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Paper Citation Record · LEDGER

Randomized product formulas beyond optimal deterministic scaling

As of 12 August 2026, this Paper Citation Record lists 58 of 58 outbound references and 0 inbound Pith citation observations for arXiv:2608.07720.

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

pith.paper-citation-record.v1
2608.07720 v1

Coverage vector

measured 58 of 58 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:37:58.325168Z

measured 58 of 58 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

58 of 58 outbound references displayed

  • verified exact3
  • verified fuzzy11
  • unresolved43
  • parse uncertain0
  • malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 83ddb542-7dd3-4850-9bb2-63950b1819ed · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 1

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Observation 639e24b7-dfba-436d-86fc-6ed875abfcb4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 2

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Observation 10d10dab-15af-4c9a-8fe6-09eb3f0c9e9f · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 3

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source=pdf_text observed=2026-08-11T00:37:58.102799Z digest=sha256:781b805769a5c82ed02b74cff1ef678f0bf7ebb1d7b98bdcc9801b9cdde0267c

Observation acf4d276-427d-4ab7-a06d-aa85643aa321 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 4

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Observation 413abaf2-da8d-430e-a9c5-6a453e2c69bd · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 5

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Observation 58694c73-db10-4db7-8319-7139405419f0 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 6

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Observation 589f638a-5ae5-47d8-a2ac-4d795084f733 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 7

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Observation a059ee98-c774-4d1e-85b1-cdcf439ff52e · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 8

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Observation 7485708e-b072-4816-b118-1d2b2d926d35 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 9

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source=pdf_text observed=2026-08-11T00:37:58.126243Z digest=sha256:fa3326cc67d3922a57639506926f3d5ba219f25ee2daab663eee8511587a54e3

Observation 0c10dcdf-74dc-4406-b36d-7a5a7b5eddac · outbound

This paper cites Suzuki, Fractal decomposition of exponential opera- tors with applications to many-body theories and monte carlo simulations, Physics Letters A146, 319 (1990).

Randomized product formulas beyond optimal deterministic scaling Suzuki, Fractal decomposition of exponential opera- tors with applications to many-body theories and monte carlo simulations, Physics Letters A146, 319 (1990)

Reference 10

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Observation f35cae06-2556-4118-9c5c-578f09782ca1 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 11

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Observation e68ba28c-9526-46b0-bb36-c671d61d140b · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 12

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Observation d52080b5-9c28-4e60-ba7c-2f68eca463df · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 13

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Observation dd836807-5f45-4235-969e-91b11ae651ec · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 14

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Observation 89fe6523-4805-458e-ad5f-9561f265d73d · outbound

This paper cites Observation of separated dynamics of charge and spin in the Fermi-Hubbard model.

Randomized product formulas beyond optimal deterministic scaling Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Reference 15

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Observation 8a3dec34-73b0-423c-822a-eb339969ea42 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 16

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Observation dd1b66b5-0e0f-4040-aa31-453c8df60fd2 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 17

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 50162783-8c97-4141-a441-36cd78221986 · outbound

This paper cites Viola and E.

Randomized product formulas beyond optimal deterministic scaling Viola and E

Reference 18

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation d9e8b611-36da-4d75-85af-dc6ade4adf24 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 19

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 7059ea20-a584-4ebf-894f-3132d1bd32da · outbound

This paper cites Boixo, E.

Randomized product formulas beyond optimal deterministic scaling Boixo, E

Reference 20

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Observation 723931aa-efb4-4435-9a14-972b4adb3bbc · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 21

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Observation 0d990e5d-aa34-49b2-a4ab-81b28ba8dd17 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 22

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Observation 1a419c82-df3e-4f96-bc72-fb8f237ac9d4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 23

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation bb792b6a-e5a5-4f08-a6b5-6f472d6e347d · outbound

This paper cites Gosset, R.

Randomized product formulas beyond optimal deterministic scaling Gosset, R

Reference 24

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Observation da7e6aa5-3f60-4ed5-8c6e-8fe6b45d05a3 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 25

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 2b9a48e9-4fb5-45f3-9902-da64a709b3a4 · outbound

This paper cites Randomized Quantum Optimal Control.

Randomized product formulas beyond optimal deterministic scaling Randomized Quantum Optimal Control

Reference 26

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Observation ba90f11b-ae84-4cf8-ac7f-43fff6a73162 · outbound

This paper cites G¨ unther, F.

Randomized product formulas beyond optimal deterministic scaling G¨ unther, F

Reference 27

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation d204c30b-bf9e-4085-906a-d0ac2444ff39 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 28

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source=pdf_text observed=2026-08-11T00:37:58.204017Z digest=sha256:4592b2af8154e571f73627b3c6b7fe7e104f0f48800585e80f69afa0173ec175

Observation a76b01f7-a223-4ab0-bee9-b9bd816798eb · outbound

This paper cites Campbell, Random compiler for fast Hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019).

Randomized product formulas beyond optimal deterministic scaling Campbell, Random compiler for fast Hamiltonian sim- ulation, Physical Review Letters123, 070503 (2019)

Reference 29

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Observation 9ee5bb7b-5af3-4482-8e9a-381c6a709ef6 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 30

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Observation db4a0308-c87c-4d0d-a77d-a718c48fa981 · outbound

This paper cites Ouyang, D.

Randomized product formulas beyond optimal deterministic scaling Ouyang, D

Reference 31

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Observation c50a7b2d-2c0b-455b-97bf-63e97a5a2f3e · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 32

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source=pdf_text observed=2026-08-11T00:37:58.221493Z digest=sha256:6aa98861c4564d38a2b7e58289a403ebf864f21aed388b8c998566c4203642eb

Observation fe407acf-9081-43d3-9f24-76a72f9b2774 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 33

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation af556f46-0510-45b1-b5ee-19725bfd6fad · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 34

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 267a82b5-0f98-46fc-87ae-4de94c559381 · outbound

This paper cites Hamiltonian Simulation in the Interaction Picture.

Randomized product formulas beyond optimal deterministic scaling Hamiltonian Simulation in the Interaction Picture

Reference 35

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Observation 49c59a1c-b8ee-4bff-8fed-00e16bddf049 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 36

Resolution
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raw_fallback, observed 2026-08-11T00:37:58.870953Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation c97852ff-a779-4365-a2d0-d7e6ba2036a9 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 37

Resolution
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raw_fallback, observed 2026-08-11T00:37:58.859721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 594abc50-e50e-46b3-beb4-c9d682d1a4b7 · outbound

This paper cites Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion.

Randomized product formulas beyond optimal deterministic scaling Hamiltonian Simulation in the Interaction Picture Using the Magnus Expansion

Reference 38

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source=pdf_text observed=2026-08-11T00:37:58.247303Z digest=sha256:af9495984c221adaa8a131b166c7c2674017ac7b4c1bdea12ba20bb706d548ef

Observation 8bbb3504-17b7-452a-931a-ba72de6b22d4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 39

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source=pdf_text observed=2026-08-11T00:37:58.251200Z digest=sha256:8c5156b3eff346c3769bf229cbfce93fa4d699423ef52e1f5a48182e93e94070

Observation f79cda87-80f7-4aab-8cbf-689ecf5369cf · outbound

This paper cites Bagherimehrab, L.

Randomized product formulas beyond optimal deterministic scaling Bagherimehrab, L

Reference 40

Resolution
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raw_fallback, observed 2026-08-11T00:37:58.849289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.254952Z digest=sha256:3237015391dd60ca9ee0df4b4df4bc10d2138babf5592f0266d6c908e1bd2965

Observation a18af6eb-c652-4479-9210-4af470381d86 · outbound

This paper cites Watrous,The Theory of Quantum Information(Cam- bridge University Press, Cambridge, 2018).

Randomized product formulas beyond optimal deterministic scaling Watrous,The Theory of Quantum Information(Cam- bridge University Press, Cambridge, 2018)

Reference 41

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.258443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.258443Z digest=sha256:1f6b47d3dab9c2b4128e0a05ea3146bfebeedf1304a406c5e2b5f841214e90c5

Observation 8f298854-e2a4-4934-8f82-93c8fa7429e4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.261861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.261861Z digest=sha256:a17d951db67dc395a6c4fd3eaead4aa4f3c52bddc2971c62721e0a2051f8bea0

Observation 8ab3d686-b651-4f3d-b274-e146ba626025 · outbound

This paper cites Akibue, G.

Randomized product formulas beyond optimal deterministic scaling Akibue, G

Reference 43

Resolution
verified exact
doi, observed 2026-08-11T00:37:58.361386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.265207Z digest=sha256:22fc4d43dc57143058770e88b273d698ea2ccebfe067725375cd65009555b7ca

Observation 35f82285-1cae-4384-baa8-bd00304d2996 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 44

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.825622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.268736Z digest=sha256:533461913a51638c5b63255ad86af1412e4de7d32c11ca3a4435f5b2f4ec6533

Observation a6ce1f5b-f77c-4bef-86ee-b28727a73341 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.272538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.272538Z digest=sha256:488cf766bddd65334ff2137d4bede788e224c485ce9f71188ca7f3e0a35a5c62

Observation 2781bc3d-88c8-487e-b8ec-4b13f738f442 · outbound

This paper cites Campbell, Shorter gate sequences for quantum com- puting by mixing unitaries, Physical Review A95, 042306 (2017).

Randomized product formulas beyond optimal deterministic scaling Campbell, Shorter gate sequences for quantum com- puting by mixing unitaries, Physical Review A95, 042306 (2017)

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.806633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.276384Z digest=sha256:541b235035a370b014ed005e04360533fc4641658e57e313ac68ea2a0987f863

Observation d3bcb65e-f4f2-46d3-868a-aa45832b923a · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 47

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.280538Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.280538Z digest=sha256:d30917ed6960f1b269242be13e84f89f7f2776df32849d31cc4404f95f993655

Observation e1ff6466-45ca-4516-bc71-26906451968f · outbound

This paper cites Chen, H.-Y.

Randomized product formulas beyond optimal deterministic scaling Chen, H.-Y

Reference 48

Resolution
unresolved
no resolver link, observed 2026-08-11T00:37:58.284269Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T00:37:58.284269Z digest=sha256:e652a3872a171780818492af691795c68b29a546fec4e49025ffda4298883882

Observation 0cd9511e-ae6d-4752-88d1-a74c32cd6c3c · outbound

This paper cites Kim and M.

Randomized product formulas beyond optimal deterministic scaling Kim and M

Reference 49

Resolution
verified exact
raw_fallback, observed 2026-08-11T00:37:58.465883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.288142Z digest=sha256:c9bab3a708260969afd20c9841a19bbe9f562ea90572f0d3ac8a14f79d3d7cef

Observation 38fc3059-f490-4ea7-bbcc-5a841aee95ef · outbound

This paper cites Aharonov, A.

Randomized product formulas beyond optimal deterministic scaling Aharonov, A

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.778236Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.291807Z digest=sha256:355b9f6dbba50b1275c137d15122d01c5c725d90d6cad32043ee8c0bafea4d34

Observation e1fc1071-020a-4d7c-a541-d14bf0e5a020 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 51

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.764671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.295798Z digest=sha256:f20b80fb7f70d184d727e264d7f0eb7cf05ea7f0affe7158e4e7ee76daf85527

Observation d01d8742-97df-4044-a616-ea2c354c6c96 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 52

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.751510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.300145Z digest=sha256:65025ecdb0819b3a0b9cf8721abb746559accb8675fdb3bf89aad8cf8ae0eb71

Observation b65f85c5-9848-41d9-9e93-6afc752c8458 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 53

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.738285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.304227Z digest=sha256:b6c1f6a8a2a9e363e6553ed40a10b046ee022255916f3a9dee49b40a77f23ba8

Observation a6079df4-e209-40b9-838e-d082256d1dfd · outbound

This paper cites (28) 11 S3.3.

Randomized product formulas beyond optimal deterministic scaling (28) 11 S3.3

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.724425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.308215Z digest=sha256:e9be6bfa6f29ac1f453b85b16b6ac996368611ef21af1b7d6bca61dea1827b4b

Observation bbe3815e-561e-4579-92bf-bc88c16412b0 · outbound

This paper cites The sampling distribution is chosen so that the averaged second-order 9 contribution of these corrections is the negative of the leadingα 2 error in Eq.

Randomized product formulas beyond optimal deterministic scaling The sampling distribution is chosen so that the averaged second-order 9 contribution of these corrections is the negative of the leadingα 2 error in Eq

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.710228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.313063Z digest=sha256:8f3e0cfabf02227f42f63a7c9525b1f0bd038309af072b115cf162944e03c632

Observation 469c6c0e-1869-42b6-9675-4f2dcb3bc310 · outbound

This paper cites For an explicit implementation, it is convenient to sample this distribution hierarchically rather than enumerate all tuples (a, b, n, q).

Randomized product formulas beyond optimal deterministic scaling For an explicit implementation, it is convenient to sample this distribution hierarchically rather than enumerate all tuples (a, b, n, q)

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T00:37:58.696164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.317280Z digest=sha256:33c4d7a80eb27130cdab014e0b59dc980b20ab57504e37740c036cb6dfdab9b7

Observation 3fa63c04-1b07-4f4e-86c8-07c7e66d32c4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 57

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.682256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.321374Z digest=sha256:582be0f6dc56d6c4e79ccd24b7e424b29740faeafc0820c61af573ba33107dbf

Observation ae216321-c94c-410e-ac7b-4a58fbeed0b4 · outbound

This paper cites an unresolved cited work.

Randomized product formulas beyond optimal deterministic scaling Unresolved cited work

Reference 58

Resolution
unresolved
raw_fallback, observed 2026-08-11T00:37:58.669176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-11T00:37:58.325168Z digest=sha256:ac3b47a63125bad0fb1e63427a6f689587fff81bffc040b8b922f2dab27a2866

Pith citing papers

No inbound Pith citation observations are available.