Paper Citation Record · LEDGER

Homotopical Observables and the Langlands Program via $\infty$-Topoi

As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2505.22558.

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

pith.paper-citation-record.v1
2505.22558 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:14:06.831608Z

measured 35 of 35 standing notices

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measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

35 of 35 outbound references displayed

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External citation measurements

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Outbound references

Observation 02c84e5c-f3e4-4741-b514-d9a99a96965d · outbound

This paper cites Artin and J.-L.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Artin and J.-L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:14.558057Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 09d2596d-e310-4e62-bfff-64f42e773b83 · outbound

This paper cites Arthur, The Selberg trace formula for groups of F-rank one , Ann.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Arthur, The Selberg trace formula for groups of F-rank one , Ann

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:14.272820Z

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Observation de1cec3a-8596-435c-979b-fe27339e7847 · outbound

This paper cites Arthur, An introduction to the trace formula , in: Harmonic analysis, the trace formula, and Shimura varieties, Clay Math.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Arthur, An introduction to the trace formula , in: Harmonic analysis, the trace formula, and Shimura varieties, Clay Math

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:14.026828Z

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Observation e0bdddce-c27c-4ea6-8f40-2a6536d64681 · outbound

This paper cites Awodey, Category Theory, Oxford Logic Guides, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Awodey, Category Theory, Oxford Logic Guides, vol

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:13.682875Z

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Observation 3ae6b899-a945-414a-b04d-5aa68efe8d5a · outbound

This paper cites Awodey and K.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Awodey and K

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:13.436788Z

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Observation 304e851c-9cab-4bfe-86f1-c2bfef8cd092 · outbound

This paper cites Bhatt and P.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Bhatt and P

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:13.271718Z

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Observation 79eb5327-a417-4929-b3b6-2a56d49d7c02 · outbound

This paper cites Carlitz, A class of polynomials , Trans.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Carlitz, A class of polynomials , Trans

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:13.010438Z

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Observation f6525c2a-9b22-46ec-befc-41bb24f01860 · outbound

This paper cites Connes, Noncommutative Geometry, Academic Press, 1994.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Connes, Noncommutative Geometry, Academic Press, 1994

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:12.737486Z

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Observation cf7c0ae0-c9ac-42c5-ae0a-6a2c89668ee4 · outbound

This paper cites Drinfeld, Elliptic modules , Math.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Drinfeld, Elliptic modules , Math

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:12.490188Z

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Observation e9504648-39ca-4bef-bb0a-98ff5fe81a41 · outbound

This paper cites Drinfeld, Proof of the Langlands conjecture for GL(2) over functional ﬁ elds, Invent.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Drinfeld, Proof of the Langlands conjecture for GL(2) over functional ﬁ elds, Invent

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:12.198012Z

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Observation bb980617-bef7-49ce-a27e-06bdd57bc0a1 · outbound

This paper cites Faltings, A proof for the Langlands conjecture for GL(n) over function ﬁ elds, preprint.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Faltings, A proof for the Langlands conjecture for GL(n) over function ﬁ elds, preprint

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:11.965700Z

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Observation 53057a7f-9ac8-4631-956d-24306bb4f7b6 · outbound

This paper cites Grothendieck, ´El´ ements de g´ eom´ etrie alg´ ebrique, Publ.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Grothendieck, ´El´ ements de g´ eom´ etrie alg´ ebrique, Publ

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:11.764647Z

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Observation 1bc93c5b-3f0e-4c18-91ad-cab8452a84d3 · outbound

This paper cites Grothendieck and J.L.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Grothendieck and J.L

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:10.915144Z

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Observation 4fd43209-d428-46ca-9965-0ea348e18e57 · outbound

This paper cites Jacobs, Introduction to Coalgebra: Towards Mathematics of States and Observation, Cam- bridge University Press, 2016.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Jacobs, Introduction to Coalgebra: Towards Mathematics of States and Observation, Cam- bridge University Press, 2016

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:10.545619Z

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Observation 700fa430-52a0-4ea8-b45e-f6a5c186af57 · outbound

This paper cites Jacobs, Categorical Logic and Type Theory , Studies in Logic and the Foundations of Math- ematics, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Jacobs, Categorical Logic and Type Theory , Studies in Logic and the Foundations of Math- ematics, vol

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:10.401335Z

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Observation 9d1981f8-aa4d-4b0b-8a5f-fde535a190d7 · outbound

This paper cites Johnstone, Topos Theory, London Mathematical Society Monographs, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Johnstone, Topos Theory, London Mathematical Society Monographs, vol

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:10.210637Z

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Observation ca895409-16ee-4085-aabd-e2ffdf502b26 · outbound

This paper cites Johnstone, Sketches of an Elephant: A Topos Theory Compendium , 2 vols., Oxford Logic Guides, vols.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Johnstone, Sketches of an Elephant: A Topos Theory Compendium , 2 vols., Oxford Logic Guides, vols

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:10.120807Z

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Observation 510b796d-37e4-427f-9560-a6d977b5c325 · outbound

This paper cites Kozen, Semantics of probabilistic programs , J.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Kozen, Semantics of probabilistic programs , J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.945994Z

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Observation f9330ce6-f78e-490f-a978-eb70f1225117 · outbound

This paper cites Laﬀorgue, Chtoucas de Drinfeld et correspondance de Langlands , Invent.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Laﬀorgue, Chtoucas de Drinfeld et correspondance de Langlands , Invent

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.813085Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 91cc0001-bdb2-466f-8c4e-683ec3412d2c · outbound

This paper cites Langlands, Problems in the theory of automorphic forms , in: Lectures in modern analysis and applications III, LNM 170, Springer, 1970, pp.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Langlands, Problems in the theory of automorphic forms , in: Lectures in modern analysis and applications III, LNM 170, Springer, 1970, pp

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.693761Z

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Observation 05400e42-4274-4483-aa1f-0f0499d89b5a · outbound

This paper cites Lawvere, Cohesive toposes and Cantor’s ”lauter Einsen” , Philos.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Lawvere, Cohesive toposes and Cantor’s ”lauter Einsen” , Philos

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.565747Z

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Observation f2909905-4905-4339-901e-f42ccbacfb83 · outbound

This paper cites Lawvere, Quantiﬁers and sheaves , in: Actes du Congr` es International des Math´ ematiciens (Nice, 1970), Tome 1, Gauthier-Villars, 1971, pp.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Lawvere, Quantiﬁers and sheaves , in: Actes du Congr` es International des Math´ ematiciens (Nice, 1970), Tome 1, Gauthier-Villars, 1971, pp

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.406550Z

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Observation f89bce62-ad7b-459c-a2a5-fd8f7a71d887 · outbound

This paper cites Lurie, Higher Topos Theory, Annals of Mathematics Studies, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Lurie, Higher Topos Theory, Annals of Mathematics Studies, vol

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.279268Z

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Observation 42870a30-b4cc-46fb-8d2f-d4ddeb91195e · outbound

This paper cites Lurie, Spectral Algebraic Geometry, available at https://www.math.ias.edu/~lurie/papers/SAG-rootfil.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Lurie, Spectral Algebraic Geometry, available at https://www.math.ias.edu/~lurie/papers/SAG-rootfil

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.126810Z

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Observation f0731b13-dced-465d-9681-7de34ab8d471 · outbound

This paper cites Mac Lane and I.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Mac Lane and I

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:09.004140Z

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Observation 60765084-6492-4415-92db-856a4ab70666 · outbound

This paper cites Milnor, On spaces having the homotopy type of CW-complex , Trans.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Milnor, On spaces having the homotopy type of CW-complex , Trans

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.889498Z

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Observation 81effba6-65ac-4d7b-aff6-18c241f8599c · outbound

This paper cites Quillen, Homotopical Algebra, Lecture Notes in Mathematics, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Quillen, Homotopical Algebra, Lecture Notes in Mathematics, vol

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.728396Z

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Observation 1358b0f9-0f76-455b-95e4-dcc73c1b6fa6 · outbound

This paper cites Rutten, Universal coalgebra: a theory of systems , Theoret.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Rutten, Universal coalgebra: a theory of systems , Theoret

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.552788Z

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Observation 8593ecf0-0174-4b0a-8718-9bcd94c71153 · outbound

This paper cites Rutten, Automata and coinduction (an exercise in coalgebra) , in: CONCUR’98, LNCS 1466, Springer, 1998, pp.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Rutten, Automata and coinduction (an exercise in coalgebra) , in: CONCUR’98, LNCS 1466, Springer, 1998, pp

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.456721Z

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Observation e0f713ef-4de8-4614-8053-36db4215781d · outbound

This paper cites Scholze, Perfectoid spaces, Publ.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Scholze, Perfectoid spaces, Publ

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.332311Z

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Observation d691f3b4-75ac-4793-900e-aad2fbd48f7b · outbound

This paper cites Serre, Galois Cohomology, Springer Monographs in Mathematics, Springer-Verlag, 19 97.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Serre, Galois Cohomology, Springer Monographs in Mathematics, Springer-Verlag, 19 97

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.188043Z

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Observation cc87806a-b199-4016-8a8b-83b2e129f6d4 · outbound

This paper cites Vickers, Topology via Logic , Cambridge Tracts in Theoretical Computer Science, vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Vickers, Topology via Logic , Cambridge Tracts in Theoretical Computer Science, vol

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:08.070496Z

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Observation 8d6e8315-dedf-419c-beba-3a671a48eb9d · outbound

This paper cites Voevodsky, Triangulated categories of motives over a ﬁeld , in: Cycles, transfers, and motivic homology theories, Ann.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Voevodsky, Triangulated categories of motives over a ﬁeld , in: Cycles, transfers, and motivic homology theories, Ann

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:07.798862Z

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Observation 62d5a382-5228-4783-9d41-270786a867f1 · outbound

This paper cites Voevodsky, A1-homotopy theory , in: Proceedings of the International Congress of Mathe- maticians (Berlin, 1998), Vol.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Voevodsky, A1-homotopy theory , in: Proceedings of the International Congress of Mathe- maticians (Berlin, 1998), Vol

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:07.461697Z

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Observation b81bb9d2-b794-4f25-aa05-48744071aea0 · outbound

This paper cites Witten, Quantum ﬁeld theory and the Jones polynomial , Comm.

Homotopical Observables and the Langlands Program via $\infty$-Topoi Witten, Quantum ﬁeld theory and the Jones polynomial , Comm

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T13:14:07.104047Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

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