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Paper Citation Record · LEDGER

More on consecutive multiplicatively dependent triples of integers

As of 12 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2411.12009.

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

pith.paper-citation-record.v1
2411.12009 v2

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T18:11:19.607217Z

measured 24 of 24 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 2026-08-06T16:57:17.266590Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T16:57:20.069394Z

Reference resolution

23 of 23 outbound references displayed

  • verified exact10
  • verified fuzzy5
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 97f73b1e-3dae-4fcf-850e-12dd23500337 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 1

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.843845Z

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.

source=pdf_text observed=2026-08-12T18:11:19.498573Z digest=sha256:419c79ce3d03707c6c94d6de25e2a1b14373fb2e7ebbee52a14e64e964bd25d8

Observation d903aec9-4f05-4b6c-a1d8-39ce7a7b2fdf · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 2

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.829092Z

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.

source=pdf_text observed=2026-08-12T18:11:19.504519Z digest=sha256:75344f253cd655b121c646ce0fb898cb82fd6b730d610188d071643b8b85f196

Observation c1974ff5-1ad7-4a73-afcb-b4e3a44d44b5 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 3

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.509778Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.509778Z digest=sha256:e9c5ca277995f4bd1d845ac04565d1e1dfbcd9fa8ea7cf66da06879b93b8f0d5

Observation 9b8e085a-4a6a-472e-af50-5863087d6c27 · outbound

This paper cites Bugeaud, M.

More on consecutive multiplicatively dependent triples of integers Bugeaud, M

Reference 4

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.804251Z

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.

source=pdf_text observed=2026-08-12T18:11:19.514508Z digest=sha256:3e2d533d177a67a9239471a70195f7c46e317932b71264ba5b9469c879592cfb

Observation 5ff01a18-938f-4fed-9187-fb9b617b4114 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.519171Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.519171Z digest=sha256:d3f976af1a55619e14bd2d64c1e9293fe98c96e891a52f637182c6096f7261f7

Observation 8259086b-0df9-4d65-a2a7-0e1f422ad1eb · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 6

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.780168Z

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.

source=pdf_text observed=2026-08-12T18:11:19.524678Z digest=sha256:a405342bb685e0a7affb116628fe084c532ca022cf469eea1471690ff3519e5f

Observation 26c375c3-3760-4ee8-8040-91bceb6d54d2 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.529776Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.529776Z digest=sha256:0cf0f5e680b93ed76dfccfd1253653ae26dbff8ae0b305f8860c14dac8bc5392

Observation c3a3a14a-37c3-4e5e-bf67-88470a98e3bd · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-12T18:11:19.958639Z

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.

source=pdf_text observed=2026-08-12T18:11:19.534611Z digest=sha256:edfacf5f74041ebcf8f7f6e3fa0291d0c0958faa5d8de0a2ddc48f8c67ae2119

Observation b88a8442-6c29-4dad-a9fe-7247c375dd2a · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 9

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.740684Z

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.

source=pdf_text observed=2026-08-12T18:11:19.544574Z digest=sha256:75a1193ec1c0fb0d4da56a2c870fcafb25ce5115f968786b1bde78e9cb80ba59

Observation 2c279677-7d34-445e-8eab-3c49157897ba · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 10

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.721374Z

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.

source=pdf_text observed=2026-08-12T18:11:19.549363Z digest=sha256:f19429afba8136ccb84ad64eac7ca29acbff78d638cb3760a6c4271a9f5e1431

Observation bca6291a-55e1-40b9-8b6b-d361801b7488 · outbound

This paper cites Ljunggren.

More on consecutive multiplicatively dependent triples of integers Ljunggren

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T18:11:19.943178Z

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.

source=pdf_text observed=2026-08-12T18:11:19.553946Z digest=sha256:a7d19c49d4657eac6094fdbb1f10ead57a07d40590d50518f94e3eee10599673

Observation 898516d7-5d47-46a3-820e-df6d88104130 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.558746Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.558746Z digest=sha256:b359a77ad36322f947d78666853e124fa02ee1760d14c991907c39fcd36499f7

Observation b6a51d6a-4afb-4853-aaa7-f8806a546be2 · outbound

This paper cites Mih˘ ailescu.

More on consecutive multiplicatively dependent triples of integers Mih˘ ailescu

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.564257Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.564257Z digest=sha256:bda550d6467eca1b2f2712838e568e6cd60360dbec482dd1abb30cca5cefdd7a

Observation 2ec476eb-6bd4-4978-963d-6ef04c5def85 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 14

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.685782Z

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.

source=pdf_text observed=2026-08-12T18:11:19.568759Z digest=sha256:d991e857f9f2da4423237df0b9ef1be63c2f66892b70831d8fda38099fb62928

Observation bf1e5cc6-ef2d-4dba-bd14-4ebfbcbeef43 · outbound

This paper cites Pappalardi, M.

More on consecutive multiplicatively dependent triples of integers Pappalardi, M

Reference 15

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.669411Z

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.

source=pdf_text observed=2026-08-12T18:11:19.573511Z digest=sha256:06eff54415b55e72f72bafc3d9d3b7ec6309cb3309450a25bd75df9523a21e27

Observation 2d521e3e-dd76-4294-8efd-bae4e7f01944 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-12T18:11:19.925071Z

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.

source=pdf_text observed=2026-08-12T18:11:19.578026Z digest=sha256:e15d4244cc0d12c3452f5d8756f5e6ed4c04a7902af4779a81bd3367478fa900

Observation 5e880ac1-39d6-462a-ab2a-01250ffdc9a3 · outbound

This paper cites St¨ ormer.

More on consecutive multiplicatively dependent triples of integers St¨ ormer

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T18:11:19.908618Z

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.

source=pdf_text observed=2026-08-12T18:11:19.582287Z digest=sha256:8d1a70ad0ceabe6f72081dfea66c4b43fcd840764a73242b18c80bb4ed81576c

Observation 774a24a7-b01f-4190-9138-1fc7268a7ed7 · outbound

This paper cites Tervooren.

More on consecutive multiplicatively dependent triples of integers Tervooren

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T18:11:19.892368Z

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.

source=pdf_text observed=2026-08-12T18:11:19.586958Z digest=sha256:37d316bc70f9a0f0d7430398f3bbba092c212707381663620c4e7f875b562287

Observation de21eda1-308d-49fd-b26c-dfc1c81ebc81 · outbound

This paper cites SageMath, the Sage Mathematics Software System (Version 9.

More on consecutive multiplicatively dependent triples of integers SageMath, the Sage Mathematics Software System (Version 9

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T18:11:19.876644Z

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.

source=pdf_text observed=2026-08-12T18:11:19.592544Z digest=sha256:0a5f79585050c31c8b15ae99f9c72ce714fc27a23bedf7e47ccfb75946947c3b

Observation 98cd301a-3b32-47d3-a617-7b12b0979650 · outbound

This paper cites Vukusic and V.

More on consecutive multiplicatively dependent triples of integers Vukusic and V

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-12T18:11:19.860061Z

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.

source=pdf_text observed=2026-08-12T18:11:19.597168Z digest=sha256:46c240c8201b73043d9bb6106e6e084705565b8c0693f6d041a80496172d6527

Observation 1488b74b-d449-429a-961d-3a3f625d4b82 · outbound

This paper cites Zsigmondy.

More on consecutive multiplicatively dependent triples of integers Zsigmondy

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-12T18:11:19.607217Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T18:11:19.607217Z digest=sha256:90f00082835ba9ded37defdd637811c802bcc958008223b92630fa0dc3c171a1

Observation 8dc34142-7c02-40c6-b6dd-159d7803d802 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 1991

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.755678Z

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.

source=pdf_text observed=2026-08-12T18:11:19.539685Z digest=sha256:5e3b54f936b52aa53fe628d61c41f182fc68ef164eb36c93aaf9c69304d02685

Observation 8a1ba3b7-317b-4379-a6d2-ead4bf89d9b3 · outbound

This paper cites an unresolved cited work.

More on consecutive multiplicatively dependent triples of integers Unresolved cited work

Reference 2021

Resolution
verified exact
doi, observed 2026-08-12T18:11:19.653683Z

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.

source=pdf_text observed=2026-08-12T18:11:19.601974Z digest=sha256:92d2b1b578befadc261deab393bb1d4782a2e8a9b100d2ada7bb11f5b8f7a92d

Pith citing papers

Observation 7cd6e429-ec48-495c-95f7-512c8104fe82 · inbound

On the Lebesgue-Nagell equation $x^2-2 = y^p$ cites this paper.

On the Lebesgue-Nagell equation $x^2-2 = y^p$ More on consecutive multiplicatively dependent triples of integers

Reference 2

Resolution
metadata mismatch
local_arxiv, observed 2026-08-06T16:57:20.182149Z

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.

source=pdf_text observed=2026-08-06T16:57:17.266590Z digest=sha256:3f555903bffa5a3d9e69c6e6ee6de8349fdaf47ea984bf7c7de6bf0eb1a56f23