Paper Citation Record · LEDGER

Graded Frobenius Algebras

As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2412.13909.

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

pith.paper-citation-record.v1
2412.13909 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T12:47:08.095448Z

measured 21 of 21 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

21 of 21 outbound references displayed

verified exact6
verified fuzzy10
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0a4408d0-876d-447b-8205-ce5d7761f15e · outbound

This paper cites Two-dimensional topological quantum field theories and F robenius algebras.

Graded Frobenius Algebras Two-dimensional topological quantum field theories and F robenius algebras

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.641075Z

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.

Observation b73c9ecb-679b-43ef-883f-403bdd2623ca · outbound

This paper cites A polarized view of string topology.

Graded Frobenius Algebras A polarized view of string topology

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.620889Z

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.

Observation f6e7a552-44d2-4260-85ce-a8a23d23dd69 · outbound

This paper cites La th\'eorie de l'homotopie des 2-cat\'egories.

Graded Frobenius Algebras La th\'eorie de l'homotopie des 2-cat\'egories

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.379947Z

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.

Observation cb498d41-86bd-4a24-b403-bfa90fe38ccd · outbound

This paper cites Poincar\'e duality for loop spaces.

Graded Frobenius Algebras Poincar\'e duality for loop spaces

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T12:47:07.982767Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7c2f6f1a-95ab-4f00-888f-2a2a3c7bf2c7 · outbound

This paper cites Loop coproduct in M orse and F loer homology.

Graded Frobenius Algebras Loop coproduct in M orse and F loer homology

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.602183Z

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.

Observation 46f462b9-73dc-4f3d-9430-7276dea6e3bc · outbound

This paper cites Reduced symplectic homology and string topology.

Graded Frobenius Algebras Reduced symplectic homology and string topology

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.327997Z

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.

Observation 25a7a05b-6051-46df-9469-db0e92c4ff1f · outbound

This paper cites Topological Frobenius algebras.

Graded Frobenius Algebras Topological Frobenius algebras

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T12:47:08.002704Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0e3e7ed-6870-4dd1-aa94-2d639e2ed2af · outbound

This paper cites Rabinowitz Floer homology as a Tate vector space.

Graded Frobenius Algebras Rabinowitz Floer homology as a Tate vector space

Reference 8

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.279424Z

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.

Observation 4d586c3f-6ed1-467a-b84f-1c408647acd7 · outbound

This paper cites Comparing fat graph models of moduli space.

Graded Frobenius Algebras Comparing fat graph models of moduli space

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.252659Z

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.

Observation 106c7f56-c25c-4622-8aa6-76be0e4fc019 · outbound

This paper cites Koszul duality for dioperads.

Graded Frobenius Algebras Koszul duality for dioperads

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.229782Z

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.

Observation 114cd540-2240-43a6-a0ac-a771b879b2ed · outbound

This paper cites Loop products and closed geodesics.

Graded Frobenius Algebras Loop products and closed geodesics

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.578570Z

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.

Observation 92d8ce36-3acc-4cad-9290-94d35a1cbd5c · outbound

This paper cites Modular operads.

Graded Frobenius Algebras Modular operads

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.558698Z

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.

Observation 09b85228-16f5-4a49-8b15-d0cb6c7e243a · outbound

This paper cites Higher string topology operations.

Graded Frobenius Algebras Higher string topology operations

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T12:47:08.048221Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 52266702-14f7-4db5-985f-d95747c52fd9 · outbound

This paper cites Algebraic Topology.

Graded Frobenius Algebras Algebraic Topology

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T12:47:08.057758Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57b69fa6-236b-4e6a-b73e-70ea9b0d79b3 · outbound

This paper cites Product and coproduct in string topology.

Graded Frobenius Algebras Product and coproduct in string topology

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-11T12:47:08.182606Z

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.

Observation 38ed7a02-6041-46bd-83cd-5b711f7ef51e · outbound

This paper cites Frobenius algebras and 2-d topological quantum field theories.

Graded Frobenius Algebras Frobenius algebras and 2-d topological quantum field theories

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.500522Z

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.

Observation 20ee1b99-f0a1-4de9-9160-abeca57b92c1 · outbound

This paper cites Pre-Calabi-Yau algebras and topological quantum field theories.

Graded Frobenius Algebras Pre-Calabi-Yau algebras and topological quantum field theories

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T12:47:08.075084Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7060514-43a1-4dd8-a287-9cbbb63b0501 · outbound

This paper cites Open--closed strings: T wo-dimensional extended TQFT s and Frobenius algebras.

Graded Frobenius Algebras Open--closed strings: T wo-dimensional extended TQFT s and Frobenius algebras

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.474378Z

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.

Observation f0e6282d-0249-49f5-ae33-cf228781eba4 · outbound

This paper cites Operads and PROPs.

Graded Frobenius Algebras Operads and PROPs

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.452974Z

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.

Observation 5f92f178-0c47-4ff5-b63c-9e50e11580e5 · outbound

This paper cites Loop coproducts in string topology and triviality of higher genus TQFT operations.

Graded Frobenius Algebras Loop coproducts in string topology and triviality of higher genus TQFT operations

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.430978Z

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.

Observation 58deb307-f28d-49ab-b48e-6af8912b5452 · outbound

This paper cites Hochschild homology of structured algebras.

Graded Frobenius Algebras Hochschild homology of structured algebras

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T12:47:08.410246Z

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.

Pith citing papers

No inbound Pith citation observations are available.