Paper Citation Record · LEDGER

Tropical Circuits with Scalar Multiplication Gates

As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.11540.

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

pith.paper-citation-record.v1
2607.11540 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T04:53:15.571065Z

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

10 of 10 outbound references displayed

verified exact0
verified fuzzy0
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 57e596f0-6fb0-45be-ab48-49fd84709e93 · outbound

This paper cites The monotone circuit complexity of Boolean functions.

Tropical Circuits with Scalar Multiplication Gates The monotone circuit complexity of Boolean functions

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a63aebc-a698-4f78-b2ff-c12e4910b615 · outbound

This paper cites On the Depth of Monotone ReLU Neural Networks and ICNNs.

Tropical Circuits with Scalar Multiplication Gates On the Depth of Monotone ReLU Neural Networks and ICNNs

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ab96e7f-dd6c-4135-a4e6-b3b23cc0d6be · outbound

This paper cites Negations are powerful even in small depth.

Tropical Circuits with Scalar Multiplication Gates Negations are powerful even in small depth

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f540959a-ebb8-49d9-8713-8b354ae883a6 · outbound

This paper cites Monotone and partially monotone neural networks.

Tropical Circuits with Scalar Multiplication Gates Monotone and partially monotone neural networks

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 098f014a-bcb4-4b0f-b9b7-4004fe8add5d · outbound

This paper cites Con- vexity in ReLU neural networks: beyond ICNNs?.

Tropical Circuits with Scalar Multiplication Gates Con- vexity in ReLU neural networks: beyond ICNNs?

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6d9565dd-86da-49a8-af09-ddac5fbd8810 · outbound

This paper cites To- wards lower bounds on the depth of ReLU neural networks.

Tropical Circuits with Scalar Multiplication Gates To- wards lower bounds on the depth of ReLU neural networks

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be44a17f-e3da-4f2e-83b1-91282de852bc · outbound

This paper cites Neural Networks and (Virtual) Extended Formulations.

Tropical Circuits with Scalar Multiplication Gates Neural Networks and (Virtual) Extended Formulations

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e3174e0-28ea-4c05-8221-214b43dc3ba5 · outbound

This paper cites Greedy can beat pure dynamic programming.

Tropical Circuits with Scalar Multiplication Gates Greedy can beat pure dynamic programming

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c72ca478-f783-41d4-8906-1536e2371602 · outbound

This paper cites Size and depth of monotone neural networks: interpolation and approximation.

Tropical Circuits with Scalar Multiplication Gates Size and depth of monotone neural networks: interpolation and approximation

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f13a3e8e-1683-4e30-9ebd-1158255bef9c · outbound

This paper cites The matching polytope has exponential extension complexity.

Tropical Circuits with Scalar Multiplication Gates The matching polytope has exponential extension complexity

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T04:53:15.571065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.