Paper Citation Record · LEDGER

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

As of 22 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 7 inbound Pith citation observations for arXiv:1908.02613.

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

pith.paper-citation-record.v1
1908.02613 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:55:03.853703Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 7 of 7 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-12T13:57:59.379600Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T03:20:48.968545Z

Reference resolution

16 of 16 outbound references displayed

verified exact0
verified fuzzy11
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d1ec349f-bcff-407d-9b89-7a9046ee582b · outbound

This paper cites 4a, the resulting positions of the two ﬁnal anyons are exchanged in the two processes.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ 4a, the resulting positions of the two ﬁnal anyons are exchanged in the two processes

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.168748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b94c1e16-c81b-452b-89c9-70bc4fec3050 · outbound

This paper cites boundary state.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ boundary state

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.185760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6ee2cee5-5f6a-47d2-b9cd-e99e794646e3 · outbound

This paper cites 38: The 3+1D bulk state that we have constructed is a Zn-1-SPT state labeled by m∈{ 0, 1,··· , 2n−1}, protected by an on-site (anomaly- free) Zn-1-symmetry.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ 38: The 3+1D bulk state that we have constructed is a Zn-1-SPT state labeled by m∈{ 0, 1,··· , 2n−1}, protected by an on-site (anomaly- free) Zn-1-symmetry

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.151078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f7a126cc-0f23-4ab7-9059-d6416436404f · outbound

This paper cites an unresolved cited work.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:55:04.130857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b6ae61cf-8b78-4284-ae23-46d8c171be23 · outbound

This paper cites an unresolved cited work.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:55:04.111692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dacd6f47-e143-4587-87bb-e4961441a1a3 · outbound

This paper cites an unresolved cited work.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:55:04.092496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4a757e40-041e-41bb-a48f-b0bdb5c5767d · outbound

This paper cites S-structure.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ S-structure

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.073287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 29db271b-3507-4113-84ea-14690d3e6177 · outbound

This paper cites no-crossing.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ no-crossing

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.055018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e5c26478-2fa5-4b45-8629-c87319e53162 · outbound

This paper cites quotient- remainder.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ quotient- remainder

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.037008Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 533296b4-2f3e-40b2-bff6-0c421ff9dbc7 · outbound

This paper cites The space-time has boundaries at t = 0,T , where the ﬁeld conﬁgurations are given by{a0} and{aT}.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ The space-time has boundaries at t = 0,T , where the ﬁeld conﬁgurations are given by{a0} and{aT}

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:04.017945Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1105ce75-5c44-4c07-bab2-9bdf1acdcb1a · outbound

This paper cites In order to deﬁne the transfer ma- trix, we need to specify the background gauge ﬁeld ˆB on the spacetime M3×I.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ In order to deﬁne the transfer ma- trix, we need to specify the background gauge ﬁeld ˆB on the spacetime M3×I

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:03.995660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e718b735-da48-4384-9508-d19fdb08cbe7 · outbound

This paper cites Deﬁne|ψ0⟩ = 1 Nψ ∑ {a} e2πi ∫ M3φ3[a]|{a}⟩ with normal- ization Nψ = √ nNl,M3.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Deﬁne|ψ0⟩ = 1 Nψ ∑ {a} e2πi ∫ M3φ3[a]|{a}⟩ with normal- ization Nψ = √ nNl,M3

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:03.975647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5e029b91-c726-44c3-ad9d-627c2c40aa1c · outbound

This paper cites an unresolved cited work.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:55:03.954670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5457c734-6cd9-4b7e-b2dd-f605390107f7 · outbound

This paper cites ⃗ rij = ⃗ n+ ˆα 2 denote the mid-point of ij = (⃗0, ˆα)⃗ n, ⃗1 2 := ( 1 2, 1 2, 1 2), and Fβγ(⃗ r) := daZn(⃗0, ˆβ, ˆβ + ˆγ)⃗ r− ˆβ 2− ˆγ 2 − (β↔γ).

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ ⃗ rij = ⃗ n+ ˆα 2 denote the mid-point of ij = (⃗0, ˆα)⃗ n, ⃗1 2 := ( 1 2, 1 2, 1 2), and Fβγ(⃗ r) := daZn(⃗0, ˆβ, ˆβ + ˆγ)⃗ r− ˆβ 2− ˆγ 2 − (β↔γ)

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:03.935672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 921e55c9-e7a0-4de9-bbe2-32652185ff3c · outbound

This paper cites reference.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ reference

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:55:03.916658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2624a3ab-b21a-4c1e-8652-46b7394ad3dc · outbound

This paper cites Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order.

Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$ Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order

Reference 16

Resolution: malformed identifier; no resolver link, observed 2026-08-14T14:55:03.853703Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 24ab2e2f-2383-4794-9bed-8f729f9bdf58 · inbound

Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry cites this paper.

Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-12T13:57:59.379600Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83ef0fc0-1eee-435a-b01a-2872ae8d206d · inbound

Generalized Symmetries Phase Transitions with Local Quantum Fields cites this paper.

Generalized Symmetries Phase Transitions with Local Quantum Fields Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T05:43:06.367123Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5dfdbe3-c02a-474d-89ed-643b80eac5e9 · inbound

Onsiteability of Higher-Form Symmetries cites this paper.

Onsiteability of Higher-Form Symmetries Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 39

Resolution: verified exact; arxiv_id, observed 2026-05-18T03:20:48.971914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 606e0b52-3f5c-499f-9881-274529634e9a · inbound

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates cites this paper.

Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-17T20:20:11.653100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a7a04d04-c695-47ff-9c9d-61eaeddb4f0a · inbound

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata cites this paper.

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-01T07:04:52.505379Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 147be398-e939-43c1-a0a9-870683667b8e · inbound

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata cites this paper.

Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-03T01:57:30.405997Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e10f66b-fe0b-4747-a03e-3f271afd4f26 · inbound

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations cites this paper.

Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations Lattice models that realize $\mathbb{Z}_n$-1-symmetry protected topological states for even $n$

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-01T06:57:48.954892Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.