Paper Citation Record · LEDGER

Variants on the $abc$-Conjecture using Alternative Quality Metrics

As of 12 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2606.08416.

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

pith.paper-citation-record.v1
2606.08416 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T17:57:02.361629Z

measured 35 of 35 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 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

35 of 35 outbound references displayed

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verified fuzzy0
unresolved35
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malformed identifier0
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External citation measurements

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Outbound references

Observation edb8ce28-e859-4b7d-ab4c-756b22cf60ff · outbound

This paper cites th´ eoreme.

Variants on the $abc$-Conjecture using Alternative Quality Metrics th´ eoreme

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30742860-b4fd-40a6-b372-5c19caf40b5e · outbound

This paper cites Open problems.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Open problems

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 264f89c4-c80c-4904-b2c7-a35256fd26af · outbound

This paper cites Modular elliptic curves and Fermat’s last theorem.Annals of mathematics, 141(3):443–551, 1995.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Modular elliptic curves and Fermat’s last theorem.Annals of mathematics, 141(3):443–551, 1995

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 8d0171e1-63b6-40b7-929b-a4a3cced14e0 · outbound

This paper cites Lecture on theabcconjecture and some of its consequences.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Lecture on theabcconjecture and some of its consequences

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 3d368eb1-b8a9-47b1-b0c8-98f5837f9ebf · outbound

This paper cites Factoring integers with the number field sieve.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Factoring integers with the number field sieve

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 4459ed00-ee16-4740-9aee-7e892c4c6d5e · outbound

This paper cites It’s as easy asabc.Notices of the AMS, 49(10):1224–1231, 2002.

Variants on the $abc$-Conjecture using Alternative Quality Metrics It’s as easy asabc.Notices of the AMS, 49(10):1224–1231, 2002

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation c78da418-f064-43cc-a1eb-7d13fc28e92f · outbound

This paper cites ABC Triples.https://pub.math.leidenuniv.nl/ ~smitbde/abc/, 2020.

Variants on the $abc$-Conjecture using Alternative Quality Metrics ABC Triples.https://pub.math.leidenuniv.nl/ ~smitbde/abc/, 2020

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation cd91e744-22d8-4c36-8839-f2163313242e · outbound

This paper cites Algorithms for finding good examples for theabcand Szpiro conjectures.Experimental Mathematics, 2(3):223–230, 1993.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Algorithms for finding good examples for theabcand Szpiro conjectures.Experimental Mathematics, 2(3):223–230, 1993

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation daba1357-ab29-49f0-9490-3bb43516b1d2 · outbound

This paper cites An algorithm for finding goodabc-examples.Comptes rendus de l’Acad´ emie des sciences.

Variants on the $abc$-Conjecture using Alternative Quality Metrics An algorithm for finding goodabc-examples.Comptes rendus de l’Acad´ emie des sciences

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 8bcac6fe-3c7a-4469-b121-caba73c06040 · outbound

This paper cites Theabcconjecture home page, 2010.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Theabcconjecture home page, 2010

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation bda042a0-55d9-4819-b81f-e8e9536ce8c1 · outbound

This paper cites Masters thesis, Universiteit Leiden, 2010.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Masters thesis, Universiteit Leiden, 2010

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 20fb6ae4-ba22-474a-bc59-4023238caa75 · outbound

This paper cites The ABC’s of number theory.The Harvard College Mathematics Review, 1(1):57–76, 2007.

Variants on the $abc$-Conjecture using Alternative Quality Metrics The ABC’s of number theory.The Harvard College Mathematics Review, 1(1):57–76, 2007

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 897f9ad1-da7c-41c0-98a8-93f74be72cb0 · outbound

This paper cites an unresolved cited work.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation fab155b9-2928-4c4f-8767-c61e744b14b4 · outbound

This paper cites Cambridge University Press, 1984.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Cambridge University Press, 1984

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 6517fcd2-9396-485f-9cb0-e7e89d335418 · outbound

This paper cites Polynomial identities and Hauptmoduln.The Quarterly Journal of Mathematics, 32(3):349–370, 1981.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Polynomial identities and Hauptmoduln.The Quarterly Journal of Mathematics, 32(3):349–370, 1981

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 432596a3-db76-4495-a5c5-2ac84c7efac8 · outbound

This paper cites On theabcconjecture, II.Duke Mathematical Journal, 108(1):169–181, 2001.

Variants on the $abc$-Conjecture using Alternative Quality Metrics On theabcconjecture, II.Duke Mathematical Journal, 108(1):169–181, 2001

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation ec04e799-93df-48f4-827d-02d6c0f22300 · outbound

This paper cites Algorithms for Diophantine equations.CWI tracts, 65, 1989.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Algorithms for Diophantine equations.CWI tracts, 65, 1989

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Unavailable: canonical work link unavailable.

Observation a1621e8a-b977-486a-ae89-bf3fbdd65d56 · outbound

This paper cites Some remarks on theabc-conjecture.Mathematics of Computation, 62(206):931– 939, 1994.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Some remarks on theabc-conjecture.Mathematics of Computation, 62(206):931– 939, 1994

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 0fb036cd-8f37-445c-b63d-d288b6ed5ec5 · outbound

This paper cites Fermat numbers.University of Washington, 2010.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Fermat numbers.University of Washington, 2010

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 4e7b0850-0195-4eb7-8ffa-b4dca3c11c70 · outbound

This paper cites Mersenne primes: History, theorems and lists.Prime Pages, 2014.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Mersenne primes: History, theorems and lists.Prime Pages, 2014

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Unavailable: canonical work link unavailable.

Observation 0ed4147f-3720-404a-ac24-277e0d665b77 · outbound

This paper cites List Of Known Mersenne Prime Numbers, 2022.

Variants on the $abc$-Conjecture using Alternative Quality Metrics List Of Known Mersenne Prime Numbers, 2022

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation c87fb5f8-40d2-4b94-bc23-82532a92de2f · outbound

This paper cites Recent developments in primality testing.The Mathematical Intelligencer, 3(3):97–105, 1981.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Recent developments in primality testing.The Mathematical Intelligencer, 3(3):97–105, 1981

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation c796a928-d5cd-4329-b0bf-16b01575e471 · outbound

This paper cites Hardy and John E.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Hardy and John E

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 1af0a236-40ee-4b7e-b6af-e44e1bb37a29 · outbound

This paper cites On the representation of a large even integer as the sum of a prime and the product of at most two primes.Scientia Sinica, 16:157–176, 1973.

Variants on the $abc$-Conjecture using Alternative Quality Metrics On the representation of a large even integer as the sum of a prime and the product of at most two primes.Scientia Sinica, 16:157–176, 1973

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Unavailable: canonical work link unavailable.

Observation e7d1fafa-ba89-4132-9713-4c143cd7d6c7 · outbound

This paper cites Primary cyclotomic units and a proof of Catalan’s conjecture.Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal), 2004(572):167–195, 2004.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Primary cyclotomic units and a proof of Catalan’s conjecture.Journal f¨ ur die reine und angewandte Mathematik (Crelles Journal), 2004(572):167–195, 2004

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 8564233f-f75b-46ca-af72-588b2818ffba · outbound

This paper cites Springer-Verlag, Berlin, New York, 1987.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Springer-Verlag, Berlin, New York, 1987

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 91bc4ff9-7a9e-47f0-ad0e-cfa8264948af · outbound

This paper cites Explicit upper bounds for the solutions of some Diophantine equations.Publicationes Mathematicae Debrecen, 26(1-2):119–132, 1979.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Explicit upper bounds for the solutions of some Diophantine equations.Publicationes Mathematicae Debrecen, 26(1-2):119–132, 1979

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 52600853-215f-4f22-8c48-f72a6845a3c5 · outbound

This paper cites Silverman.The Arithmetic of Elliptic Curves, volume 106 ofGraduate Texts in Mathematics.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Silverman.The Arithmetic of Elliptic Curves, volume 106 ofGraduate Texts in Mathematics

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 586f517a-44e1-4152-bd4d-ab87dbafc721 · outbound

This paper cites Links between stable elliptic curves and certain Diophantine equations.Annales Universitatis Saraviensis.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Links between stable elliptic curves and certain Diophantine equations.Annales Universitatis Saraviensis

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 36e6d24d-dfa7-4732-9b1b-317b9bce6f4c · outbound

This paper cites Propri´ et´ es num´ eriques du faisceau dualisant relatif.Ast´ erisque, 86:44–78, 1981.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Propri´ et´ es num´ eriques du faisceau dualisant relatif.Ast´ erisque, 86:44–78, 1981

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Unavailable: canonical work link unavailable.

Observation 5a55453a-6985-482b-81ca-4a6d339040fa · outbound

This paper cites Zur theorie der elementaren mittel.Mathematische Zeitschrift, 74(1):91–98, 1960.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Zur theorie der elementaren mittel.Mathematische Zeitschrift, 74(1):91–98, 1960

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation f340de5b-3a08-4edb-81c2-2717244f0a9d · outbound

This paper cites Baker and Glyn Harman.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Baker and Glyn Harman

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation f0300673-988e-437e-ac8f-3fe8f831d916 · outbound

This paper cites Oxford university press, 1979.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Oxford university press, 1979

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 55c37dc4-d666-4d50-bf6b-811c84e443d6 · outbound

This paper cites Primes is in p.Annals of Mathematics, pages 781–793, 2004.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Primes is in p.Annals of Mathematics, pages 781–793, 2004

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Observation 86867577-65ad-46bd-9a4f-bf709994729a · outbound

This paper cites Springer, Berlin, Heidelberg, 3rd edition, 2008.

Variants on the $abc$-Conjecture using Alternative Quality Metrics Springer, Berlin, Heidelberg, 3rd edition, 2008

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-27T17:57:02.361629Z

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Pith citing papers

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