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Paper Citation Record · LEDGER

Sum of Squares Submodularity

As of 16 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 1 inbound Pith citation observation for arXiv:2510.24550.

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

pith.paper-citation-record.v1
2510.24550 v2

Coverage vector

measured 59 of 59 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:50:36.904130Z

measured 60 of 60 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-20T17:20:29.589792Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

59 of 59 outbound references displayed

  • verified exact1
  • verified fuzzy50
  • unresolved8
  • parse uncertain0
  • malformed identifier0
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External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 67a2cf31-4244-49ce-87ff-91f4dbe2b03d · outbound

This paper cites DC decomposition of nonconvex polynomials with algebraic techniques.

Sum of Squares Submodularity DC decomposition of nonconvex polynomials with algebraic techniques

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 4e301bda-eeeb-46c2-84a9-6111e0bb8544 · outbound

This paper cites A complete characterization of the gap between convexity and sos-convexity.

Sum of Squares Submodularity A complete characterization of the gap between convexity and sos-convexity

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.573721Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.703537Z digest=sha256:2c8f21b83b9cc5a12bc692ea8c1a6724536b1f031c41127cc9e7ade9152fd667

Observation 6e27fa3e-f142-4dbe-ba63-cd0d9144f078 · outbound

This paper cites NP -hardness of deciding convexity of quartic polynomials and related problems.

Sum of Squares Submodularity NP -hardness of deciding convexity of quartic polynomials and related problems

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.562710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.707298Z digest=sha256:55779292fe8d5daec94adccb38cac05a7a449eefa5ed1b819b33ab55693f5d7a

Observation da87a7e9-678d-41c1-8c5f-d3c0ef8477c8 · outbound

This paper cites Submodularity in conic quadratic mixed 0--1 optimization.

Sum of Squares Submodularity Submodularity in conic quadratic mixed 0--1 optimization

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.551563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.711662Z digest=sha256:40cec2e366ad5108cb312883d7ff170190985f84e28c3ac17474528a593a6776

Observation cf28e3e4-0361-47f5-a5c3-9c12ba1071f9 · outbound

This paper cites Submodular functions: from discrete to continuous domains.

Sum of Squares Submodularity Submodular functions: from discrete to continuous domains

Reference 5

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.715460Z digest=sha256:556dc31c39ca5401241091d7ace566a46fe7a6c67b8d09f71102217bc3bbbf39

Observation 2173671a-27f6-4c50-bd64-57379f0358e1 · outbound

This paper cites Learning with submodular functions: A convex optimization perspective.

Sum of Squares Submodularity Learning with submodular functions: A convex optimization perspective

Reference 6

Resolution
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raw_fallback, observed 2026-08-15T15:50:37.528536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.718918Z digest=sha256:c26a2920c1d67638ad1664e3c3986390a5a0dc0deb5a4cd5d20c5f9e871457db

Observation 3addf231-14e2-4919-ab04-f419b36fa971 · outbound

This paper cites Learning submodular functions.

Sum of Squares Submodularity Learning submodular functions

Reference 7

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.723043Z digest=sha256:2d92b948534524335804e5e44efa194a41de42b23e37713bca1607b4aba6e7bf

Observation ab3cb0b6-6a4e-4a69-852e-29ede35c40d3 · outbound

This paper cites Submodular functions: Learnability, structure, and optimization.

Sum of Squares Submodularity Submodular functions: Learnability, structure, and optimization

Reference 8

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 85c82a29-32de-4fff-b519-d0fcb1a3646d · outbound

This paper cites Guarantees for greedy maximization of non-submodular functions with applications.

Sum of Squares Submodularity Guarantees for greedy maximization of non-submodular functions with applications

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.493629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.730117Z digest=sha256:beef95fe5145d3821028e1f9b73c7ae23470cec6317f08398e40d33873895684

Observation f98f231e-c29c-4775-8d59-89d8d0a6d118 · outbound

This paper cites Continuous Submodular Function Maximization.

Sum of Squares Submodularity Continuous Submodular Function Maximization

Reference 10

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unresolved
no resolver link, observed 2026-08-15T15:50:36.733820Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.733820Z digest=sha256:637a4e56ad9bafff722d938d8bd1cc44dca6ea136d38eb71d6e4dc4fa0098cef

Observation f9ac604b-f6d9-49ba-95d2-f4ab3c94d237 · outbound

This paper cites Maximizing a supermodular pseudoboolean function: A polynomial algorithm for supermodular cubic functions.

Sum of Squares Submodularity Maximizing a supermodular pseudoboolean function: A polynomial algorithm for supermodular cubic functions

Reference 11

Resolution
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raw_fallback, observed 2026-08-15T15:50:37.481144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.738113Z digest=sha256:12215a3023110b741e9a33a3ed496c4611e1979120a426a1c031b1b484d7a133

Observation 2f38a1b3-e5de-4eeb-b647-e0abf2c7d355 · outbound

This paper cites Submodularity In Machine Learning and Artificial Intelligence.

Sum of Squares Submodularity Submodularity In Machine Learning and Artificial Intelligence

Reference 12

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.741798Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.741798Z digest=sha256:16eb76aee62a505ec739d0756e2ee2592fc4c8e4aa67e324932aa51503777619

Observation 5ba048c5-dac0-404c-a1c0-5a46caecb269 · outbound

This paper cites Semidefinite O ptimization and C onvex A lgebraic G eometry.

Sum of Squares Submodularity Semidefinite O ptimization and C onvex A lgebraic G eometry

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.469076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.745041Z digest=sha256:31e8c738b1daa6df719849d20a628b4073e74ace3dff1af62fdaa1fd79eb259d

Observation 8243abff-4279-4a02-bc6f-8a3c316019c7 · outbound

This paper cites Undominated DC decompositions of quadratic functions and applications to branch-and-bound approaches.

Sum of Squares Submodularity Undominated DC decompositions of quadratic functions and applications to branch-and-bound approaches

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.456844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.748227Z digest=sha256:c68b4437b6baac92afcf28b92e2a23c8a7226b46cac540c274e665650b0751ec

Observation 5af7183a-16b7-4c83-ba70-77b7aeda26ad · outbound

This paper cites Convex O ptimization.

Sum of Squares Submodularity Convex O ptimization

Reference 15

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation c3a65b5e-f47f-4218-bea1-94c72a86b26c · outbound

This paper cites Decomposition Polyhedra of Piecewise Linear Functions.

Sum of Squares Submodularity Decomposition Polyhedra of Piecewise Linear Functions

Reference 16

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.754438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.754438Z digest=sha256:6eceda66613c8c6fb85ebe29f7e560c555455bba1be7283cf904aea6d9c79684

Observation d305c51f-a8ef-4c6f-ba8e-f09589e2b577 · outbound

This paper cites On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems.

Sum of Squares Submodularity On the Semidefinite Representability of Continuous Quadratic Submodular Minimization With Applications to Moment Problems

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.758276Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.758276Z digest=sha256:b2819c56dfd90ea15804e5881a81a1005b078a21d18e10588244404e377dbbd3

Observation 3f4a6ff3-9a9f-470b-a701-8fe1e014e3a9 · outbound

This paper cites Recognition problems for special classes of polynomials in 0--1 variables.

Sum of Squares Submodularity Recognition problems for special classes of polynomials in 0--1 variables

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.434783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a917c30c-0540-4d5f-9572-b14b8404810a · outbound

This paper cites Boolean F unctions: T heory, A lgorithms, and A pplications.

Sum of Squares Submodularity Boolean F unctions: T heory, A lgorithms, and A pplications

Reference 19

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.765701Z digest=sha256:e1f185213fc28861c28141a2b5d7c2a5f78b5e28a372a86ecbfa93fb17c62147

Observation 117ef802-76ae-4ce7-8673-f051e06174c2 · outbound

This paper cites Shape-constrained regression using sum of squares polynomials.

Sum of Squares Submodularity Shape-constrained regression using sum of squares polynomials

Reference 20

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.769311Z digest=sha256:f05fb535b04c20fe99d35c883eae34cf88f090ea78ad671aa0753c9ec7575a9f

Observation acebe48a-2bae-460d-810d-48e5e1ee31d7 · outbound

This paper cites Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection.

Sum of Squares Submodularity Approximate submodularity and its applications: Subset selection, sparse approximation and dictionary selection

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.772714Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.772714Z digest=sha256:f5fcf1388e7aa9ba6c853423c7f3fdcae3801e14be40bc7887859cca16d0ee6e

Observation f4bddf59-3190-4065-b2f5-f9b4f9f375f2 · outbound

This paper cites Neural estimation of submodular functions with applications to differentiable subset selection.

Sum of Squares Submodularity Neural estimation of submodular functions with applications to differentiable subset selection

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.394521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation cc4901a6-18fe-43a3-ab56-979e39fbb83b · outbound

This paper cites Deep submodular functions: Definitions and learning.

Sum of Squares Submodularity Deep submodular functions: Definitions and learning

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.385543Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation e98b4fa8-354f-4950-9d6d-27f5142a3930 · outbound

This paper cites Submodular functions, matroids, and certain polyhedra.

Sum of Squares Submodularity Submodular functions, matroids, and certain polyhedra

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.375539Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation d00a3f1d-c65f-4c8f-935f-87872ccdee74 · outbound

This paper cites Difference of submodular minimization via DC programming.

Sum of Squares Submodularity Difference of submodular minimization via DC programming

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.364552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 8369e0e9-940e-4dd5-8507-1add430d1db2 · outbound

This paper cites Sparse sum-of-squares certificates on finite abelian groups.

Sum of Squares Submodularity Sparse sum-of-squares certificates on finite abelian groups

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.354249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.790361Z digest=sha256:bcb4b28c991608bc6cb3161c6049df371533db458c61d2b6142de128d6ddb923

Observation 096bb0ac-bd73-4a49-a341-78f4376fe570 · outbound

This paper cites Optimal bounds on approximation of submodular and xos functions by juntas.

Sum of Squares Submodularity Optimal bounds on approximation of submodular and xos functions by juntas

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.343433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.793956Z digest=sha256:3a4d2ecbc25c2f6826e955ef8e7334cf4a1e66c3a7ea664cd1c61a4294f2269a

Observation f276d24f-1470-4f30-9574-a2b1aac0c91b · outbound

This paper cites Representation, approximation and learning of submodular functions using low-rank decision trees.

Sum of Squares Submodularity Representation, approximation and learning of submodular functions using low-rank decision trees

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.331082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation dfbf3625-794c-4b8e-a602-7849f4780abb · outbound

This paper cites Submodular functions in graph theory.

Sum of Squares Submodularity Submodular functions in graph theory

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.319253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 67a419c5-a7d3-4c2e-817f-ac499f9c433b · outbound

This paper cites Submodular F unctions and O ptimization , volume 58.

Sum of Squares Submodularity Submodular F unctions and O ptimization , volume 58

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.307560Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a8ab76d3-b3e0-45a2-87e4-12816663a5cc · outbound

This paper cites On the supermodular knapsack problem.

Sum of Squares Submodularity On the supermodular knapsack problem

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.296838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 2f5be08c-c125-4523-892a-84ff54bfbf91 · outbound

This paper cites Approximating submodular functions everywhere.

Sum of Squares Submodularity Approximating submodular functions everywhere

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.285899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.811230Z digest=sha256:7a35cba02cef80e6685a091cbc11773d81d448d145e0c5ea9c40abeb06b1e4e2

Observation 452272b9-0ae1-44ce-ae0f-12e71dc040d0 · outbound

This paper cites PEP it: computer-assisted worst-case analyses of first-order optimization methods in python.

Sum of Squares Submodularity PEP it: computer-assisted worst-case analyses of first-order optimization methods in python

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.273897Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 8507be87-9b75-4640-a898-6a051c28fbeb · outbound

This paper cites Equivalent representations of set functions.

Sum of Squares Submodularity Equivalent representations of set functions

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.262712Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.818265Z digest=sha256:51f1b64a075c6f20b1dd41242687d91539e4fe3e2d0e4f079fd844d30913c86e

Observation 1474a413-99d9-49fc-959c-968402d709bc · outbound

This paper cites Semidefinite representation of convex sets.

Sum of Squares Submodularity Semidefinite representation of convex sets

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.251588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.821239Z digest=sha256:eeb46173b2aac3c4d8475e9d93f0df8fec78f9e9d48ddaddff3b303e44d2bf22

Observation 43e06e57-1cd8-4b7c-8dbe-13c9ca5cc335 · outbound

This paper cites Maximization of approximately submodular functions.

Sum of Squares Submodularity Maximization of approximately submodular functions

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.240548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.824836Z digest=sha256:178bd12c57b36d5c800b7871d2f7a09e192b6f3183ed2c04180d81a337d93a44

Observation 24ac79ac-af82-424b-be73-0c92395ba9cb · outbound

This paper cites Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications.

Sum of Squares Submodularity Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications

Reference 37

Resolution
verified exact
local_arxiv, observed 2026-08-15T15:50:36.952171Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.828440Z digest=sha256:58f5efc0057d66d5f8880605ac8d6a03f24cd1f691186b68ff4620a2590a4a8e

Observation 687ebf45-243d-4ced-bf4b-15867895c9b0 · outbound

This paper cites Submodularity beyond submodular energies: coupling edges in graph cuts.

Sum of Squares Submodularity Submodularity beyond submodular energies: coupling edges in graph cuts

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.229907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.832308Z digest=sha256:55028c1f2cae83ddb562447f37a6b3ddc226181dd01dceef283ca028ca046ad6

Observation 929c236f-0399-444f-a440-55a86b70b03b · outbound

This paper cites Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies.

Sum of Squares Submodularity Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies

Reference 39

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.836305Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.836305Z digest=sha256:f8184d209e052bb36bbdfb36a84084823e4c038174c4ca4fd91cc465c2f4e5f0

Observation baf9fcaf-5a1e-48c9-99e3-ecac918491f5 · outbound

This paper cites Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope.

Sum of Squares Submodularity Lower bound for the number of iterations in semidefinite hierarchies for the cut polytope

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.210036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.840058Z digest=sha256:8d35095919583bb4246be2cf12d851180cc6df8b42cb1cfc696280ffafb6241c

Observation e674f7a5-271a-449b-8ea6-0d75121d21ac · outbound

This paper cites Sums of squares, moment matrices and optimization over polynomials.

Sum of Squares Submodularity Sums of squares, moment matrices and optimization over polynomials

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.199005Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.843880Z digest=sha256:eaf27e7f71e502a898cebdec06d4c61b2a4a64cbdfd8ba26d849dc9bc119b2b3

Observation 54368282-315d-4dc0-95dc-20b04713aadf · outbound

This paper cites Learning Mixtures of Submodular Shells with Application to Document Summarization.

Sum of Squares Submodularity Learning Mixtures of Submodular Shells with Application to Document Summarization

Reference 42

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.847568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.847568Z digest=sha256:0abd8a5f37ba19a7ffaae0aae1e496cc4104e4e680dba6286d0f91e28fda7daf

Observation f348769c-4603-4841-9d8f-1d5f913827d2 · outbound

This paper cites A submodular-supermodular procedure with applications to discriminative structure learning.

Sum of Squares Submodularity A submodular-supermodular procedure with applications to discriminative structure learning

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.188004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.851886Z digest=sha256:fca17842a223752ef9675f67c9e527d2e91a953e16837db9626958e28eecc358

Observation cd49fc29-ecb1-4396-8c11-8068061ef436 · outbound

This paper cites Submodular F unctions and E lectrical N etworks , volume 54.

Sum of Squares Submodularity Submodular F unctions and E lectrical N etworks , volume 54

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.177613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.855785Z digest=sha256:890de1740ae15c144aa65e19372c613bc98e55cf11f61a47ba652848048b9e29

Observation 1cf7aaf5-ecc6-4481-bcc8-50a74ebc5704 · outbound

This paper cites An analysis of approximations for maximizing submodular set functions—i.

Sum of Squares Submodularity An analysis of approximations for maximizing submodular set functions—i

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.166360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.859409Z digest=sha256:79e7ae25698b6579bc486b29ceeaa2bdd891db194f42f05f94e8948def3fd194

Observation 38545426-8fd0-4b80-a411-ece50900fd84 · outbound

This paper cites Multilinear extensions of games.

Sum of Squares Submodularity Multilinear extensions of games

Reference 46

Resolution
unresolved
no resolver link, observed 2026-08-15T15:50:36.862728Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-15T15:50:36.862728Z digest=sha256:7d6722130cf145eddd22d3e2ac10a039add24fbe5e20956aad2725b3a1f05cc1

Observation 2ba6ac69-6e1d-4afa-b702-c94f29d8a81d · outbound

This paper cites Selecting a monomial basis for sums of squares programming over a quotient ring.

Sum of Squares Submodularity Selecting a monomial basis for sums of squares programming over a quotient ring

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.149097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.865935Z digest=sha256:bab67f1d9a3a0ffcf764801fcac7c65a21d971e4a6f00983c188f61bdee38888

Observation e11c2c24-6d61-4867-951b-e442ffee75e3 · outbound

This paper cites The quadratic unconstrained binary optimization problem.

Sum of Squares Submodularity The quadratic unconstrained binary optimization problem

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.138791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.869745Z digest=sha256:351aebb61398f454db09806c20c624e86b5364d24ff31872d409a5160bb32045

Observation 4129fdc0-d8fc-426d-9e3f-fcd44bb71b6d · outbound

This paper cites Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds.

Sum of Squares Submodularity Scheduling unit jobs with compatible release dates on parallel machines with nonstationary speeds

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.126995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.873132Z digest=sha256:f01adfa2bcc3a4567dcbb6c2a458babf6fe9ccd1d6728aec4ba739ac0eadc5af

Observation 41785ef7-0df2-47fe-a56f-5f8171a0ac57 · outbound

This paper cites Exact sdp relaxations with truncated moment matrix for binary polynomial optimization problems.

Sum of Squares Submodularity Exact sdp relaxations with truncated moment matrix for binary polynomial optimization problems

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.113891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.876231Z digest=sha256:ab85a783bd6822000c5bfbec13675b009f1c0a20d884251439e571b15f63a194

Observation ea867ab6-02a6-4e4f-8220-fe5d49f084b1 · outbound

This paper cites A combinatorial algorithm minimizing submodular functions in strongly polynomial time.

Sum of Squares Submodularity A combinatorial algorithm minimizing submodular functions in strongly polynomial time

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.101705Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.879495Z digest=sha256:6fa735604a0d38733f51169cfe56eb8c82ccc04e162e5b515a559b3e79a0b119

Observation b4a18369-47e0-44cc-996c-03d46c716f51 · outbound

This paper cites Is submodularity testable? Algorithmica, 69 0 (1): 0 1--25, 2014.

Sum of Squares Submodularity Is submodularity testable? Algorithmica, 69 0 (1): 0 1--25, 2014

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.090970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.883109Z digest=sha256:2d777f7dd96d148684573009d69f2d5bd8782ae7a69abf271cdec407594bde44

Observation 857665f8-06f0-4f98-a4a5-a881110c7ed0 · outbound

This paper cites Large-margin learning of submodular summarization models.

Sum of Squares Submodularity Large-margin learning of submodular summarization models

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.081250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.886611Z digest=sha256:a0734a8eaae2af7a34d666d28584ac0b6d566bcb20fd016325d4e9b98e37dd3a

Observation 2c42ba12-3bb1-4a43-a517-669a06e64fca · outbound

This paper cites Introduction to the T heory of C omputation.

Sum of Squares Submodularity Introduction to the T heory of C omputation

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.069813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.889492Z digest=sha256:53b21d3ad5b7d42cf3f2873e9ab4386e3c03127d354e95d292efcc20b368bddd

Observation 2658cb85-959d-47b9-9dc4-584d765c6c68 · outbound

This paper cites Learning F ourier sparse set functions.

Sum of Squares Submodularity Learning F ourier sparse set functions

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.057555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.892331Z digest=sha256:a14142fc7866b3e5b6f17547aa71340feffe4b8f2acda2fad8419723790be041

Observation 9fbf0e44-414e-4331-837d-ea505a824dfc · outbound

This paper cites Minimizing a submodular function on a lattice.

Sum of Squares Submodularity Minimizing a submodular function on a lattice

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.045627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.895057Z digest=sha256:169884a5c7307d7c834eca383bc71e6b8019655ec9ebd84f7d486b96629381aa

Observation a6414b66-17c2-4f50-a201-8c6c8af34c2d · outbound

This paper cites Supermodularity and C omplementarity.

Sum of Squares Submodularity Supermodularity and C omplementarity

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.033408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.898041Z digest=sha256:63ca13089af6c124237a4baa5f15b510553ca214d6cfe7ad0681542caffc0ccc

Observation 7a57e04e-2542-4db1-9ddd-9842a6e346b2 · outbound

This paper cites Learning mixtures of submodular functions for image collection summarization.

Sum of Squares Submodularity Learning mixtures of submodular functions for image collection summarization

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.021959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.900978Z digest=sha256:352a1f7b4ceb388b938891c7f0e745192a845574d8814b353c7e18dd06131f6f

Observation de62ea74-d44a-4011-9ba6-41868b0ccb00 · outbound

This paper cites The concave-convex procedure.

Sum of Squares Submodularity The concave-convex procedure

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T15:50:37.010256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-08-15T15:50:36.904130Z digest=sha256:c43642dc0b2d94d0108cf39d06afb059f27928785ba73e594791b8ebdadf983b

Pith citing papers

Observation 4279d50b-ca15-4792-8ca4-1abefb09ec75 · inbound

Copositive Matrices with Ordered Off-Diagonal Entries cites this paper.

Copositive Matrices with Ordered Off-Diagonal Entries Sum of Squares Submodularity

Reference 72

Resolution
verified exact
arxiv_id, observed 2026-06-29T02:14:52.228958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=arxiv_source observed=2026-05-20T17:20:29.589792Z digest=sha256:3b4ff7bc43050802ff99e3e5aaa61e9cee60c622cdec0a56fd470af93bbefe1a