · outbound
This paper cites Coste,An Introduction to Semialgebraic Geometry, lecture notes, Univ.
The basic tropical polynomials generate the semifield of $r$-symmetric tropical rational functions Coste,An Introduction to Semialgebraic Geometry, lecture notes, Univ
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T19:35:12.908836Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.