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Paper Citation Record · LEDGER

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules

As of 16 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:1908.03648.

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

pith.paper-citation-record.v1
1908.03648 v2

Coverage vector

measured 15 of 15 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:15:25.054961Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

15 of 15 outbound references displayed

  • verified exact1
  • verified fuzzy12
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1fb4601b-8f45-4459-bea7-47266096f173 · outbound

This paper cites 361-374, 2000.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules 361-374, 2000

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.295570Z

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.

source=pdf_text observed=2026-08-14T14:15:24.989177Z digest=sha256:001db210f0658faf1d05cb55acad49375bde50b61ed3c415268fa4358ae390ae

Observation c8eb13d0-6eb2-4df4-a1d2-61fb663f1967 · outbound

This paper cites The non- Lefschetz locus, Journal of Algebra 505: 288-320 (2018).

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules The non- Lefschetz locus, Journal of Algebra 505: 288-320 (2018)

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.282112Z

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.

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Observation 401dc5ef-1a81-473d-a1f3-86abaf2c5534 · outbound

This paper cites Springer-Verlag New York, Inc.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Springer-Verlag New York, Inc

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.268636Z

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.

source=pdf_text observed=2026-08-14T14:15:24.999097Z digest=sha256:4ca1b86cdeeb76ec13023ba4d7ad02cf6d2ebfa80b0f43ce5912106636d765fc

Observation 37cdaceb-c300-4b39-8759-9ac68b6dd5e6 · outbound

This paper cites Springer Science+Business Media, Inc.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Springer Science+Business Media, Inc

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.254438Z

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.

source=pdf_text observed=2026-08-14T14:15:25.003996Z digest=sha256:974fad8363fd4c38826776daaae13a5d1add40ba8383be9d994b0a6d3289842b

Observation d683eb3d-bc99-49a5-9b44-85ad764aadc4 · outbound

This paper cites On the Weak Lefschetz Property for Vector Bundles on $\mathbb P^2$.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules On the Weak Lefschetz Property for Vector Bundles on $\mathbb P^2$

Reference 5

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:15:25.094924Z

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.

source=pdf_text observed=2026-08-14T14:15:25.008893Z digest=sha256:b76e2328705222bae168c0dbaf9a54b6addd5e935c4737a4e02c391b4ffaef74

Observation f281ee9e-9b5b-4144-9866-51cab6d01ff8 · outbound

This paper cites Matematiche (Catania 67 (1), pp.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Matematiche (Catania 67 (1), pp

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.238808Z

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.

source=pdf_text observed=2026-08-14T14:15:25.013817Z digest=sha256:5c4cc66fceb96f1912fbb1c014f10add8fda1b23cd44e3dea264f14cb4201bd4

Observation 26d79abd-96a0-4402-ac6b-05710a09c714 · outbound

This paper cites and Merle M., Singularit´ es isol´ ees et sections planes de vari´ et´ es d´eterminantielles.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules and Merle M., Singularit´ es isol´ ees et sections planes de vari´ et´ es d´eterminantielles

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.224156Z

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.

source=pdf_text observed=2026-08-14T14:15:25.018395Z digest=sha256:d3a45ebce18e84848ef453dbb21a98f90c7d2df65372e71dc70fef7a03d88d46

Observation 1cb9f2c6-6ad7-42c3-bf0a-93cdb7785348 · outbound

This paper cites an unresolved cited work.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:15:25.209097Z

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.

source=pdf_text observed=2026-08-14T14:15:25.023137Z digest=sha256:50299ba9754c18dd6b52eea2bbf54bb11c17443080f83e7486f04e58f0d6def1

Observation 052a45d0-7da1-4fb0-9fba-c8244925e53d · outbound

This paper cites Journal of Algebra 262(1), pp.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Journal of Algebra 262(1), pp

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.194773Z

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.

source=pdf_text observed=2026-08-14T14:15:25.028303Z digest=sha256:09458145e59a9604535340f98cc908487e620b51f70e0e8572dc293ea2cacc8f

Observation 0fa3b222-6aca-44b9-a8b3-63b8f6add007 · outbound

This paper cites Mathematische Nachrichten 284(7), pp.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Mathematische Nachrichten 284(7), pp

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.181020Z

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.

source=pdf_text observed=2026-08-14T14:15:25.032803Z digest=sha256:31f7e865de6bf43f6e33285311e659c7501a88028ae6a9d1a81cb5a0854e119c

Observation 6f7edd74-7129-4091-a32e-0cbc7385f3d3 · outbound

This paper cites 63-80, 1992.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules 63-80, 1992

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.166107Z

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.

source=pdf_text observed=2026-08-14T14:15:25.037157Z digest=sha256:d39bbb97c398beee1ef6e2b2a90bb77d66a3dc35a65cd385df1e95e8fbec6e52

Observation 3730f954-63d5-4bf7-b29b-c9aa600254a9 · outbound

This paper cites Monomial Ideals, Almost Complete Intersections and the W eak Lefschetz Property, Trans.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Monomial Ideals, Almost Complete Intersections and the W eak Lefschetz Property, Trans

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.152215Z

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.

source=pdf_text observed=2026-08-14T14:15:25.041586Z digest=sha256:affe8532ae890f9a2a77a7cf7bf9c88766297559e9d4194f35dfad9b912393f8

Observation c8d73792-fd69-4ad2-99ad-23a70c330661 · outbound

This paper cites Journal of Commutative Algebra Vol.5 No.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Journal of Commutative Algebra Vol.5 No

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.138705Z

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.

source=pdf_text observed=2026-08-14T14:15:25.046576Z digest=sha256:c9ca0e85f8e98aa6ff1a751fe15002c7a5216fc4d25275f9742ae1bce89f32b6

Observation 1b1bff0a-fbea-43e4-860e-c68e4a6b7209 · outbound

This paper cites Birkh¨ auser Boston.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Birkh¨ auser Boston

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:15:25.124502Z

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.

source=pdf_text observed=2026-08-14T14:15:25.050820Z digest=sha256:dd7bfe8ea4d397a6695ac57c37c6f2ba7a808b456ec486120201e56f09f27047

Observation bf62eb2d-42ba-4630-a26f-49e9e30b7805 · outbound

This paper cites an unresolved cited work.

Symmetry, Unimodality, and Lefschetz Properties for Graded Modules Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:15:25.110270Z

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.

source=pdf_text observed=2026-08-14T14:15:25.054961Z digest=sha256:624e192d75d30631015d2937aa6341ac1c804f6ea0a7eadda68bcdcecdaee2e6

Pith citing papers

No inbound Pith citation observations are available.