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Paper Citation Record · LEDGER

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

As of 19 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 3 inbound Pith citation observations for arXiv:2505.04304.

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

pith.paper-citation-record.v1
2505.04304 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T23:40:20.479434Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:15:56.057143Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T00:44:48.295282Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 17c4d313-1822-4cce-991b-5a3497e5e396 · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.772133Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.392939Z digest=sha256:a47da272aab2972787cfa714db344cc5cce1c9c497ef16e242485d29711455a8

Observation 06007cda-0cab-4b45-b67f-d33e0b24f612 · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.759733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.398097Z digest=sha256:28bef42151772be4fb8c192de01adb5c9921fc483d5b37775b8a8b8d8b8a34f2

Observation 0c2e4913-8093-4c96-a537-7bc101b1a487 · outbound

This paper cites Boyle, M.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Boyle, M

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.747037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.402295Z digest=sha256:87b44184b0339793fba39212963126a0124513568a78c46f6ad5f9aac70dc5cb

Observation 199fb72b-0fdd-4b06-b028-5d86a1789dc3 · outbound

This paper cites Calderer, A.P.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Calderer, A.P

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.734965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.406583Z digest=sha256:3fee9e10d9c00ed7514375ab130b579cbd9780b9d79c76ed5db1712894557e9a

Observation e514a59d-e0eb-488e-9f37-925f1aa9e52b · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.722863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.411280Z digest=sha256:f67b01725f7775f04abe1845cde54862aef7726616975f10fd2d6208a5be9a22

Observation a57d2a43-1f1a-44d9-bb80-198d477f1fdf · outbound

This paper cites Childs, Y.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Childs, Y

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.710634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.415573Z digest=sha256:8b7c99d0975e7e88d8149586977c398d964422be36371e8fba378e3a58db9f15

Observation 1de2b9de-f7c3-4fe4-bd2a-85c6baf57407 · outbound

This paper cites Qiskit: An opensource framework for quantum computing.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Qiskit: An opensource framework for quantum computing

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.698222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.420231Z digest=sha256:16dc7443b35b796ed309b200c0c8098f63bd9b19cbb1572a3b9dfd184a3d5139

Observation b014bda2-28cc-4ad2-b0de-af4f85d9edae · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.684673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.424484Z digest=sha256:e7edb11300929b82355205d190b53653baee172e40d55093f910423c9ec95e2c

Observation d540de6b-248f-4039-aad2-721d8831889b · outbound

This paper cites Jin and N.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Jin and N

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.672507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.428378Z digest=sha256:ab2395de55392d109a6594ec037f270cfc8bca7ec345923b5c41137b9baa84eb

Observation e5539795-c6a4-4f92-b326-115bfaef35a4 · outbound

This paper cites On Schr\"odingerization based quantum algorithms for linear dynamical systems with inhomogeneous terms.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation On Schr\"odingerization based quantum algorithms for linear dynamical systems with inhomogeneous terms

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-15T23:40:20.432619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T23:40:20.432619Z digest=sha256:863fd4b5294374c9525463cc0097157209d2701ff14555e47f1b33bb1e651cf1

Observation e84094e2-b3e8-4bb2-8062-f8a28651b7d4 · outbound

This paper cites Schr\"odingerisation based computationally stable algorithms for ill-posed problems in partial differential equations.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Schr\"odingerisation based computationally stable algorithms for ill-posed problems in partial differential equations

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-15T23:40:20.437314Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T23:40:20.437314Z digest=sha256:87c7124d36bd300ab46fa7871e733ebaf8f1599e2dd6a7cbabbb3ca2d37a1c7c

Observation 2376cf8d-6f4c-4652-bd27-a305ac6e0ce6 · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.660257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.442080Z digest=sha256:2879bf1566399048b6c2d5d555708f52352ca4f27d85da9ad4a93d3047e4fc2e

Observation f39727a9-13b1-40f0-aa46-98ba0dcc2fd1 · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.647476Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.446362Z digest=sha256:c73bcdb054cd1e4985f73890db754bf197fdfb0b16486eddcac0c3fddddbe967

Observation 15b174d1-e912-493d-becc-31c037d0e359 · outbound

This paper cites Lecture Notes on Quantum Algorithms for Scientific Computation.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Lecture Notes on Quantum Algorithms for Scientific Computation

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-15T23:40:20.450194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T23:40:20.450194Z digest=sha256:b5b626061bb5d9e70a09f89e46559eeaceabd8daa805b61ed9d05949dd32c65b

Observation 2c2477ff-2d68-4b47-bc0b-c8f4cdc23797 · outbound

This paper cites Nielsen and I.L Chuang.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Nielsen and I.L Chuang

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.634513Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.454505Z digest=sha256:1ed827ac12840cb6273cc8a9b5e41664d29677d443eab9318a2fdc71fbcc2ae4

Observation f4fb4963-0291-4f12-a3a7-e98be7781aa8 · outbound

This paper cites Rebentrost, B.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Rebentrost, B

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.620212Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.458328Z digest=sha256:68808261ff797857f672ba5efcd6f7a40bd0867a0d4c79c1c8e102acdc49c5b4

Observation 2a54adf6-82e7-4498-ba39-998bd4ada9c8 · outbound

This paper cites Roul and V .M.K.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Roul and V .M.K

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.606969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.462274Z digest=sha256:e26ab65020dbe022cd884ef0b05b2728fed970ae0ab5ebe1cfc49d5d011e1f93

Observation 5b980485-446d-4cf4-8195-ddfaf09a0dc9 · outbound

This paper cites Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-15T23:40:20.466196Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T23:40:20.466196Z digest=sha256:a09bd761e6a9484ce11c40b24fb4cb668c26ca5ae4b1e789582af7cb42962fba

Observation 5f3183b4-d059-446a-980e-a155176ccecd · outbound

This paper cites Stamatopoulos, D.J.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Stamatopoulos, D.J

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.593596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.470380Z digest=sha256:cbec9c2a656cf11516310765b52397b2b77d90a13b75e118fb61f9c3bbc12e04

Observation b986f0a3-70c7-4496-8fc8-95b5a64751da · outbound

This paper cites Vale, T.M.D.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Vale, T.M.D

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T23:40:20.580281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.474535Z digest=sha256:969aac3cabdf25651988163df289693d71d27861286a1f151f2473f9bc8cfc74

Observation 7d57134f-3e9b-4c94-8fc0-2d0e5e0cb726 · outbound

This paper cites an unresolved cited work.

Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-15T23:40:20.566738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T23:40:20.479434Z digest=sha256:f445c2681c964e5c6041c8984eb642af2a062d7ea65c2f0038caa059baa3df98

Pith citing papers

Observation 9ef28780-603f-472d-9fdc-cdcd74c5aa0c · inbound

Quantum simulation of multiscale linear transport equations via Schr\"odingerization and exponential integrators cites this paper.

Quantum simulation of multiscale linear transport equations via Schr\"odingerization and exponential integrators Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

Reference 33

Resolution
unresolved
no resolver link, observed 2026-08-15T18:15:56.057143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T18:15:56.057143Z digest=sha256:36081c7c447f83d30bafed7bb423d7cd335f2b3c64e095dcbdf2f07176ba18e8

Observation 18c3a362-ccdb-47a6-b785-9ca38c029833 · inbound

Explicit block-encoding for partial differential equation-constrained optimization cites this paper.

Explicit block-encoding for partial differential equation-constrained optimization Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

Reference 67

Resolution
unresolved
no resolver link, observed 2026-08-03T21:47:34.365966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-03T21:47:34.365966Z digest=sha256:e9972897fcbfc8af8bcc175c26c22ad3f0dda8cc4855393003757f159284d626

Observation 2b6f42ac-f458-4586-919f-0f5b09fa3ea3 · inbound

Hamiltonian simulation for 3D elastic wave equations in homogeneous elastic media cites this paper.

Hamiltonian simulation for 3D elastic wave equations in homogeneous elastic media Quantum Circuits for the Black-Scholes equations via Schr\"{o}dingerisation

Reference 25

Resolution
verified exact
arxiv_id, observed 2026-05-10T00:44:48.296553Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-05-10T00:44:35.499019Z digest=sha256:1012aa7e8a79dab6c279780ab59af37b6a0d9c29fb87d8d6d816cfdfbad01d6f