Paper Citation Record · LEDGER

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

As of 15 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2507.16100.

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

pith.paper-citation-record.v1
2507.16100 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:28:34.747554Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:22:16.345421Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-11T05:22:16.607077Z

Reference resolution

10 of 10 outbound references displayed

verified exact2
verified fuzzy3
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d828b21f-cf45-49b1-9c18-f1f5fd65c83d · outbound

This paper cites Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:28:35.164661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 51ffbd2b-4906-4d30-ac44-cc89f0301693 · outbound

This paper cites Bj¨ orklund, B.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Bj¨ orklund, B

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:28:36.298392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation f9ccc4f4-46af-47c7-8c8f-b9fa94b0e76f · outbound

This paper cites Quesada, L.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Quesada, L

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:28:36.049570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 202035ad-4543-4862-96ea-ff326565f88e · outbound

This paper cites Kruse, C.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Kruse, C

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T15:28:34.174251Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b3ac965f-d2cf-4da7-b0f6-a3ea39b06521 · outbound

This paper cites an unresolved cited work.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T15:28:34.234339Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb4aa727-ad3a-4827-a5f2-3b198af30ffb · outbound

This paper cites Combinatorics of Partial Derivatives.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Combinatorics of Partial Derivatives

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:28:34.975852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 5aee7826-982b-4dff-b15f-2c4db4fbd872 · outbound

This paper cites an unresolved cited work.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:28:35.822633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 189432eb-befa-42b3-91b9-9d65fd2dd883 · outbound

This paper cites Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika12, 134 (1918).

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Isserlis, On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables, Biometrika12, 134 (1918)

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T15:28:34.537246Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c93abef-a615-41b7-8324-f235df599f48 · outbound

This paper cites Wick, The evaluation of the collision matrix, Phys.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Wick, The evaluation of the collision matrix, Phys

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:28:35.607868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 596cd039-33dc-4bf2-a8eb-046c9a47797f · outbound

This paper cites an unresolved cited work.

Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:28:35.349001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Pith citing papers

Observation 101e0531-521d-41bb-900b-c9016872bb3d · inbound

Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation cites this paper.

Simulating lossy and partially distinguishable quantum optical circuits: theory, algorithms and applications to experiment validation and state preparation Derivation of the Loop Hafnian Generating Function for Arbitrary Symmetric Matrices via Gaussian Integration

Reference 71

Resolution: verified exact; local_arxiv, observed 2026-08-11T05:22:16.614659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.