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Paper Citation Record · LEDGER

A note on the sample complexity of multi-target detection

As of 22 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2501.11980.

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

pith.paper-citation-record.v1
2501.11980 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:47:00.527167Z

measured 37 of 37 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-19T06:39:43.135599Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T06:42:07.461415Z

Reference resolution

36 of 36 outbound references displayed

  • verified exact1
  • verified fuzzy29
  • unresolved6
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation fd2b6b29-774c-48c5-9897-c0f2d5874a06 · outbound

This paper cites Multireference alignment is easier with an aperiodic translation distribution.

A note on the sample complexity of multi-target detection Multireference alignment is easier with an aperiodic translation distribution

Reference 1

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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.

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Observation b58fc333-c7ce-4860-870b-3eadcc9dbe88 · outbound

This paper cites Fundamental limits in multi-image align- ment.

A note on the sample complexity of multi-target detection Fundamental limits in multi-image align- ment

Reference 2

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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.

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Observation e8baffba-131d-4e58-a8b3-1c7ce67e8db6 · outbound

This paper cites Einstein from noise: Statistical analysis.

A note on the sample complexity of multi-target detection Einstein from noise: Statistical analysis

Reference 3

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Observation 911fd68e-2420-41f9-a16b-58ac2d5d3d40 · outbound

This paper cites Estimation under group actions: recovering orbits from invariants.

A note on the sample complexity of multi-target detection Estimation under group actions: recovering orbits from invariants

Reference 4

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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.

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Observation f6da19a4-5ffc-45e3-9d38-b0bd952af16e · outbound

This paper cites Multireference alignment using semidefinite programming.

A note on the sample complexity of multi-target detection Multireference alignment using semidefinite programming

Reference 5

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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.

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Observation f866441c-e7e9-405a-9aaa-32a7d61d2a2e · outbound

This paper cites Single- particle cryo-electron microscopy: Mathematical theory, compu- tational challenges, and opportunities.

A note on the sample complexity of multi-target detection Single- particle cryo-electron microscopy: Mathematical theory, compu- tational challenges, and opportunities

Reference 6

Resolution
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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.

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Observation 768f18df-fa80-4e42-844c-f5276e4c00c1 · outbound

This paper cites Multi-target detection with application to cryo- electron microscopy.

A note on the sample complexity of multi-target detection Multi-target detection with application to cryo- electron microscopy

Reference 7

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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.

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Observation 1a61d6e4-bfde-471e-b689-cd152b205f9d · outbound

This paper cites Toward single particle reconstruction without particle picking: Breaking the detection limit.

A note on the sample complexity of multi-target detection Toward single particle reconstruction without particle picking: Breaking the detection limit

Reference 8

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Observation 3568e620-7ba0-48b9-b15a-340c9b514234 · outbound

This paper cites A transversality theorem for semi-algebraic sets with application to signal recovery from the second moment and cryo-EM.

A note on the sample complexity of multi-target detection A transversality theorem for semi-algebraic sets with application to signal recovery from the second moment and cryo-EM

Reference 9

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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.

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Observation 99386e4e-6a32-4c29-8597-732dbe56fd15 · outbound

This paper cites Dihedral multi-reference alignment.

A note on the sample complexity of multi-target detection Dihedral multi-reference alignment

Reference 10

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

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Observation b2cfc2f0-73f5-435d-a4d7-93a2f259fdd1 · outbound

This paper cites Multi-target detection with rotations.

A note on the sample complexity of multi-target detection Multi-target detection with rotations

Reference 11

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

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Observation ccce8ee2-c4b7-4d77-8ae3-7276987e6a9c · outbound

This paper cites Detection and recovery of hidden submatrices.

A note on the sample complexity of multi-target detection Detection and recovery of hidden submatrices

Reference 12

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

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Observation 22a7fa8c-b2ea-45a1-bdb8-f30fdbd38552 · outbound

This paper cites Generic orbit recovery from invariants of very low degree.

A note on the sample complexity of multi-target detection Generic orbit recovery from invariants of very low degree

Reference 13

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 83abec5e-ab64-4340-8fab-2ef31f0d41d6 · outbound

This paper cites The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of un- stained biological molecules.

A note on the sample complexity of multi-target detection The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of un- stained biological molecules

Reference 14

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Observation 036fb378-4c91-4404-96a0-2f069cffaf77 · outbound

This paper cites Avoiding the pitfalls of single particle cryo- electron microscopy: Einstein from noise.

A note on the sample complexity of multi-target detection Avoiding the pitfalls of single particle cryo- electron microscopy: Einstein from noise

Reference 15

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Observation 5607d569-d0ad-41a7-9a46-a5aaab125b0c · outbound

This paper cites Two-dimensional multi- target detection: An autocorrelation analysis approach.

A note on the sample complexity of multi-target detection Two-dimensional multi- target detection: An autocorrelation analysis approach

Reference 16

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

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Observation 994384e3-8795-42a8-888c-f9e35478a1f0 · outbound

This paper cites An approxi- mate expectation-maximization for two-dimensional multi-target detection.

A note on the sample complexity of multi-target detection An approxi- mate expectation-maximization for two-dimensional multi-target detection

Reference 17

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

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Observation 17801c73-f981-4d34-aaad-4f780511f420 · outbound

This paper cites A stochas- tic approximate expectation-maximization for structure deter- mination directly from cryo-EM micrographs.

A note on the sample complexity of multi-target detection A stochas- tic approximate expectation-maximization for structure deter- mination directly from cryo-EM micrographs

Reference 18

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Unavailable: canonical work link unavailable.

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Observation 2e0ec2a6-08ba-4859-9eee-433c9a991fdd · outbound

This paper cites Multi-target detection with an arbitrary spacing distribution.

A note on the sample complexity of multi-target detection Multi-target detection with an arbitrary spacing distribution

Reference 19

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Observation 257f8aec-02d8-482f-909b-b64d2c999d70 · outbound

This paper cites Heterogeneous multireference alignment for images with application to 2D classification in single particle reconstruc- tion.

A note on the sample complexity of multi-target detection Heterogeneous multireference alignment for images with application to 2D classification in single particle reconstruc- tion

Reference 20

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Observation ee87ff11-b633-4c6f-956e-e344cae98e6d · outbound

This paper cites Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions.

A note on the sample complexity of multi-target detection Fast expansion into harmonics on the disk: a steerable basis with fast radial convolutions

Reference 21

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Observation 4b467311-5546-44e8-b43f-da99842bc3fc · outbound

This paper cites Chapter 36 large sample estimation and hypothesis testing.

A note on the sample complexity of multi-target detection Chapter 36 large sample estimation and hypothesis testing

Reference 22

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Observation 2071d267-d892-4f27-9ec2-24a918cb8709 · outbound

This paper cites The development of cryo-EM into a mainstream structural biology technique.

A note on the sample complexity of multi-target detection The development of cryo-EM into a mainstream structural biology technique

Reference 23

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Observation 0d916491-8bbe-482a-bfe5-a1865418dd78 · outbound

This paper cites Multi- reference alignment in high dimensions: sample complexity and phase transition.

A note on the sample complexity of multi-target detection Multi- reference alignment in high dimensions: sample complexity and phase transition

Reference 24

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Observation b42d5ea7-3823-4919-9841-939396506978 · outbound

This paper cites Theory of statistics.

A note on the sample complexity of multi-target detection Theory of statistics

Reference 25

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

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Observation c5ba838a-81f1-4270-b76f-e8cdf31c8235 · outbound

This paper cites Computational methods for single-particle electron cryomicroscopy.

A note on the sample complexity of multi-target detection Computational methods for single-particle electron cryomicroscopy

Reference 26

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raw_fallback, observed 2026-08-10T17:47:00.845379Z

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.

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Observation 3abff561-5101-4037-8b92-33ec99273269 · outbound

This paper cites an unresolved cited work.

A note on the sample complexity of multi-target detection Unresolved cited work

Reference 27

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

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Observation e3ce16d1-757a-4e61-86d4-7efd6796dd0e · outbound

This paper cites (A.27) Combining (A.26) and (A.27) with (A.5) and (A.6), and summing over −L ≤ k < Lcompletes the proof.

A note on the sample complexity of multi-target detection (A.27) Combining (A.26) and (A.27) with (A.5) and (A.6), and summing over −L ≤ k < Lcompletes the proof

Reference 28

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Observation 6ca83dde-672b-43e5-84f7-3d17ca56d02a · outbound

This paper cites Now, we must examine the convergence of the entire empirical autocorrelation tensor (in the Frobenius norm) to the ensemble mean.

A note on the sample complexity of multi-target detection Now, we must examine the convergence of the entire empirical autocorrelation tensor (in the Frobenius norm) to the ensemble mean

Reference 29

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Observation b64722ed-4f9d-48f1-ab81-acfd34309f3a · outbound

This paper cites To achieve this, it is essential that some additional mild conditions would hold, as proved in Lemma A.7.

A note on the sample complexity of multi-target detection To achieve this, it is essential that some additional mild conditions would hold, as proved in Lemma A.7

Reference 30

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Observation 3e3f6cf2-dd89-40f3-a76c-4c16206ca76b · outbound

This paper cites an unresolved cited work.

A note on the sample complexity of multi-target detection Unresolved cited work

Reference 31

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

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Observation f519598a-589d-4474-971a-0c9a8eda4578 · outbound

This paper cites − − →Q0 (G · x) , (A.40) where Q0 (G · x) indicates the expected value of the right-hand-side of (A.38), given by ¯µ( ¯d) G·x,.

A note on the sample complexity of multi-target detection − − →Q0 (G · x) , (A.40) where Q0 (G · x) indicates the expected value of the right-hand-side of (A.38), given by ¯µ( ¯d) G·x,

Reference 32

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source=pdf_text observed=2026-08-10T17:47:00.512442Z digest=sha256:6994aa952e72f1ac2055a0c95d2dd1bdd08c1b572df850fc8d0f4a450acfd4d2

Observation 0c047e1a-bd77-4b0f-9280-ce5cb0921131 · outbound

This paper cites an unresolved cited work.

A note on the sample complexity of multi-target detection Unresolved cited work

Reference 33

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

source=pdf_text observed=2026-08-10T17:47:00.516819Z digest=sha256:c2d0272f6e62e0bfa3d75c8b7a093d947389ea17ba513f17b4d928b00fff4a07

Observation d6cc835c-b4f0-421d-aa2f-d5f28cdb362f · outbound

This paper cites Then, by applying [22, Theorem 2.1], where all the condition of the theorem are satisfied, we obtain the result: [G · x P − →G · x.

A note on the sample complexity of multi-target detection Then, by applying [22, Theorem 2.1], where all the condition of the theorem are satisfied, we obtain the result: [G · x P − →G · x

Reference 34

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raw_fallback, observed 2026-08-10T17:47:00.764383Z

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.

source=pdf_text observed=2026-08-10T17:47:00.520408Z digest=sha256:4acafd6f1db334f206a113052ef5175bf9b5b42e48b712f09229b4b50b79034b

Observation 73cdc6ca-eb03-420e-97d8-17af57db6737 · outbound

This paper cites an unresolved cited work.

A note on the sample complexity of multi-target detection Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-10T17:47:00.752473Z

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.

source=pdf_text observed=2026-08-10T17:47:00.523832Z digest=sha256:6203b7ad605fef8dd591f57bb05441560f856f9be173f0c16a274e9b3129a308

Observation ca335d5c-6298-477b-ae9c-2769e2203a5e · outbound

This paper cites Clearly, the map defined above is a measurable map and defines the non-overlapping MTD model in (I.1), according to any unknown locations {si}N −1 i=0.

A note on the sample complexity of multi-target detection Clearly, the map defined above is a measurable map and defines the non-overlapping MTD model in (I.1), according to any unknown locations {si}N −1 i=0

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:47:00.742558Z

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.

source=pdf_text observed=2026-08-10T17:47:00.527167Z digest=sha256:43f386d00e0c133676215657ed01fef06e1491cc2c6058fcc17e4c8a158be93b

Pith citing papers

Observation a631ea36-300a-495a-88f4-8871ff9eb1d8 · inbound

Structure from Noise: Confirmation Bias in Particle Picking in Structural Biology cites this paper.

Structure from Noise: Confirmation Bias in Particle Picking in Structural Biology A note on the sample complexity of multi-target detection

Reference 5

Resolution
verified exact
arxiv_id, observed 2026-05-19T06:42:07.463840Z

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.

source=pdf_text observed=2026-05-19T06:39:43.135599Z digest=sha256:264745f03b989dfa7dd4608c33d41d75d1e6e7158a50844e3dc9db44effbb7aa