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Paper Citation Record · LEDGER

Polynomial potentials and nilpotent groups

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.835051Z digest=sha256:30c9c5db2b203688bb3ebf51e2d2b19eda722d497788a46bd2ee7a1da11a2cf4

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.844646Z digest=sha256:18950a77b348c2d49ebb121daad2f71e3488e1660261cd621dd8d52df86b91a4

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:d2792d0b99cb6a9ac14d3eb9ec2e927ec85359d869dff7bfc380fee3573f8c78

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.853182Z digest=sha256:308b85a03e723d14d60487ecd901c1186bef15378270541fc26b59e9530b319c

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

Resolution
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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=sha256:5a2673fdf164d8bd347ee06b11e1ac726fb1af76aa9e54db4aa5477e4f46b1f8

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.862199Z digest=sha256:ba0f77ae71bbc88a3169ebccfb20a79186d4f9751bd50e9808c379492bf8ad90

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.866294Z digest=sha256:f7541794b4348fa8f4dc552a8102ec309ec982db471e543862f780eacc373153

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.871281Z digest=sha256:c9bfb237a588e94607b70e449d25e28f71e122bbe386d3544910e8bf2bdb717b

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:bfc96580ba13c2cc6b94e5dc9eb2a0dfb2c8d59586f112bab62d46ffde01bba9

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

This paper cites Manimegalai, S.

Polynomial potentials and nilpotent groups Manimegalai, S

Reference 12

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

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:24:49.879381Z digest=sha256:d9486affdba32838f25b024ede5593a62f98142ebece66380634aa5664927e7f

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.882923Z digest=sha256:ef805266aa49d52b57e436ba188d86dea6c23ae78743c499f32e43cb5ef9e807

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.886914Z digest=sha256:23a15fed4a55a1ec799ab116d8ca7f8c10ff0f6eda7fd10360d96aec627d995b

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.890780Z digest=sha256:0753034cd1263fa46f9e3182f43de408bcb2354eb472786f853cbc44830d4911

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.894501Z digest=sha256:0767e8b06098c8745e806210f0e9bac5f72fdc92f2c149b9c37ecdc71d1a21c5

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.898490Z digest=sha256:68b4c3c5352398bddfe0a42aeeb957a0f762382cde71fa8cc31c3d1b6d397f63

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.902210Z digest=sha256:17f25935a9dde9fcab9fea1fed353e3ba410f325d8366a153783c296049cfc68

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.906442Z digest=sha256:3950e9014b99bee85bcea289a66c6bb1d11c346fdcd49e9d2bd47d13aa907ea7

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.914071Z digest=sha256:c98a2f0baa10fc95085c9082dbf9f0e85eaa8bfa118ada2d647d02c6c3c76249

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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

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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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.926543Z digest=sha256:658397a22939efee6918fe46f240fb8819f5c0d0958fa4903b0fd8a8842d9b15

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=sha256:9eeaf5e8aea41be144bbc05b70438d5c363eb12228b715633005c94bc15b431c

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.937784Z digest=sha256:19cca02f6ad0e27d77dcb033a320e31b73430e4c6d6558b7e36c60e439797111

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.942251Z digest=sha256:83c2a5ec25731a7bca76c31ff40fba540df90339f874b50670daf343699bfc17

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

This paper cites an unresolved cited work.

Polynomial potentials and nilpotent groups Unresolved cited work

Reference 28

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

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.946297Z digest=sha256:a7c780a45e1d559bd7d206106d953ccb2a34947871d1ad4b68a5e533d17bb276

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-11T15:24:49.950267Z digest=sha256:994e593046452e2036de9897b7a72640e2ffdbf677deefb8ccdb7bdf1bad9be9

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
unresolved
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=sha256:90624a2ab41d13b7fbba9b5d1d8422c5b6341e770bdae92b4bec79fefa7e86d3

Pith citing papers

No inbound Pith citation observations are available.