Explosive connectivity and mechanical rigidity in cubic lattice structures | Paper Citation Record

Observation 464a5103-6c77-4eae-86d1-56d5b8652582 · outbound

This paper cites Let e={u,v} be a candidate edge not in Gt−1.

Explosive connectivity and mechanical rigidity in cubic lattice structures Let e={u,v} be a candidate edge not in Gt−1

Reference 1

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Observation 12a93c12-864d-4b97-a675-e47ae03e3ae1 · outbound

This paper cites force balance constraints.

Explosive connectivity and mechanical rigidity in cubic lattice structures force balance constraints

Reference 2

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Observation ed95728a-d0e2-4456-ba07-00f6e79ed302 · outbound

This paper cites Stauffer and A.

Explosive connectivity and mechanical rigidity in cubic lattice structures Stauffer and A

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This paper cites Christensen and N.

Explosive connectivity and mechanical rigidity in cubic lattice structures Christensen and N

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Observation 0ef51f7f-3c3c-41fd-aa8a-ff345d8d2b19 · outbound

This paper cites Majewski and K.

Explosive connectivity and mechanical rigidity in cubic lattice structures Majewski and K

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation b121d88c-7dbd-45a2-bb8e-b9b7ad97bcbf · outbound

This paper cites Xun and R.

Explosive connectivity and mechanical rigidity in cubic lattice structures Xun and R

Reference 7

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Observation 29880039-43f0-46ba-932c-906753a8da8d · outbound

This paper cites Meloni, M.

Explosive connectivity and mechanical rigidity in cubic lattice structures Meloni, M

Reference 8

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Observation 76b6ad9b-bf28-41e1-aadf-671be35bd966 · outbound

This paper cites Sahimi,Applications of Percolation Theory, Applied Mathe- matical Sciences, V ol.

Explosive connectivity and mechanical rigidity in cubic lattice structures Sahimi,Applications of Percolation Theory, Applied Mathe- matical Sciences, V ol

Reference 9

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Observation 967073ff-4fcb-4250-8452-e4ec66e18722 · outbound

This paper cites Achlioptas, R.

Explosive connectivity and mechanical rigidity in cubic lattice structures Achlioptas, R

Reference 10

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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This paper cites Radicchi and S.

Explosive connectivity and mechanical rigidity in cubic lattice structures Radicchi and S

Reference 12

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This paper cites Riordan and L.

Explosive connectivity and mechanical rigidity in cubic lattice structures Riordan and L

Reference 13

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation 23b843d8-1e86-44ef-bd07-bdc31e46f2f4 · outbound

This paper cites Asimow and B.

Explosive connectivity and mechanical rigidity in cubic lattice structures Asimow and B

Reference 17

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Observation 72feec1f-2706-435d-8f9e-93913efbfe2d · outbound

This paper cites Moukarzel, J.

Explosive connectivity and mechanical rigidity in cubic lattice structures Moukarzel, J

Reference 18

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This paper cites Cheng and M.

Explosive connectivity and mechanical rigidity in cubic lattice structures Cheng and M

Reference 19

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation db72734c-f422-4e3c-8792-9233b74c9fab · outbound

This paper cites Lee and I.

Explosive connectivity and mechanical rigidity in cubic lattice structures Lee and I

Reference 21

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This paper cites Li and G.

Explosive connectivity and mechanical rigidity in cubic lattice structures Li and G

Reference 22

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Observation b9d44509-ccd6-42de-8ea9-c3055c31494d · outbound

This paper cites Rigidity control of general origami structures.

Explosive connectivity and mechanical rigidity in cubic lattice structures Rigidity control of general origami structures

Reference 23

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

Reference 27

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Observation eb28910b-88ea-40f1-b0c2-9d789cd3404a · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation a9f150ea-cc88-4306-80d4-9fb17bffe9d1 · outbound

This paper cites Garamvölgyi, S.

Explosive connectivity and mechanical rigidity in cubic lattice structures Garamvölgyi, S

Reference 29

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Observation ecf8c2e6-d821-461c-94df-5b1d2b91ca8a · outbound

This paper cites Laman, J.

Explosive connectivity and mechanical rigidity in cubic lattice structures Laman, J

Reference 30

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Observation 2f0f684a-ebee-4873-9580-cd79fedc48e7 · outbound

This paper cites Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach.

Explosive connectivity and mechanical rigidity in cubic lattice structures Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach

Reference 31

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

Reference 32

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Observation 8b668760-f4f7-4816-981e-2287c6c9aa19 · outbound

This paper cites Minimum degree conditions for graph rigidity.

Explosive connectivity and mechanical rigidity in cubic lattice structures Minimum degree conditions for graph rigidity

Reference 33

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Observation 1f5e6f3b-9c84-4bfe-b966-b1f421b5905a · outbound

This paper cites Binder, Z.

Explosive connectivity and mechanical rigidity in cubic lattice structures Binder, Z

Reference 34

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This paper cites Efron, inBreakthroughs in Statistics, Springer Series in Statis- tics, edited by S.

Explosive connectivity and mechanical rigidity in cubic lattice structures Efron, inBreakthroughs in Statistics, Springer Series in Statis- tics, edited by S

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Observation 65650037-db50-4033-b8b7-08564faea2d0 · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation a03f3b82-1117-412d-8176-ada582ce680c · outbound

This paper cites Goerdt, Theor.

Explosive connectivity and mechanical rigidity in cubic lattice structures Goerdt, Theor

Reference 38

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Observation 5fb2e242-31d7-4e73-9d84-6304531deda2 · outbound

This paper cites Lichev, D.

Explosive connectivity and mechanical rigidity in cubic lattice structures Lichev, D

Reference 39

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation 59cd1c6c-bb85-49aa-843a-1f508a4e4be1 · outbound

This paper cites Gómez-Gardeñes, S.

Explosive connectivity and mechanical rigidity in cubic lattice structures Gómez-Gardeñes, S

Reference 41

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This paper cites Selke, J.

Explosive connectivity and mechanical rigidity in cubic lattice structures Selke, J

Reference 42

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation 6a8496c6-5e1f-4a70-a909-b71be10cd16f · outbound

This paper cites Frieze and M.

Explosive connectivity and mechanical rigidity in cubic lattice structures Frieze and M

Reference 44

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Observation 88b25e63-7e7b-4059-91c9-49c3f0cc0117 · outbound

This paper cites Duminil-Copin, Jpn.

Explosive connectivity and mechanical rigidity in cubic lattice structures Duminil-Copin, Jpn

Reference 45

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Observation ca89fe79-c807-4113-9a16-3135e02bcd7b · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Perkins, Bull

Reference 46

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This paper cites Xing and K.

Explosive connectivity and mechanical rigidity in cubic lattice structures Xing and K

Reference 47

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This paper cites Durrett,Probability: Theory and Examples, 5th ed., Cam- bridge Series in Statistical and Probabilistic Mathematics, V ol.

Explosive connectivity and mechanical rigidity in cubic lattice structures Durrett,Probability: Theory and Examples, 5th ed., Cam- bridge Series in Statistical and Probabilistic Mathematics, V ol

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Observation 1cd77f50-5ee1-4243-9e5f-0c92a42f8cfe · outbound

This paper cites Binder and D.

Explosive connectivity and mechanical rigidity in cubic lattice structures Binder and D

Reference 49

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This paper cites Chae, S.-H.

Explosive connectivity and mechanical rigidity in cubic lattice structures Chae, S.-H

Reference 50

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Olvera-Cravioto, J

Reference 52

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This paper cites Grassberger, C.

Explosive connectivity and mechanical rigidity in cubic lattice structures Grassberger, C

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation 26b6f2c0-8819-41f3-8647-4f24f42ae7c3 · outbound

This paper cites Geometrically Frustrated Assembly at Finite Temperature: Phase Transitions from Self-Limiting to Bulk States.

Explosive connectivity and mechanical rigidity in cubic lattice structures Geometrically Frustrated Assembly at Finite Temperature: Phase Transitions from Self-Limiting to Bulk States

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Resolution: verified exact; local_arxiv, observed 2026-08-04T00:34:13.887424Z

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Observation 98c06f3d-bac3-40f3-89e5-53b61140f7d1 · outbound

This paper cites Double-network-inspired mechanical metamaterials.

Explosive connectivity and mechanical rigidity in cubic lattice structures Double-network-inspired mechanical metamaterials

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Resolution: verified exact; local_arxiv, observed 2026-08-04T00:34:13.583745Z

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Observation 78e006f6-6368-41a4-a153-129abf3af332 · outbound

This paper cites Mehta, M.

Explosive connectivity and mechanical rigidity in cubic lattice structures Mehta, M

Reference 58

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This paper cites Ghrist, Bull.

Explosive connectivity and mechanical rigidity in cubic lattice structures Ghrist, Bull

Reference 59

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation d215081e-8264-4288-9686-1fa18114e27a · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Friedgut, J

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Observation 9c786fb5-0e07-4793-b0e2-42c4b611330f · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Krivelevich, A

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This paper cites On the Rigidity of Random Graphs in high-dimensional spaces.

Explosive connectivity and mechanical rigidity in cubic lattice structures On the Rigidity of Random Graphs in high-dimensional spaces

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Explosive connectivity and mechanical rigidity in cubic lattice structures Molloy and B

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Explosive connectivity and mechanical rigidity in cubic lattice structures Molloy and B

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Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

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Explosive connectivity and mechanical rigidity in cubic lattice structures Bollobás, inModern Graph Theory, Graduate Texts in Math- ematics, V ol

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Observation a517f905-a1f4-4241-b022-6b8592775cff · outbound

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Explosive connectivity and mechanical rigidity in cubic lattice structures Waagen and R

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Observation 8075baf2-ed65-4d8d-893d-9f4fb982e2ad · outbound

This paper cites Definition S1.1(Graph).A (simple) graph G= (V,E) consists of a finite set V ofverticesand a set E⊆ {{u,v}:u,v∈V,u̸= v}ofedges.

Explosive connectivity and mechanical rigidity in cubic lattice structures Definition S1.1(Graph).A (simple) graph G= (V,E) consists of a finite set V ofverticesand a set E⊆ {{u,v}:u,v∈V,u̸= v}ofedges

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.449894Z

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Observation 824fd2a0-5258-4456-a577-ae46126985fc · outbound

This paper cites Call thisk 2-setS t ={e t,1 ,.

Explosive connectivity and mechanical rigidity in cubic lattice structures Call thisk 2-setS t ={e t,1 ,

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.452868Z

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Observation 1e9f2ae7-a99b-439b-9fc8-8bb1534f0a4e · outbound

This paper cites ,et,k1} ⊂St, and define thek 2-set for the larger-kprocess asS (k2) t =S t.

Explosive connectivity and mechanical rigidity in cubic lattice structures ,et,k1} ⊂St, and define thek 2-set for the larger-kprocess asS (k2) t =S t

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.455620Z

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Observation cbce00ec-1c6a-4ebf-a7b1-37dfabd77f7e · outbound

This paper cites an unresolved cited work.

Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.458117Z

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Observation f0a69520-29c7-4bf1-9eb5-6a5e340fb315 · outbound

This paper cites the largest component has size at least m by time t.

Explosive connectivity and mechanical rigidity in cubic lattice structures the largest component has size at least m by time t

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.460621Z

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Observation 32d5a613-a016-4b72-b952-aea2849e75f8 · outbound

This paper cites floppy” or “rigid.

Explosive connectivity and mechanical rigidity in cubic lattice structures floppy” or “rigid

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.463351Z

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Observation 924a67a5-a29e-49c8-ac50-c33af12ea7be · outbound

This paper cites Therigidification cost ∆t(G,P) is the minimal number of edges one must add to G to obtain a graph H⊇G such that (H,P) has f(H,P) =0 (i.e., is infinitesimally rigid).

Explosive connectivity and mechanical rigidity in cubic lattice structures Therigidification cost ∆t(G,P) is the minimal number of edges one must add to G to obtain a graph H⊇G such that (H,P) has f(H,P) =0 (i.e., is infinitesimally rigid)

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.466129Z

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Observation c7396661-14d6-4ba9-bc07-24734caf8f57 · outbound

This paper cites layered shear.

Explosive connectivity and mechanical rigidity in cubic lattice structures layered shear

Reference 77

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.469178Z

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Observation 9f1674c3-694a-4574-9688-95c2a45027a3 · outbound

This paper cites This means ∆(k) =0 for all k≥1.

Explosive connectivity and mechanical rigidity in cubic lattice structures This means ∆(k) =0 for all k≥1

Reference 78

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.472384Z

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Observation e91af6ee-1510-4984-a491-902448eb5ad4 · outbound

This paper cites A critical part of this argument is that for a large, dense component, adding another internal edge is almost certainly redundant.

Explosive connectivity and mechanical rigidity in cubic lattice structures A critical part of this argument is that for a large, dense component, adding another internal edge is almost certainly redundant

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.474715Z

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Observation 056f31aa-df58-4ae3-8890-9d5a9e50a41c · outbound

This paper cites unbiased.

Explosive connectivity and mechanical rigidity in cubic lattice structures unbiased

Reference 80

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.477379Z

Source-reported events for the cited work

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Observation 53cdf950-e6f2-4858-aa82-e60121b42a51 · outbound

This paper cites an unresolved cited work.

Explosive connectivity and mechanical rigidity in cubic lattice structures Unresolved cited work

Reference 81

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.479644Z

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Observation 16728ff4-399f-497c-9b2a-b3f3bbe8a283 · outbound

This paper cites This provides a solid mathematical foundation for Hypothesis IV .50.

Explosive connectivity and mechanical rigidity in cubic lattice structures This provides a solid mathematical foundation for Hypothesis IV .50

Reference 82

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.482252Z

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Observation a0d00d78-b516-460b-8201-e078d590003a · outbound

This paper cites If vertices u and v are in different connected components of G, then the edge e={u,v} is non- redundant (rgain(e) =1).

Explosive connectivity and mechanical rigidity in cubic lattice structures If vertices u and v are in different connected components of G, then the edge e={u,v} is non- redundant (rgain(e) =1)

Reference 83

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.484509Z

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Observation 10254c13-a933-4b7b-b483-8a52b991ddc8 · outbound

This paper cites Justification.The product-rule disfavors adding edges inside large components, pushing the process towards either merging or adding to small components.

Explosive connectivity and mechanical rigidity in cubic lattice structures Justification.The product-rule disfavors adding edges inside large components, pushing the process towards either merging or adding to small components

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.487042Z

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Observation 27efd3b1-5c4a-4908-af83-1c66b4a93932 · outbound

This paper cites We must show P(s1)≥ P(s2).

Explosive connectivity and mechanical rigidity in cubic lattice structures We must show P(s1)≥ P(s2)

Reference 85

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.489614Z

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Observation 868bbd69-f6d3-48ca-9f42-e398dcc8912b · outbound

This paper cites We have P(s1) =1 from Theorem S5.2 and P(s2)≤1.

Explosive connectivity and mechanical rigidity in cubic lattice structures We have P(s1) =1 from Theorem S5.2 and P(s2)≤1

Reference 86

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.491965Z

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Observation 386d98c6-b957-47e5-a6a0-9bf79a1d7c91 · outbound

This paper cites This implies |C1|< |C2|.

Explosive connectivity and mechanical rigidity in cubic lattice structures This implies |C1|< |C2|

Reference 87

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.494253Z

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Observation d4bc5806-68fd-44f6-a1ff-161bd8a64a14 · outbound

This paper cites Video 6 (intra_sus):The susceptibility, χ, versus the edge density p for the Intra model.

Explosive connectivity and mechanical rigidity in cubic lattice structures Video 6 (intra_sus):The susceptibility, χ, versus the edge density p for the Intra model

Reference 88

Resolution: unresolved; no resolver link, observed 2026-08-04T00:31:30.496778Z

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