Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T21:31:52.954755Z
Paper Citation Record · LEDGER
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
As of 16 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 6 inbound Pith citation observations for arXiv:2505.09697.
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 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-15T14:23:15.296875Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-03T13:28:18.398193Z
Reference resolution
36 of 36 outbound references displayed
- verified exact1
- verified fuzzy14
- unresolved21
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 45e5c253-a556-4949-9921-4862b20514a0 · outbound
This paper cites Bradlyn, L.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Bradlyn, L
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.501055Z
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 71f70f15-92a7-4fc0-8426-1d33c29017ab · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.516504Z
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 48551c12-0963-421d-999a-0eaf76ad1303 · outbound
This paper cites Zak, Phys.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Zak, Phys
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.802303Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 39594c7a-fc26-4faa-be6f-8b8c6731edff · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.797674Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 16abbd22-1120-4abf-af07-43c2cafef25f · outbound
This paper cites Kruthoff, J.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Kruthoff, J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.451432Z
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 b81feee2-e9e9-401c-b6bd-d2bb78e6035e · outbound
This paper cites Zak, Phys.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Zak, Phys
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.807596Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 164223c4-1444-48fb-a9d6-44324733d530 · outbound
This paper cites Aroyo, J.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Aroyo, J
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.414647Z
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 a9f469fa-c127-426d-af55-d166e92e29b2 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.434211Z
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 85f90463-51e9-428a-a2fb-7c6943f45f92 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.378378Z
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 00fefe4c-834c-49d0-bdf0-1c85afbd2066 · outbound
This paper cites Bradlyn, L.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Bradlyn, L
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.395617Z
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 b3343932-6727-4c4b-acd7-4715064d69a1 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.842910Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 35bcbfdd-b11b-4159-8cb1-afa62c243305 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.363264Z
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 2695f262-bb54-48ea-808b-84fa5a8b461e · outbound
This paper cites Peri, Z.-D.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Peri, Z.-D
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.320829Z
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 7186c981-564f-498d-a2f0-6eae80b3445d · outbound
This paper cites Cano and B.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Cano and B
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.336707Z
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 7132e2ef-185c-4faf-bb18-fc696593dc5c · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.303431Z
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 1a9f5301-ddaf-4636-9ba0-3be2cb59bf11 · outbound
This paper cites Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Three-Dimensional Real Space Invariants, Obstructed Atomic Insulators and A New Principle for Active Catalytic Sites
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.856715Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cf47ac7a-c08f-4750-aa28-1a32aa3507cc · outbound
This paper cites Altmann and P.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Altmann and P
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.269488Z
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 bdb5f12d-be50-4d44-9913-98190ddbe092 · outbound
This paper cites Elcoro, B.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Elcoro, B
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.286266Z
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 be8c14e0-8123-4d27-a131-2ed0ca166dfc · outbound
This paper cites Cohen, A course in computational algebraic number theory , Vol.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Cohen, A course in computational algebraic number theory , Vol
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.233856Z
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 7c4c2cbb-8b58-4c5c-a5e9-2fa8632aaf80 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.252044Z
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 7f983345-2679-4392-9157-fea948931909 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.194631Z
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 a8a4ca73-481c-45f7-b5c3-f10069045e3f · outbound
This paper cites Elcoro, Z.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Elcoro, Z
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.213889Z
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 48739db4-542e-4ad7-aec3-9408be2246dc · outbound
This paper cites For each space group, we list its number in the International Tables for Crystallography, Vol.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators For each space group, we list its number in the International Tables for Crystallography, Vol
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.534949Z
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 adc133ee-67d0-45dc-b656-fa68057ad761 · outbound
This paper cites Belov, N.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Belov, N
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.175977Z
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 c1c2a893-58ee-4c30-9a6d-f2b34a2eb626 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.901479Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1bea90b0-0fa4-4c78-83c0-4479e67e3fa6 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.148909Z
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 eceb39a7-3c55-44c6-bb94-534a80305a9b · outbound
This paper cites Hwang, J.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Hwang, J
Reference 27
- Resolution
- verified exact
- doi, observed 2026-08-15T21:31:53.006778Z
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 058f8c98-c6d1-41c8-9360-a37c0c7e4275 · outbound
This paper cites Schindler and B.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Schindler and B
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.132132Z
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 70762b60-ac38-49a4-9d67-b31efe9a75ed · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-15T21:31:53.116613Z
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 3253cd2a-b07a-49a1-8db2-372f3459d371 · outbound
This paper cites Bouhon, A.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Bouhon, A
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-15T21:31:53.099296Z
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 42f36d62-43e3-4d6c-9c6e-a39f2473d527 · outbound
This paper cites Bradlyn, Z.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Bradlyn, Z
Reference 31
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.929225Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8218930b-cd4f-4802-9d2d-7c221521e87e · outbound
This paper cites Shiozaki and M.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Shiozaki and M
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.934032Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7a93b11f-dff5-4d90-8240-b94e6f89a1b2 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 33
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.940765Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 68db3b67-cf9b-465c-8791-73815eeef8f9 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.945562Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d7b6e31f-cae0-4890-8c2d-3a8dea52455b · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.949710Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0fd6e40e-f104-4a91-921d-804890926852 · outbound
This paper cites an unresolved cited work.
Stable Real-Space Invariants and Topology Beyond Symmetry Indicators Unresolved cited work
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T21:31:52.954755Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 78bd180c-a66f-4bdb-962a-bef9c9cee837 · inbound
Topological Dislocation Response in Elementary Semiconductors cites this paper.
Topological Dislocation Response in Elementary Semiconductors Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 48
- Resolution
- unresolved
- no resolver link, observed 2026-08-02T21:21:41.682123Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2a76afc7-de35-4123-a79c-3f22676531c0 · inbound
Crystalline topological invariants in quantum many-body systems cites this paper.
Crystalline topological invariants in quantum many-body systems Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 53
- Resolution
- metadata mismatch
- arxiv_id, observed 2026-07-20T00:18:13.927387Z
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 d608f0ee-1368-40ab-9e89-291bbb4ad773 · inbound
Stable Wave-Function Zeros Indicate Exciton Topology cites this paper.
Stable Wave-Function Zeros Indicate Exciton Topology Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 15
- Resolution
- verified exact
- arxiv_id, observed 2026-07-20T00:18:13.927387Z
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 40050c6c-853e-4391-8597-a81693605187 · inbound
Composite Quantum Geometry and Semiclassical Dynamics cites this paper.
Composite Quantum Geometry and Semiclassical Dynamics Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 10
- Resolution
- verified exact
- arxiv_id, observed 2026-07-20T00:18:13.927387Z
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 4b1386a4-6810-49e0-a61c-c02f693c9652 · inbound
Fragile Topology is Unstable Under Translation Refinement cites this paper.
Fragile Topology is Unstable Under Translation Refinement Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 51
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T15:38:51.904711Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2e23dd4a-0ad4-4540-896c-b72194dbf97a · inbound
Higher-Order Topological States with Cleavage-Dependent Dirac Mass cites this paper.
Higher-Order Topological States with Cleavage-Dependent Dirac Mass Stable Real-Space Invariants and Topology Beyond Symmetry Indicators
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-15T14:23:15.296875Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.