Paper Citation Record · LEDGER

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors

As of 7 August 2026, this Paper Citation Record lists 48 of 48 outbound references and 0 inbound Pith citation observations for arXiv:2507.07972.

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

pith.paper-citation-record.v1
2507.07972 v1

Coverage vector

measured 48 of 48 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:34:20.210815Z

measured 48 of 48 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

48 of 48 outbound references displayed

verified exact2
verified fuzzy3
unresolved43
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0c0ca528-207e-4c0a-b439-58d6e6e16b4c · outbound

This paper cites torch.Tensor.stride — PyTorch Documentation.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors torch.Tensor.stride — PyTorch Documentation

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:22.042434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2721407c-93fe-44ee-97c2-6ec661df7901 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:15.946941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35874e27-c70c-45e7-b932-a0eb7acff174 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:16.060132Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a83b9098-1db8-43f4-9f3d-5b57603a0ed7 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:16.290426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d7c5df66-9be5-4809-8d66-c9f1df5ac8cb · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:16.394311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8825ff7f-7d3e-42d0-9f93-c3e1b1782d66 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.997121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 03a140f3-b8e8-4205-954c-fe9867763cbc · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.980942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b8319018-326e-4e5e-a7ac-f453452bed86 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.964146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 863ac283-1eee-4c47-9467-ded6ab5c1255 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.947235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a175755d-f3a9-421f-8321-9ccfd1963b46 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.931753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 128603ab-dc5a-4db1-9d94-6dd524c649bc · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.915753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 07189fd8-adbc-4491-860d-cb8c834ebc8e · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.866005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 76089d99-135c-4637-aee5-c9e27715c07a · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.849260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 05be5849-1829-4fec-953c-d24a2ea24f25 · outbound

This paper cites cuDNN: Efficient Primitives for Deep Learning.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors cuDNN: Efficient Primitives for Deep Learning

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:17.971233Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b18f834-ddbc-4718-b2cb-00f6b0c1d987 · outbound

This paper cites Cryptology ePrint Archive, Paper 2018/931.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Cryptology ePrint Archive, Paper 2018/931

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:21.883299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 710c62c4-a0b5-4ec3-89d8-d78e35a35ad4 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.815706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 499ca43f-9ba9-4943-9cab-8d1f8a3d4656 · outbound

This paper cites Lee, and Brandon Reagen.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Lee, and Brandon Reagen

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.193904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f2299b4-3d44-4297-9048-9b3a8b659844 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.284833Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e35599b-c113-4c38-b02b-21c396e7f9e3 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.833222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 584f7c9a-d867-4544-920a-4eba223b36a6 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.797186Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 76706986-6fb0-469a-88dd-ce99b5ba543e · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.780351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8caa8a4f-64b0-4e84-852a-5f91e172f036 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.497051Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf61f351-b5cd-43a5-bdb9-ee45c836438a · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.340358Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1334995-13c4-4b28-b4f8-696fecb083bb · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.763509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2a2aebaf-b500-4ab8-9e75-ddb92b391a0d · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.724379Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3b9217d7-aedd-47d9-a3af-46f993164afc · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.815594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b665baa9-821f-44bc-8dae-012d168668a1 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:18.575974Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation becc902f-548b-427d-ba02-e754db642b7a · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-08-06T18:34:20.387244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2d9bd6df-6d58-4f16-9a66-ea977a0e1b9e · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.731388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b040dbe1-9fc8-4fc3-ba88-e29576d51870 · outbound

This paper cites Harris, K.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Harris, K

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.088332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0bd5afdf-7caf-4ddf-a3ac-2e63c9dc13d7 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.747301Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c377c874-7111-41d4-a7dc-349faea3bbf6 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.243883Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b80340b4-4a35-4582-ae7e-0bb3025634f2 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.699913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 060e7256-7374-4cf2-ad47-5289b4e1f6c4 · outbound

This paper cites Lawson, Richard Hanson, David Kincaid, and Fred Krogh.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Lawson, Richard Hanson, David Kincaid, and Fred Krogh

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.387368Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c8849a0-5197-48f6-9371-24b98d0edbf8 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.152128Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b95557b9-afbc-4673-9410-a28c9522d97d · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.548012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 211facd3-72d3-459a-82bf-3431f8e065e0 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.666447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 73c39dc7-737c-424d-a44b-0e4bef40a6cd · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.649812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b00ad21b-9d01-4887-a6ed-dd57d53d1794 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.682512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f65bd474-e7c9-4504-8070-622c562ed8c2 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 41

Resolution: verified exact; raw_fallback, observed 2026-08-06T18:34:20.784746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 568e66f0-2a2f-4b51-85bb-1f9915ec5c6e · outbound

This paper cites Attention Is All You Need.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Attention Is All You Need

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:19.905809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ebcf473f-4f11-4496-b0c0-e123fb118f21 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.614602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d7a11dd5-316e-4d32-9771-d2bd11105bdc · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.631531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3ac53206-9ecb-4ac4-b018-50a85afb8b1f · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 45

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.581490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a8824a74-5b60-4767-aecc-7b956a445d5b · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:21.598807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6cbe2b4a-6c29-45c0-9c01-c2add9ea7341 · outbound

This paper cites an unresolved cited work.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Unresolved cited work

Reference 2015

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:34:22.014634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 48914150-6304-4d20-a632-a0ae686a8fc5 · outbound

This paper cites Cryptology ePrint Archive, Paper 2018/153.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Cryptology ePrint Archive, Paper 2018/153

Reference 2018

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:34:21.900387Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e6a0dd5d-0385-4734-8d23-ca58239127bc · outbound

This paper cites Hilfer fractional advection-diffusion equations with power-law initial condition; a Numerical study using variational iteration method.

EinHops: Einsum Notation for Expressive Homomorphic Operations on RNS-CKKS Tensors Hilfer fractional advection-diffusion equations with power-law initial condition; a Numerical study using variational iteration method

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-06T18:34:16.606529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.