Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T22:45:20.177662Z
Paper Citation Record · LEDGER
Defect Networks for Topological Phases Protected By Modulated Symmetries
As of 10 August 2026, this Paper Citation Record lists 79 of 79 outbound references and 5 inbound Pith citation observations for arXiv:2508.06604.
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 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-03T07:02:21.886470Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-18T04:55:54.187551Z
Reference resolution
79 of 79 outbound references displayed
- verified exact0
- verified fuzzy70
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation cfc704ab-5a2c-403c-abfd-85bcdd5529d1 · outbound
This paper cites Z2 Nˆ Z2 (90) where s stands for “site.
Defect Networks for Topological Phases Protected By Modulated Symmetries Z2 Nˆ Z2 (90) where s stands for “site
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.300554Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 56bad46b-817e-402d-967e-99ae5cfc5060 · outbound
This paper cites Then a does not have a multiplicative inverse modulo N , and one can check that every positive power of A (resp.
Defect Networks for Topological Phases Protected By Modulated Symmetries Then a does not have a multiplicative inverse modulo N , and one can check that every positive power of A (resp
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.272336Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation ff7d5f86-f90d-49b2-9186-91d7fb32ebbd · outbound
This paper cites Gint¸ GΣd´1 , the LHS spectral sequence degenerates at the E2 page and shows that Hd`1pK, Up1qq includes a subgroup H0pGΣd´1 , Hd`1pGint, Up1qqq“ Hd`1pGint, Up1qqS.
Defect Networks for Topological Phases Protected By Modulated Symmetries Gint¸ GΣd´1 , the LHS spectral sequence degenerates at the E2 page and shows that Hd`1pK, Up1qq includes a subgroup H0pGΣd´1 , Hd`1pGint, Up1qqq“ Hd`1pGint, Up1qqS
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.313923Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f637b09d-12a2-48f0-b5b5-07df41d4227c · outbound
This paper cites In this case, the mth power of A (resp.
Defect Networks for Topological Phases Protected By Modulated Symmetries In this case, the mth power of A (resp
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.286101Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0d987408-065e-4704-ba47-8b81f8321571 · outbound
This paper cites e 2πi N 2 gxphx`kx´rhx`kxsq (119) ωII “ e 2πi N 2 gQphx`kx´rhx`kxsq (120) whererg` hs denotes addition mod N and the subscript denotes the “type.
Defect Networks for Topological Phases Protected By Modulated Symmetries e 2πi N 2 gxphx`kx´rhx`kxsq (119) ωII “ e 2πi N 2 gQphx`kx´rhx`kxsq (120) whererg` hs denotes addition mod N and the subscript denotes the “type
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.258730Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation e44ad834-3d39-4072-bd41-8bda3b9d77de · outbound
This paper cites ω. Obviously shifting ν by a 2-cocycle will not change the fact that ν trivializes T˚ x ω{ω. Hence, the naive 1-cell data is given by µh“ zh µv“ $ & % νzv N even andrωs“ ´.
Defect Networks for Topological Phases Protected By Modulated Symmetries ω. Obviously shifting ν by a 2-cocycle will not change the fact that ν trivializes T˚ x ω{ω. Hence, the naive 1-cell data is given by µh“ zh µv“ $ & % νzv N even andrωs“ ´
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.245500Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 4653e1f4-c2d8-41f9-b461-d80b60861890 · outbound
This paper cites Given that T˚ y ν“ ν on the nose, we can insert the data in Eq.
Defect Networks for Topological Phases Protected By Modulated Symmetries Given that T˚ y ν“ ν on the nose, we can insert the data in Eq
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.232064Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7631bd0f-5ec9-4bcf-b56b-2b0d7a534a7f · outbound
This paper cites ” ωpQq I ı.
Defect Networks for Topological Phases Protected By Modulated Symmetries ” ωpQq I ı
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.217019Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation d9003012-90db-4e9c-9c86-39ce01b95238 · outbound
This paper cites ” ωpxq I ı ,.
Defect Networks for Topological Phases Protected By Modulated Symmetries ” ωpxq I ı ,
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.203291Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 4cbdd4a8-7bb8-41a0-92d6-d331799b0882 · outbound
This paper cites We follow the same case analysis as we did for the 1-cells.
Defect Networks for Topological Phases Protected By Modulated Symmetries We follow the same case analysis as we did for the 1-cells
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.189680Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9485d63e-1488-490a-81b2-c59051583572 · outbound
This paper cites Turner, and Masaki Oshikawa.
Defect Networks for Topological Phases Protected By Modulated Symmetries Turner, and Masaki Oshikawa
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.175859Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 13dd376a-d20e-46ab-b616-c8af4df99953 · outbound
This paper cites Classification of gapped symmetric phases in one-dimensional spin systems.
Defect Networks for Topological Phases Protected By Modulated Symmetries Classification of gapped symmetric phases in one-dimensional spin systems
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.162253Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 500b5607-6fe0-451d-b337-3df5faddb9c5 · outbound
This paper cites Complete classification of one-dimensional gapped quantum phases in interacting spin systems.
Defect Networks for Topological Phases Protected By Modulated Symmetries Complete classification of one-dimensional gapped quantum phases in interacting spin systems
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.148594Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 3517687d-7487-4a20-9e92-1da227cabc53 · outbound
This paper cites Classifying quantum phases using matrix product states and projected entangled pair states.
Defect Networks for Topological Phases Protected By Modulated Symmetries Classifying quantum phases using matrix product states and projected entangled pair states
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.134535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 3de7ce5b-b4c8-4920-aef2-d2c2f0975833 · outbound
This paper cites Symmetry protected topological orders and the group cohomology of their symmetry group.
Defect Networks for Topological Phases Protected By Modulated Symmetries Symmetry protected topological orders and the group cohomology of their symmetry group
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.119780Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation d53ca49f-2046-47ec-a95b-e3ac8ea9b1fc · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:21.106077Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation c9f62002-8016-445d-bab0-55aa8e190375 · outbound
This paper cites Gaiotto, A.
Defect Networks for Topological Phases Protected By Modulated Symmetries Gaiotto, A
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.092697Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 583d6439-8a8d-4fca-8bac-cacd5fc8a55a · outbound
This paper cites McGreevy.
Defect Networks for Topological Phases Protected By Modulated Symmetries McGreevy
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.079216Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 46f305b5-44e4-4a76-b414-4d1bc6c1c0ad · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:21.065192Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation bbb7a5ec-a600-42a0-b5bc-e144acaa1aaa · outbound
This paper cites ICTP Lectures on (Non-)Invertible Generalized Symmetries, 2023.
Defect Networks for Topological Phases Protected By Modulated Symmetries ICTP Lectures on (Non-)Invertible Generalized Symmetries, 2023
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.051366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation b7130a2e-bb34-4004-863c-0e65c9ba5a6c · outbound
This paper cites Lecture notes on generalized symmetries and applications.
Defect Networks for Topological Phases Protected By Modulated Symmetries Lecture notes on generalized symmetries and applications
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.037845Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation d6a1580d-ffbd-482f-af89-2c2c0509cd84 · outbound
This paper cites Simons Lectures on Categorical Symmetries, 2024.
Defect Networks for Topological Phases Protected By Modulated Symmetries Simons Lectures on Categorical Symmetries, 2024
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.024118Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation a71d7b3c-362c-475a-ac2c-fa62d66704c4 · outbound
This paper cites Nandkishore.
Defect Networks for Topological Phases Protected By Modulated Symmetries Nandkishore
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:21.010327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1dd17899-719c-4f17-8211-a8369098e9d0 · outbound
This paper cites Scaling and localization in multipole-conserving diffusion.
Defect Networks for Topological Phases Protected By Modulated Symmetries Scaling and localization in multipole-conserving diffusion
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.996503Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 591adc03-9a6c-4420-8fa9-5d2f267704de · outbound
This paper cites Anomalous diffusion in dipole- and higher-moment-conserving systems.
Defect Networks for Topological Phases Protected By Modulated Symmetries Anomalous diffusion in dipole- and higher-moment-conserving systems
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.983244Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 46cd276f-b56f-4d2c-a16e-db75f2e16297 · outbound
This paper cites Nandkishore.
Defect Networks for Topological Phases Protected By Modulated Symmetries Nandkishore
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.969409Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 50ac091d-da6f-481a-99c7-48228465409d · outbound
This paper cites and Jensen, K.
Defect Networks for Topological Phases Protected By Modulated Symmetries and Jensen, K
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.954420Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 464847fa-c468-4dfb-94b9-e738c51d2a7d · outbound
This paper cites Ergodicity breaking arising from hilbert space fragmentation in dipole-conserving hamiltonians.
Defect Networks for Topological Phases Protected By Modulated Symmetries Ergodicity breaking arising from hilbert space fragmentation in dipole-conserving hamiltonians
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.940572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 6b2ee594-39c3-49fb-8c51-a70823b55349 · outbound
This paper cites Subdimensional particle structure of higher rank up1q spin liquids.
Defect Networks for Topological Phases Protected By Modulated Symmetries Subdimensional particle structure of higher rank up1q spin liquids
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.926871Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f8d7a965-bfdf-4880-b262-e3b7760e4609 · outbound
This paper cites Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons.
Defect Networks for Topological Phases Protected By Modulated Symmetries Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.912838Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 19c62735-fed4-4347-b551-e8899df6392d · outbound
This paper cites The fracton gauge principle.
Defect Networks for Topological Phases Protected By Modulated Symmetries The fracton gauge principle
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.898897Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2afc836d-0510-4bcf-843c-5e53e084e73b · outbound
This paper cites Towards classification of fracton phases: The multipole algebra.
Defect Networks for Topological Phases Protected By Modulated Symmetries Towards classification of fracton phases: The multipole algebra
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.885057Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7a44d7eb-9337-4b57-b555-a7b20d872bba · outbound
This paper cites Fracton topological order, generalized lattice gauge theory, and duality.
Defect Networks for Topological Phases Protected By Modulated Symmetries Fracton topological order, generalized lattice gauge theory, and duality
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.871366Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2d22e65b-b901-48de-8c8a-9a69e7c07e29 · outbound
This paper cites Topological quantum glassiness.
Defect Networks for Topological Phases Protected By Modulated Symmetries Topological quantum glassiness
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.857560Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 65a2a6c9-662d-4384-97c7-cfbcaf62872a · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.843771Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 314584e1-54f6-4fc6-972a-2f563fffe7c6 · outbound
This paper cites Bulmash and M.
Defect Networks for Topological Phases Protected By Modulated Symmetries Bulmash and M
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.830428Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation bc8b7276-7b7c-4125-bedf-da028c667185 · outbound
This paper cites Dynamics in systems with modulated symmetries.
Defect Networks for Topological Phases Protected By Modulated Symmetries Dynamics in systems with modulated symmetries
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.816702Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation b35c3e50-ef8e-42f4-a121-b75529d3f8d8 · outbound
This paper cites Quantum breakdown model: From many-body localization to chaos with scars.
Defect Networks for Topological Phases Protected By Modulated Symmetries Quantum breakdown model: From many-body localization to chaos with scars
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.802339Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2c236809-13b9-4c03-8a55-81b8235bb93a · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 39
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.788284Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 5deaf56d-238e-4c84-94a8-feab7f769484 · outbound
This paper cites Classifying local fractal subsystem symmetry-protected topological phases.
Defect Networks for Topological Phases Protected By Modulated Symmetries Classifying local fractal subsystem symmetry-protected topological phases
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.774728Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 57eacc69-e3fc-43d1-be1b-e57b00d8937a · outbound
This paper cites Strong planar subsystem symmetry-protected topological phases and their dual fracton orders.
Defect Networks for Topological Phases Protected By Modulated Symmetries Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.760696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9f6d4ded-b166-4d7c-b83c-8033768e0bee · outbound
This paper cites Topological quantum chains protected by dipolar and other modulated symmetries, 2023.
Defect Networks for Topological Phases Protected By Modulated Symmetries Topological quantum chains protected by dipolar and other modulated symmetries, 2023
Reference 42
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.746458Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 246f2d7b-2544-45f5-b8b5-4d075b5ca47b · outbound
This paper cites Classification of Dipolar Symmetry-Protected Topological Phases: Matrix Product States, Stabilizer Hamil- tonians and Finite Tensor Gauge Theories, 2023.
Defect Networks for Topological Phases Protected By Modulated Symmetries Classification of Dipolar Symmetry-Protected Topological Phases: Matrix Product States, Stabilizer Hamil- tonians and Finite Tensor Gauge Theories, 2023
Reference 43
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.732696Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2afb334d-9cc1-45b3-b0c9-223bbfe7c8e0 · outbound
This paper cites Topological dipole insulator.
Defect Networks for Topological Phases Protected By Modulated Symmetries Topological dipole insulator
Reference 44
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.718221Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0e5dfe0e-99bd-4295-9e39-2435db1b9572 · outbound
This paper cites Private communication/work in progress.
Defect Networks for Topological Phases Protected By Modulated Symmetries Private communication/work in progress
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.704731Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 97bdca5c-f86f-4630-9291-68907248c124 · outbound
This paper cites Pace, Guilherme Delfino, Ho Tat Lam, and ¨Omer M.
Defect Networks for Topological Phases Protected By Modulated Symmetries Pace, Guilherme Delfino, Ho Tat Lam, and ¨Omer M
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.690506Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fdb0295a-a5ec-46f9-a5b9-6599205e359f · outbound
This paper cites Multipole groups and fracton phenomena on arbitrary crystalline lattices.
Defect Networks for Topological Phases Protected By Modulated Symmetries Multipole groups and fracton phenomena on arbitrary crystalline lattices
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.676819Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0f88a2a1-9620-4aa3-9510-a4efd01b7576 · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 48
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.662792Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 432cc357-ee62-4add-91e6-8cb7889971ff · outbound
This paper cites Else, Sheng-Jie Huang, Abhinav Prem, and Andrey Gromov.
Defect Networks for Topological Phases Protected By Modulated Symmetries Else, Sheng-Jie Huang, Abhinav Prem, and Andrey Gromov
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.649146Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9850fb1c-930f-43a9-a296-cdb46e93ad15 · outbound
This paper cites Else and Ryan Thorngren.
Defect Networks for Topological Phases Protected By Modulated Symmetries Else and Ryan Thorngren
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.635438Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 68f847fd-1076-45a9-bcfa-cd10cd21703a · outbound
This paper cites Building crystalline topological phases from lower- dimensional states.
Defect Networks for Topological Phases Protected By Modulated Symmetries Building crystalline topological phases from lower- dimensional states
Reference 51
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.620701Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation d5f91343-f13c-41f2-b57e-442362257eae · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 52
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.606699Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9fdde782-3cb4-4181-851e-9b0384e80844 · outbound
This paper cites Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases.
Defect Networks for Topological Phases Protected By Modulated Symmetries Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
Reference 53
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.592809Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation abca552f-5c0c-4565-8674-784068ae1eca · outbound
This paper cites Construction and classification of point- group symmetry-protected topological phases in two-dimensional interacting fermionic systems.
Defect Networks for Topological Phases Protected By Modulated Symmetries Construction and classification of point- group symmetry-protected topological phases in two-dimensional interacting fermionic systems
Reference 54
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.578016Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 91a4b659-baa6-4426-9574-d8d73d126838 · outbound
This paper cites Real-space construction of crystalline topological supercon- ductors and insulators in 2D interacting fermionic systems.
Defect Networks for Topological Phases Protected By Modulated Symmetries Real-space construction of crystalline topological supercon- ductors and insulators in 2D interacting fermionic systems
Reference 55
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.564416Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 9d4b7c3e-8385-4a30-89a2-aa7875183a73 · outbound
This paper cites Williamson.
Defect Networks for Topological Phases Protected By Modulated Symmetries Williamson
Reference 56
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.550061Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation e22984fd-68db-477a-86da-559afd66c70e · outbound
This paper cites Systematic construction of gapped nonliquid states.
Defect Networks for Topological Phases Protected By Modulated Symmetries Systematic construction of gapped nonliquid states
Reference 57
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.537055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 714707df-4d9c-4d1d-91d0-579dc574c51a · outbound
This paper cites Nonliquid cellular states: Gluing gauge-higher-symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects.
Defect Networks for Topological Phases Protected By Modulated Symmetries Nonliquid cellular states: Gluing gauge-higher-symmetry-breaking versus gauge-higher-symmetry-extension interfacial defects
Reference 58
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.523343Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 5a851ada-6923-4572-ae6c-491cf51f2911 · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 59
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.509024Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 5d160a57-e449-4a25-aee9-1d4ef3dbde15 · outbound
This paper cites Pace, ¨Omer M.
Defect Networks for Topological Phases Protected By Modulated Symmetries Pace, ¨Omer M
Reference 60
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.494726Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 5e52990f-d5c4-403b-b3cd-04395702b289 · outbound
This paper cites 2D Fractons from Gauging Exponential Symmetries, 2023.
Defect Networks for Topological Phases Protected By Modulated Symmetries 2D Fractons from Gauging Exponential Symmetries, 2023
Reference 61
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.481034Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation ca34d580-9dfd-4536-9e06-2b11791b9812 · outbound
This paper cites Symmetric gapped interfaces of SPT and SET states: systematic constructions.
Defect Networks for Topological Phases Protected By Modulated Symmetries Symmetric gapped interfaces of SPT and SET states: systematic constructions
Reference 62
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.466749Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7e066161-ee08-4236-97d6-2e0741d57e52 · outbound
This paper cites Two soluble models of an antiferromagnetic chain.
Defect Networks for Topological Phases Protected By Modulated Symmetries Two soluble models of an antiferromagnetic chain
Reference 63
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.452758Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 619a4961-a68c-4beb-9ec6-a8bee557f47e · outbound
This paper cites Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice.
Defect Networks for Topological Phases Protected By Modulated Symmetries Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice
Reference 64
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.437758Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 8fd47ff2-e315-4eec-b50e-bee0bdc3cebb · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 65
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.423288Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 16630bc8-12c3-4e44-a611-20c3a32e544f · outbound
This paper cites Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface.
Defect Networks for Topological Phases Protected By Modulated Symmetries Translational symmetry and microscopic constraints on symmetry-enriched topological phases: A view from the surface
Reference 66
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.409114Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation af7d1299-06e4-4b6b-a08c-c13e34324983 · outbound
This paper cites Work in progress.
Defect Networks for Topological Phases Protected By Modulated Symmetries Work in progress
Reference 67
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.393905Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation fb91fa2a-f151-4134-8a90-51f9c1c7fae0 · outbound
This paper cites Domain Wall Decorations, Anomalies and Spectral Sequences in Bosonic Topological Phases, 2021.
Defect Networks for Topological Phases Protected By Modulated Symmetries Domain Wall Decorations, Anomalies and Spectral Sequences in Bosonic Topological Phases, 2021
Reference 68
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.379091Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation e95092b5-483e-4381-971f-4c1e8821e00e · outbound
This paper cites Symmetry-protected topological phases of mixed states in the doubled space.
Defect Networks for Topological Phases Protected By Modulated Symmetries Symmetry-protected topological phases of mixed states in the doubled space
Reference 69
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.364148Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1ddd6302-a519-4049-b332-2a9a16a6a19e · outbound
This paper cites Geraedts and Olexei I.
Defect Networks for Topological Phases Protected By Modulated Symmetries Geraedts and Olexei I
Reference 70
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.349088Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 4c95528a-1765-4d28-b37d-a6e0f7074e13 · outbound
This paper cites an unresolved cited work.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unresolved cited work
Reference 71
- Resolution
- unresolved
- raw_fallback, observed 2026-08-05T22:45:20.334157Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0f8d1123-e133-4e84-b8f0-4bbc82f696ec · outbound
This paper cites Burnell, Sanjay Moudgalya, and Abhinav Prem.
Defect Networks for Topological Phases Protected By Modulated Symmetries Burnell, Sanjay Moudgalya, and Abhinav Prem
Reference 72
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.320052Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation da629a72-4b59-406d-b171-5c0b09bac0a9 · outbound
This paper cites Fragmentation-induced localization and boundary charges in dimensions two and above.
Defect Networks for Topological Phases Protected By Modulated Symmetries Fragmentation-induced localization and boundary charges in dimensions two and above
Reference 73
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.306014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1411e9d5-b888-4387-9c9b-284924b0dd39 · outbound
This paper cites Ground state degeneracy on torus in a family of zn toric code.
Defect Networks for Topological Phases Protected By Modulated Symmetries Ground state degeneracy on torus in a family of zn toric code
Reference 74
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.290780Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f9735a5f-3d65-470a-92da-151c8c702302 · outbound
This paper cites Quantum orders in an exact soluble model.
Defect Networks for Topological Phases Protected By Modulated Symmetries Quantum orders in an exact soluble model
Reference 75
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.274677Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation de942018-f2a3-4818-9e88-0da79b25bc52 · outbound
This paper cites Pace and Xiao-Gang Wen.
Defect Networks for Topological Phases Protected By Modulated Symmetries Pace and Xiao-Gang Wen
Reference 76
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.260095Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation f1d87aad-b0d6-468b-8007-1b76466870a8 · outbound
This paper cites Unveiling UV/IR mixing via symmetry defects: A view from topological entanglement entropy.
Defect Networks for Topological Phases Protected By Modulated Symmetries Unveiling UV/IR mixing via symmetry defects: A view from topological entanglement entropy
Reference 77
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.246033Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7c261c0a-f693-4025-94f4-9693c638d75e · outbound
This paper cites Yoshitome, Heitor Casasola, Rodrigo Corso, and Pedro R.
Defect Networks for Topological Phases Protected By Modulated Symmetries Yoshitome, Heitor Casasola, Rodrigo Corso, and Pedro R
Reference 78
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.231497Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation c7558043-3ccf-4d1d-9f9b-6208adedf2b3 · outbound
This paper cites Generalized homology and Atiyah–Hirzebruch spectral se- quence in crystalline symmetry protected topological phenomena.
Defect Networks for Topological Phases Protected By Modulated Symmetries Generalized homology and Atiyah–Hirzebruch spectral se- quence in crystalline symmetry protected topological phenomena
Reference 79
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-05T22:45:20.216635Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Pith citing papers
Observation 2ce56627-535a-4b54-b188-77fa31d2d2a0 · inbound
Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies cites this paper.
Modulated symmetries from generalized Lieb-Schultz-Mattis anomalies Defect Networks for Topological Phases Protected By Modulated Symmetries
Reference 40
- Resolution
- verified exact
- arxiv_id, observed 2026-05-18T04:55:54.189815Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 771c4e1b-8845-4e75-88d7-aa688cf0ced6 · inbound
Non-invertible translation from Lieb-Schultz-Mattis anomaly cites this paper.
Non-invertible translation from Lieb-Schultz-Mattis anomaly Defect Networks for Topological Phases Protected By Modulated Symmetries
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T07:02:21.886470Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e3b6fe0e-44e1-450c-9c15-2583cad1d0e2 · inbound
Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond cites this paper.
Matrix Product States for Modulated Symmetries: SPT, LSM, and Beyond Defect Networks for Topological Phases Protected By Modulated Symmetries
Reference 50
- Resolution
- unresolved
- no resolver link, observed 2026-07-13T22:07:26.204482Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4bad0474-d66c-4504-86f5-ba3fc04a9c33 · inbound
Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints cites this paper.
Matrix Product States for Modulated Topological Phases: Crystalline Equivalence Principle and Lieb-Schultz-Mattis Constraints Defect Networks for Topological Phases Protected By Modulated Symmetries
Reference 44
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T07:55:15.047790Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 0e844055-275e-4a7e-a961-560267d89619 · inbound
Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States cites this paper.
Projector, Neural, and Tensor-Network Representations of $\mathbb{Z}_N$ Cluster and Dipolar-cluster SPT States Defect Networks for Topological Phases Protected By Modulated Symmetries
Reference 28
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T06:10:58.055056Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.