Paper Citation Record · LEDGER

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis

As of 23 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2608.11563.

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

pith.paper-citation-record.v1
2608.11563 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T00:50:58.540585Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

22 of 22 outbound references displayed

verified exact5
verified fuzzy0
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation caa3dcb1-d441-42c0-8fe7-eb34b81c9c25 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.458736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4e3af728-5a2a-45e5-8b3a-b9fa5e73f392 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.463261Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d180861-4dd5-49ed-b87f-a52fac406378 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.467911Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 897ecc41-4cea-4da2-a9b8-87130f88089d · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-16T00:50:58.706447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 20c1c57e-f4db-4bcb-b909-5d715b478ec9 · outbound

This paper cites Comput.44 519–521 (doi: 10.1090/S0025-5718-1985-0777282-X).

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Comput.44 519–521 (doi: 10.1090/S0025-5718-1985-0777282-X)

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.475986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 088bad85-0017-4121-abd9-dd95c802a05d · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.480099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eff8f2e7-c982-4fd1-95b6-0edfca3eb062 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-16T00:50:58.805242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7393f832-42b5-4eaa-9695-1fb3679090bb · outbound

This paper cites Rep.1522808 (doi: 10.1038/s41598-025-04987-1).

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Rep.1522808 (doi: 10.1038/s41598-025-04987-1)

Reference 8

Resolution: verified exact; doi, observed 2026-08-16T00:50:58.680912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 11ebbe71-73d2-4353-8853-8f1ad3d8543c · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.491471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e244c74a-3e2e-4f02-b65b-cbe2e426e06a · outbound

This paper cites Low overhead quantum computation using lattice surgery.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Low overhead quantum computation using lattice surgery

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.495042Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d47808f2-1c68-4c53-8037-fa8c6b4c0dad · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.498983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ed896726-d096-44d3-a66f-25e01421d0bf · outbound

This paper cites Process.2160 (doi: 10.1007/s11128-021-03398-1).

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Process.2160 (doi: 10.1007/s11128-021-03398-1)

Reference 12

Resolution: verified exact; doi, observed 2026-08-16T00:50:58.654990Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e3973711-a528-48c0-9b83-97d545dcf02f · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.507025Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5eac1f92-6bfd-44cb-ae6b-f55751650a2d · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 14

Resolution: verified exact; doi, observed 2026-08-16T00:50:58.636822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 046b6c18-32a1-43fb-86e9-7d5634d6486b · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.514846Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b310bc9d-663b-43cc-bef5-8f214699e525 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.518207Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 562120a7-8a75-4105-baa3-33c17b9dacba · outbound

This paper cites Phys.14123011 (doi: 10.1088/1367-2630/14/12/123011).

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Phys.14123011 (doi: 10.1088/1367-2630/14/12/123011)

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.521790Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ce9d8451-7147-4587-bafd-6914aedb419c · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.525348Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0099265c-c4d0-4d34-a624-9d73ba9fe84c · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.529136Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3398407c-985f-4cb1-ac82-f49a3e703ed7 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 20

Resolution: verified exact; doi, observed 2026-08-16T00:50:58.588223Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c5238b53-0f6e-4476-b8bc-c7a6616fdc3e · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.536885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 499f5297-1f19-4357-ac46-14cec70823e5 · outbound

This paper cites an unresolved cited work.

Efficient Quantum Modular Reduction: Crandall reduction and its Fault-tolerant resource analysis Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T00:50:58.540585Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.