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Paper Citation Record · LEDGER

Polynomial potentials and nilpotent groups

As of 22 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2412.11157.

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

pith.paper-citation-record.v1
2412.11157 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:24:49.950267Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

  • verified exact14
  • verified fuzzy5
  • unresolved5
  • parse uncertain0
  • malformed identifier5
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a857e1b5-675d-441f-875b-32ab7320ef71 · outbound

This paper cites Turbiner, A.

Polynomial potentials and nilpotent groups Turbiner, A

Reference 1

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.151039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 70db22b2-1b6c-4274-b8c4-d6b527a80c6e · outbound

This paper cites Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics, Taylor & Francis, New York, 1994.

Polynomial potentials and nilpotent groups Ushveridze, Quasi-Exactly Solvable Models in Quantum Mechanics, Taylor & Francis, New York, 1994

Reference 2

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.139420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.835051Z digest=sha256:9b36cf7fcbf75cd6662b8d43534c23c288c78ff16bd75e9ced8ea63505d8efc0

Observation 25955e97-a703-44d9-887e-a93a2e4f52a5 · outbound

This paper cites Turbiner, Quasiexactly solvable problems and SL(2) group, Commun.

Polynomial potentials and nilpotent groups Turbiner, Quasiexactly solvable problems and SL(2) group, Commun

Reference 3

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.127458Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 676e0a73-c3b8-43a8-8eea-66ce6b5e421f · outbound

This paper cites Gonz´ alez-L´ opez, N.

Polynomial potentials and nilpotent groups Gonz´ alez-L´ opez, N

Reference 4

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.115223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.844646Z digest=sha256:864998a9a4a3f620dda52b73fd631d59b97c4a4afec4edd7653fe55af04a8416

Observation 5d2fcc6a-5171-487a-95bd-014ec114d997 · outbound

This paper cites One-Dimensional Quasi-Exactly Solvable Schr\"odinger Equations.

Polynomial potentials and nilpotent groups One-Dimensional Quasi-Exactly Solvable Schr\"odinger Equations

Reference 5

Resolution
malformed identifier
no resolver link, observed 2026-08-11T15:24:49.848801Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.848801Z digest=sha256:2513a35e1c27aa8c594a6fedfe9a6a4f9a067e3bfbc6b8f135c868ea59df0837

Observation eaa1f2f4-6ed5-4cdb-b1aa-1f52d4918e2a · outbound

This paper cites Gomez-Ullate, N.

Polynomial potentials and nilpotent groups Gomez-Ullate, N

Reference 6

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.103003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.853182Z digest=sha256:542f9dbb0d8e09c2a104dcaa6d5e5b81192466c783a2b412940e47cd92afbdc1

Observation ae3f03fc-9e14-4186-bba2-971e78f01e54 · outbound

This paper cites Magyari, Exact quantum mechanical solutions for anharmonic oscil- lators, Phys.

Polynomial potentials and nilpotent groups Magyari, Exact quantum mechanical solutions for anharmonic oscil- lators, Phys

Reference 7

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no resolver link, observed 2026-08-11T15:24:49.857868Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.857868Z digest=sha256:4f5557dca65202fe79ec4fca864dc9c0ba9861889962110d2a52ffb3cfa10495

Observation 3d6e57c7-5719-485f-984f-9c52641533f9 · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 8

Resolution
malformed identifier
raw_fallback, observed 2026-08-11T15:24:50.493454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.862199Z digest=sha256:f8a93d35ba4b1b07002bd3f1860a6bef5f43b1c544eca4fe35f5c68d09042541

Observation c28a888e-0afc-427a-9684-1a2268848283 · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 9

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.083590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.866294Z digest=sha256:e16bae1e42098bb951f7bb3cff11d0039da5b59bf5701333594a8ae7b8a382c8

Observation db26c2cf-5a15-4c39-818d-62808af027ff · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 10

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.071812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation 3126d859-639b-46d8-a91d-52f8b9db2c2c · outbound

This paper cites Amore, F.

Polynomial potentials and nilpotent groups Amore, F

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-11T15:24:49.875249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.875249Z digest=sha256:690ab981c7a7b45d47e93cfd0615707c64fcba660b97990af31c6a8df6b3d4c1

Observation 3565710c-fe24-4ef8-8f97-d850109c0218 · outbound

This paper cites Manimegalai, S.

Polynomial potentials and nilpotent groups Manimegalai, S

Reference 12

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no resolver link, observed 2026-08-11T15:24:49.879381Z

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Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.879381Z digest=sha256:5efcb6905f302e60f507c0afe635d111a6727cfe2a0a5782743d731b620dd47f

Observation d96b320a-30fa-4051-b7e3-bc6af1feac1f · outbound

This paper cites Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems.

Polynomial potentials and nilpotent groups Bethe ansatz solutions and hidden $sl(2)$ algebraic structure for a class of quasi-exactly solvable systems

Reference 13

Resolution
malformed identifier
local_arxiv, observed 2026-08-11T15:24:50.381795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.882923Z digest=sha256:42225fb7824ee5dc3bb20d8c8bea38618a2233871c116896f64052f9cc9c9bd2

Observation db34a120-3722-4f0c-be19-10fe9932dbe3 · outbound

This paper cites Brandon, N.

Polynomial potentials and nilpotent groups Brandon, N

Reference 14

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.044390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.886914Z digest=sha256:74c46feebb7b6a38cb1090093c9cd5c54e2572d0626d09cdfa9bb5593aed28e2

Observation dbfcf37d-7a7c-4c53-906b-5189bc1a70f0 · outbound

This paper cites Sk´ ala, J.

Polynomial potentials and nilpotent groups Sk´ ala, J

Reference 15

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.031692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.890780Z digest=sha256:ca623686dbb3cc067a82228a90fe15e00a466c56bc27b5638ce04570676d559a

Observation e1899557-c991-46c1-8011-b2901fa81371 · outbound

This paper cites Znojil, Symmetrized quartic polynomial oscillators and their partial exact solvability, Phys.

Polynomial potentials and nilpotent groups Znojil, Symmetrized quartic polynomial oscillators and their partial exact solvability, Phys

Reference 16

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.019185Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.894501Z digest=sha256:3726e0c0db3bb2270d1e326ddffc53e5727a4176a86b48f19554af3271ac25c6

Observation 81ddc9b4-49c4-4b3e-b93d-b02a7bd93f06 · outbound

This paper cites Quesne, Quasi-exactly solvable symmetrized quartic and sextic poly- nomial oscillators, Eur.

Polynomial potentials and nilpotent groups Quesne, Quasi-exactly solvable symmetrized quartic and sextic poly- nomial oscillators, Eur

Reference 17

Resolution
verified exact
doi, observed 2026-08-11T15:24:50.005243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.898490Z digest=sha256:4837620743328c68239aa76f0d7782af364e442bf0addea3b0ec7bcea9552e50

Observation 337e8947-be3a-4ca4-93e2-d85dde4014a6 · outbound

This paper cites Polynomial Solutions of Generalized Quartic Anharmonic Oscillators.

Polynomial potentials and nilpotent groups Polynomial Solutions of Generalized Quartic Anharmonic Oscillators

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-11T15:24:50.364889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.902210Z digest=sha256:24cd871a0b2f7c2336b587645fc5efaf8a353993f278b7e857ceb0bacdb68c3c

Observation 5ca855e3-5687-4378-aa71-89a9f26a7af0 · outbound

This paper cites Jørgensen, W.

Polynomial potentials and nilpotent groups Jørgensen, W

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T15:24:50.481824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.906442Z digest=sha256:c0df2024620871b18a565d0cf3745ef9033d16d0a30f1b00c3e1ca311f563b2b

Observation c7298543-f183-4b69-a652-139c345c7376 · outbound

This paper cites Klink, Nilpotent groups and anharmonic oscillators, in: E.

Polynomial potentials and nilpotent groups Klink, Nilpotent groups and anharmonic oscillators, in: E

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T15:24:50.468905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.914071Z digest=sha256:ac2013c10c09e06e853be0f2ffde84f628749ccb63f45ae361f6d08ef2dfacbb

Observation 976feedc-a956-4b44-a6ae-56c1b86b86bd · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-11T15:24:50.455127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation e64b1f68-1eca-4873-b2b4-4ccd07bc788d · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 22

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unresolved
raw_fallback, observed 2026-08-11T15:24:50.442790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.922930Z digest=sha256:083f67fe124ce81c7b0ef899cb2649ef82149ed5e53146f8f980e9b5a74f767c

Observation a92d02cc-04c0-470b-a06c-6b8de917e636 · outbound

This paper cites Gesztesy, R.

Polynomial potentials and nilpotent groups Gesztesy, R

Reference 23

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verified fuzzy
raw_fallback, observed 2026-08-11T15:24:50.430272Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

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Observation c5970242-c61a-4414-a063-7cfd0ff90cbe · outbound

This paper cites Jafarpour, D.

Polynomial potentials and nilpotent groups Jafarpour, D

Reference 25

Resolution
malformed identifier
no resolver link, observed 2026-08-11T15:24:49.934144Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.934144Z digest=sha256:cd587fc36b033a03392e43c429e0293fbd7dedf98daaf2dda3dbc3b16239b823

Observation 6ee15df8-f818-4230-8d0d-27d94ae05a88 · outbound

This paper cites Pathak, S.

Polynomial potentials and nilpotent groups Pathak, S

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T15:24:50.417430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.937784Z digest=sha256:7bb90b09b907e70d0b5e4c0dcf53e4e0305d3cc98a448fc85f8ea47234ddadf3

Observation 7f3de7d1-b9fe-43b4-867c-4fcf4a5174b3 · outbound

This paper cites A new general approximation scheme(NGAS) in quantum theory:application to the anharmonic- and double well oscillators.

Polynomial potentials and nilpotent groups A new general approximation scheme(NGAS) in quantum theory:application to the anharmonic- and double well oscillators

Reference 27

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verified exact
local_arxiv, observed 2026-08-11T15:24:50.169602Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.942251Z digest=sha256:79ee91851dd1fcaa0edd3a334a9aa57a900b278bfd6068662a365cb470bb6b92

Observation 51ee02e7-541e-4e5c-9fb3-5597d0291b5d · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 28

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verified exact
doi, observed 2026-08-11T15:24:49.983199Z

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No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.946297Z digest=sha256:9f7485053cc425fd009293f447ccedb756e88ccec1872cfce1c1d1813172b762

Observation 6ca730d5-82fc-48ed-b7c5-99cd4f5bf39e · outbound

This paper cites Landau, E.

Polynomial potentials and nilpotent groups Landau, E

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T15:24:50.405401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-11T15:24:49.950267Z digest=sha256:2f2f485917c17e804f38b7fc5cff1d87f90dc4ab57bb5bbc9755d9837c57d885

Observation ba0f4287-ca9c-4c08-9217-d7409586ff9a · outbound

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 999

Resolution
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no resolver link, observed 2026-08-11T15:24:49.910080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.910080Z digest=sha256:b6af6d58b20dbc55eff0a877c789eb9a830724f6fe7d6fd57eea1c3dbd93994c

Pith citing papers

No inbound Pith citation observations are available.