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.

pith.paper-citation-record.v1
2505.09697 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:31:52.954755Z

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 6 of 6 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T14:23:15.296875Z

measured 0 of 1 external citation measurements

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.