Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:43:12.233790Z
Paper Citation Record · LEDGER
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems
As of 16 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 0 inbound Pith citation observations for arXiv:1908.04819.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
46 of 46 outbound references displayed
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- verified fuzzy40
- unresolved6
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- malformed identifier0
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5227ed9c-6f17-4f4c-9dc3-4353c3a5aef8 · outbound
This paper cites an unresolved cited work.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:43:12.989396Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d5563747-efc5-4833-a578-b6ea2ba2c990 · outbound
This paper cites Andr\'e, Homomorphismes r\'eguliers en characteristique p , C.R.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Andr\'e, Homomorphismes r\'eguliers en characteristique p , C.R
Reference 2
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- raw_fallback, observed 2026-08-14T13:43:12.973607Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7e7d62d3-60cb-40f5-adef-45be745a0dc9 · outbound
This paper cites Blickle and F.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Blickle and F
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.957645Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 605799bb-7c0b-4087-80e7-f194e9ad1232 · outbound
This paper cites Blum, Existence of valuations with smallest normalized volume, Comp.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Blum, Existence of valuations with smallest normalized volume, Comp
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.941891Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0811ddb9-7b3c-464e-a98a-adf8ffe75c66 · outbound
This paper cites Bourbaki, Commutative algebra, Chapters 1-7 , Elements of Mathematics , Springer-Verlag, 1989.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Bourbaki, Commutative algebra, Chapters 1-7 , Elements of Mathematics , Springer-Verlag, 1989
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.926205Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08ec0ba3-b937-42ab-b41b-44cc64f2f292 · outbound
This paper cites Cumino, S.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Cumino, S
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.910856Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 902a1376-fcb7-4490-b2ec-d3410b9d9149 · outbound
This paper cites Carvajal-Rojas, K.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Carvajal-Rojas, K
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.895921Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7c8eaa53-f22b-4221-935f-8bf173e15842 · outbound
This paper cites Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.880951Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 03416651-ef67-48dd-8d42-f04358957643 · outbound
This paper cites Datta, Uniform approximation of A bhyankar valuation ideals in function fields of prime characteristic , 2017, To appear in Trans.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Datta, Uniform approximation of A bhyankar valuation ideals in function fields of prime characteristic , 2017, To appear in Trans
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.865606Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8f0838f4-6468-4a56-b6e1-7a9ccd744783 · outbound
This paper cites de Fernex, L.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems de Fernex, L
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.850249Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f42092a1-9292-4a42-a900-a33c53f0c8b9 · outbound
This paper cites Permanence properties of $F$-injectivity.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Permanence properties of $F$-injectivity
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:43:12.065644Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a67ee0fe-2c5b-4dc4-a02e-90bad016e084 · outbound
This paper cites De Stefani, T.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems De Stefani, T
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.835457Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 89c23219-0521-4ca1-ba86-efed84e5bddf · outbound
This paper cites Dumitrescu, Reducedness, formal smoothness and approximation in characteristic p , Communications in Algebra 23 (1995), no.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Dumitrescu, Reducedness, formal smoothness and approximation in characteristic p , Communications in Algebra 23 (1995), no
Reference 13
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- raw_fallback, observed 2026-08-14T13:43:12.820456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 16efce01-e2d9-483b-b24a-3180e26c8d7a · outbound
This paper cites Grothendieck, \'El\'ements de g\'eom\'etrie alg\'ebrique : III.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Grothendieck, \'El\'ements de g\'eom\'etrie alg\'ebrique : III
Reference 14
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- raw_fallback, observed 2026-08-14T13:43:12.804865Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 13cb8e8f-7709-4990-89be-576756e7076f · outbound
This paper cites \'e tude locale des sch\'emas et des morphismes de sch\'emas, Premi\`ere partie , vol.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems \'e tude locale des sch\'emas et des morphismes de sch\'emas, Premi\`ere partie , vol
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.788579Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 1835c66b-07ae-4edd-81a7-ee23f96142fa · outbound
This paper cites \'e tude locale des sch\'emas et des morphismes de sch\'emas, Seconde partie , vol.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems \'e tude locale des sch\'emas et des morphismes de sch\'emas, Seconde partie , vol
Reference 16
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- raw_fallback, observed 2026-08-14T13:43:12.772196Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e1444fd9-045c-4daa-aaac-1f02e96d8c23 · outbound
This paper cites \'e tude locale des sch\'emas et des morphismes de sch\'emas, Troisi\`eme partie , vol.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems \'e tude locale des sch\'emas et des morphismes de sch\'emas, Troisi\`eme partie , vol
Reference 17
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- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.756607Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 46f1ec94-f6cf-4a6f-b28c-af5ecb5b1d77 · outbound
This paper cites an unresolved cited work.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:43:12.741121Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d35eef6b-e7bd-4c7f-81d3-ff076c59210f · outbound
This paper cites an unresolved cited work.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:43:12.725640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b83b6eea-ef1e-4f9d-a603-90fab5042af1 · outbound
This paper cites G \"o rtz and T.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems G \"o rtz and T
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.709456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 13043235-907c-4fb4-bbd6-286341d49631 · outbound
This paper cites Hanes, Special conditions on maximal Cohen-Macaulay modules, and applications to the theory of multiplicities , Ph.D.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Hanes, Special conditions on maximal Cohen-Macaulay modules, and applications to the theory of multiplicities , Ph.D
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.694063Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 67d7d24b-aaca-4ba2-b63a-f5aaee4a8760 · outbound
This paper cites Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.677060Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4193bb6d-200e-4585-90d0-c276dbc84626 · outbound
This paper cites Hara, A characteristic p analogue of multiplier ideals and applications, Comm.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Hara, A characteristic p analogue of multiplier ideals and applications, Comm
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.661739Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9a8cae14-2602-4dce-a5ef-c238732e74f6 · outbound
This paper cites Heinrich, Some remarks on biequidimensionality of topological spaces and Noetherian schemes , J.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Heinrich, Some remarks on biequidimensionality of topological spaces and Noetherian schemes , J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.645585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 86bb0610-e1e8-452d-b0fa-07c9f39f9522 · outbound
This paper cites Hochster and C.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Hochster and C
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.628746Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6788dd84-ba6f-4930-ab9f-b73c9ad249d6 · outbound
This paper cites Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.613083Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d1ea591f-0cd3-48b2-9aa0-5b68ff872996 · outbound
This paper cites Huneke, Hilbert--Kunz multiplicity and the F -signature , Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday (2013), pp.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Huneke, Hilbert--Kunz multiplicity and the F -signature , Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday (2013), pp
Reference 27
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- raw_fallback, observed 2026-08-14T13:43:12.597448Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c7a83eaf-89c6-4d3e-a311-0389a8e1c47d · outbound
This paper cites Jonsson and M.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Jonsson and M
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.581724Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3ef6d701-c1cf-4660-a52d-b8bf3e488f13 · outbound
This paper cites Kunz, Characterizations of regular local rings of characteristic p , Amer.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Kunz, Characterizations of regular local rings of characteristic p , Amer
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.565493Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5fecdf4d-5a11-4e3f-a261-7f42fa1c8b18 · outbound
This paper cites an unresolved cited work.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Unresolved cited work
Reference 30
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:43:12.548762Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8658bdf8-cda0-4486-8f8c-6761280e5af1 · outbound
This paper cites Li, K-semistability is equivariant volume minimization, Duke Math.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Li, K-semistability is equivariant volume minimization, Duke Math
Reference 31
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- raw_fallback, observed 2026-08-14T13:43:12.531508Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 76e28d41-a25d-4862-a3db-6a874818c991 · outbound
This paper cites Lazarsfeld and M.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Lazarsfeld and M
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.514846Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 84b0fdba-1702-42d2-9455-e8d189de5dca · outbound
This paper cites Liu, Algebraic geometry and arithmetic curves, Oxford graduate texts in mathematics , vol.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Liu, Algebraic geometry and arithmetic curves, Oxford graduate texts in mathematics , vol
Reference 33
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- raw_fallback, observed 2026-08-14T13:43:12.497830Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 25181e4b-dd09-4bca-8d7c-5738b07dbe35 · outbound
This paper cites Monsky, The Hilbert--Kunz function , Math.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Monsky, The Hilbert--Kunz function , Math
Reference 34
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- raw_fallback, observed 2026-08-14T13:43:12.481507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 593865df-d710-4a8b-87ac-254dc3ea8be7 · outbound
This paper cites Ma and K.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Ma and K
Reference 35
- Resolution
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- raw_fallback, observed 2026-08-14T13:43:12.464827Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation a8688a5b-5099-4060-aa26-cb898e24437b · outbound
This paper cites Polstra and K.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Polstra and K
Reference 36
- Resolution
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- raw_fallback, observed 2026-08-14T13:43:12.447034Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6815538b-400f-41fa-948f-455a73a70599 · outbound
This paper cites Perez, K.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Perez, K
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.429688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4c14cbe2-63a7-4cfb-8ab2-3c408f37bd2e · outbound
This paper cites Radu, Une classe d'anneaux noetheriens, Rev.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Radu, Une classe d'anneaux noetheriens, Rev
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.413010Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 794a681b-e030-468a-bf19-5f77fa4c7696 · outbound
This paper cites Grothendieck.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Grothendieck
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.396669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 37a9bdd9-e8e9-417d-9328-dd0144b748a7 · outbound
This paper cites Shepherd-Barron, On a problem of Ernst Kunz concerning certain characteristic functions of local rings , Archiv der Math.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Shepherd-Barron, On a problem of Ernst Kunz concerning certain characteristic functions of local rings , Archiv der Math
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.379537Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f1e082d2-9605-432c-a2d1-e13dfc7221bb · outbound
This paper cites Smirnov, Upper semi-continuity of the Hilbert–Kunz multiplicity , Compositio Math.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Smirnov, Upper semi-continuity of the Hilbert–Kunz multiplicity , Compositio Math
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.363412Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e820e031-f648-469d-8aaa-e09c17df48ef · outbound
This paper cites an unresolved cited work.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Unresolved cited work
Reference 42
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:43:12.214734Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d83be8e0-c820-4241-b6f0-1af80d856cc0 · outbound
This paper cites Schwede and W.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Schwede and W
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.336627Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 906af4ed-8d37-4052-944f-7f16b4c406db · outbound
This paper cites Takagi, Formulas for multiplier ideals on singular varieties, Amer.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Takagi, Formulas for multiplier ideals on singular varieties, Amer
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.320764Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0970e837-dcf3-4b3d-9517-2da08683e42a · outbound
This paper cites Tucker, F-signature exists, Invent.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Tucker, F-signature exists, Invent
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.304408Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 49064d31-25ce-439c-97a1-1b5224d23239 · outbound
This paper cites Watanabe and K.-i.
Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems Watanabe and K.-i
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:43:12.287688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.