Paper Citation Record · LEDGER

Symmetric entanglers for non-invertible SPT phases

As of 17 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 2 inbound Pith citation observations for arXiv:2509.04581.

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

pith.paper-citation-record.v1
2509.04581 v3

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:39:36.629805Z

measured 42 of 42 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:39:36.446181Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-07-01T16:25:49.575020Z

Reference resolution

40 of 40 outbound references displayed

verified exact4
verified fuzzy11
unresolved23
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 577d3bae-8e1f-4433-953a-907ad52b4882 · outbound

This paper cites an unresolved cited work.

Symmetric entanglers for non-invertible SPT phases Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:39:37.319966Z

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 f1d1d365-c7b2-4b88-ae93-23ad068fa1a2 · outbound

This paper cites trivial phase,.

Symmetric entanglers for non-invertible SPT phases trivial phase,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.291709Z

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 2f5fa32b-ca58-442a-8d1f-f813189e6526 · outbound

This paper cites Symmetric entanglers for non-invertible SPT phases.

Symmetric entanglers for non-invertible SPT phases Symmetric entanglers for non-invertible SPT phases

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.446181Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8241d5d0-4c6e-4621-8ddf-faf7ec5aee28 · outbound

This paper cites overall group element.

Symmetric entanglers for non-invertible SPT phases overall group element

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.306318Z

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 e941a3e7-5d25-4b47-b225-b71101ca705b · outbound

This paper cites internal.

Symmetric entanglers for non-invertible SPT phases internal

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.278078Z

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 758d9f02-02e2-4bc1-ae55-5358ebf22b5d · outbound

This paper cites Thorngren and Y.

Symmetric entanglers for non-invertible SPT phases Thorngren and Y

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.468442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4eb13f2-c351-4f54-a0da-740aeb7785a3 · outbound

This paper cites Zhang and C.

Symmetric entanglers for non-invertible SPT phases Zhang and C

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.253043Z

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 89d1e244-40ac-49f4-9f38-fc5d5314827d · outbound

This paper cites Bhardwaj, L.

Symmetric entanglers for non-invertible SPT phases Bhardwaj, L

Reference 8

Resolution: malformed identifier; no resolver link, observed 2026-08-15T16:39:36.478768Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33bb36ad-f584-41b8-939e-2db9cb955d10 · outbound

This paper cites Inamura, Topological field theories and symme- try protected topological phases with fusion category symmetries, Journal of High Energy Physics2021, 10.1007/jhep05(2021)204 (2021).

Symmetric entanglers for non-invertible SPT phases Inamura, Topological field theories and symme- try protected topological phases with fusion category symmetries, Journal of High Energy Physics2021, 10.1007/jhep05(2021)204 (2021)

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T16:39:36.774800Z

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 87c6f07e-5e34-433a-bb95-702d5bcdbcfd · outbound

This paper cites Inamura and S.

Symmetric entanglers for non-invertible SPT phases Inamura and S

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.488628Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2925e3c7-5639-4878-a39a-0bcde72b231e · outbound

This paper cites Fechisin, N.

Symmetric entanglers for non-invertible SPT phases Fechisin, N

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.493819Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aa199b15-1abd-4470-86ed-d3a67cbb08fb · outbound

This paper cites Seifnashri and S.-H.

Symmetric entanglers for non-invertible SPT phases Seifnashri and S.-H

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.239172Z

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 f3452de6-667a-4268-b775-fcccbd5cc6f6 · outbound

This paper cites Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry.

Symmetric entanglers for non-invertible SPT phases Non-invertible SPTs: an on-site realization of (1+1)d anomaly-free fusion category symmetry

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.501791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74424239-c45a-400e-a1e9-44369f9c0231 · outbound

This paper cites Chen, Z.-C.

Symmetric entanglers for non-invertible SPT phases Chen, Z.-C

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.507112Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 94b23000-8b3d-4ba4-b14d-a3c8b76149d2 · outbound

This paper cites Kapustin, A.

Symmetric entanglers for non-invertible SPT phases Kapustin, A

Reference 15

Resolution: verified exact; doi, observed 2026-08-15T16:39:36.744675Z

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 34d024c0-ad92-4440-b77a-d08cf7e98f0d · outbound

This paper cites Turzillo and M.

Symmetric entanglers for non-invertible SPT phases Turzillo and M

Reference 16

Resolution: verified exact; doi, observed 2026-08-15T16:39:36.730447Z

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 a13b2439-6e3f-45b8-a655-f66b477ab636 · outbound

This paper cites Bultinck, D.

Symmetric entanglers for non-invertible SPT phases Bultinck, D

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.523030Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef78f3fb-5b3f-470d-93d2-32209deabdb1 · outbound

This paper cites Ren, S.-Q.

Symmetric entanglers for non-invertible SPT phases Ren, S.-Q

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.223701Z

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 d765d721-c010-41b8-8c12-82939e4e5525 · outbound

This paper cites Turzillo and M.

Symmetric entanglers for non-invertible SPT phases Turzillo and M

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T16:39:36.710529Z

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 28ce9aee-9b14-4a7a-97ed-7438ce44e6cc · outbound

This paper cites Chen, Z.-C.

Symmetric entanglers for non-invertible SPT phases Chen, Z.-C

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.210220Z

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 cecaf81e-e97f-46e0-ae34-bc53b3f1c4f8 · outbound

This paper cites Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems.

Symmetric entanglers for non-invertible SPT phases Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.542869Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6bd07c0e-7cd9-4012-981a-dff538aa43c0 · outbound

This paper cites Tantivasadakarn, R.

Symmetric entanglers for non-invertible SPT phases Tantivasadakarn, R

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.195579Z

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 d2e1e25a-ac9c-4a7f-8634-d5ca71aaf2ca · outbound

This paper cites Zhang, Topological invariants for symmetry-protected topological phase entanglers, Physical Review B107, 235104 (2023).

Symmetric entanglers for non-invertible SPT phases Zhang, Topological invariants for symmetry-protected topological phase entanglers, Physical Review B107, 235104 (2023)

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.179219Z

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 ecbc0fbc-cb43-44b4-ba84-28a71c98741f · outbound

This paper cites Tantivasadakarn, R.

Symmetric entanglers for non-invertible SPT phases Tantivasadakarn, R

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.558769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f60004fd-ac88-4f24-ad12-e0c2c936e742 · outbound

This paper cites Gaiotto and J.

Symmetric entanglers for non-invertible SPT phases Gaiotto and J

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.563587Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6dcb22b3-386b-4fdd-af70-ed53558921c7 · outbound

This paper cites Moradi, S.

Symmetric entanglers for non-invertible SPT phases Moradi, S

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.165095Z

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 962289f8-e74f-4ff6-8958-d614073fda7b · outbound

This paper cites Bhardwaj and S.

Symmetric entanglers for non-invertible SPT phases Bhardwaj and S

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.572724Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 33feffee-79b9-4f06-aef3-8e85dcff0f26 · outbound

This paper cites Fusion categories and homotopy theory.

Symmetric entanglers for non-invertible SPT phases Fusion categories and homotopy theory

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.576160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20101cf3-136f-44ac-baea-9dc2d4e5b4f9 · outbound

This paper cites Barkeshli, P.

Symmetric entanglers for non-invertible SPT phases Barkeshli, P

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.580967Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c5a59b7-f3bd-4189-99ef-42efb7e42b25 · outbound

This paper cites Lootens, C.

Symmetric entanglers for non-invertible SPT phases Lootens, C

Reference 30

Resolution: malformed identifier; no resolver link, observed 2026-08-15T16:39:36.584954Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f051b55-5209-4ec6-9570-90eabb4ab206 · outbound

This paper cites Lootens, C.

Symmetric entanglers for non-invertible SPT phases Lootens, C

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.590279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b44caac8-2fd2-42ba-9019-36879cc5cc06 · outbound

This paper cites Phases with non-invertible symmetries in 1+1D $\unicode{x2013}$ symmetry protected topological orders as duality automorphisms.

Symmetric entanglers for non-invertible SPT phases Phases with non-invertible symmetries in 1+1D $\unicode{x2013}$ symmetry protected topological orders as duality automorphisms

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.594427Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f40f00a-350e-4eec-8037-6d62a940ee45 · outbound

This paper cites an unresolved cited work.

Symmetric entanglers for non-invertible SPT phases Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.599820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfe36873-60bb-4a02-b297-4854da254910 · outbound

This paper cites an unresolved cited work.

Symmetric entanglers for non-invertible SPT phases Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.604035Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2dbcecdc-c3a9-4e8c-b500-6054623dd0e7 · outbound

This paper cites Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs.

Symmetric entanglers for non-invertible SPT phases Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.608522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 795ce8ab-8ca7-4f66-8e6f-3ee7fc460eed · outbound

This paper cites Bulk Excitations of Invertible Phases.

Symmetric entanglers for non-invertible SPT phases Bulk Excitations of Invertible Phases

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.613187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a8f03d6a-22e8-48b6-82f8-7bb41652d7a3 · outbound

This paper cites Etingof, S.

Symmetric entanglers for non-invertible SPT phases Etingof, S

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:39:37.151303Z

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 c225e010-bc1f-4f63-98c2-e4de6b104b23 · outbound

This paper cites Garre-Rubio, L.

Symmetric entanglers for non-invertible SPT phases Garre-Rubio, L

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.621849Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6139c839-4215-4441-bcbe-73243d1fbad5 · outbound

This paper cites an unresolved cited work.

Symmetric entanglers for non-invertible SPT phases Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.625895Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69bde5be-8e2b-4616-84fa-975ec7cd24a1 · outbound

This paper cites Ignacio Cirac, D.

Symmetric entanglers for non-invertible SPT phases Ignacio Cirac, D

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-15T16:39:36.629805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 2f5fa32b-ca58-442a-8d1f-f813189e6526 · inbound