{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MTKD45YQ6AUKDTSYNORVMMPR52","short_pith_number":"pith:MTKD45YQ","canonical_record":{"source":{"id":"1505.01688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-07T12:54:11Z","cross_cats_sorted":[],"title_canon_sha256":"6ece35e292498a3de2756b380a70a92bed36a3ff23fa79e21be5140253370bc1","abstract_canon_sha256":"b42a46308de267d9884c797544faa84031e0dcbbd549beeb1b55a8cd06f5023e"},"schema_version":"1.0"},"canonical_sha256":"64d43e7710f028a1ce586ba35631f1ee9d6f87ac440523c2e8462e80e8704db8","source":{"kind":"arxiv","id":"1505.01688","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01688","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01688v1","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01688","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"MTKD45YQ6AUK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTKD45YQ6AUKDTSY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTKD45YQ","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MTKD45YQ6AUKDTSYNORVMMPR52","target":"record","payload":{"canonical_record":{"source":{"id":"1505.01688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-07T12:54:11Z","cross_cats_sorted":[],"title_canon_sha256":"6ece35e292498a3de2756b380a70a92bed36a3ff23fa79e21be5140253370bc1","abstract_canon_sha256":"b42a46308de267d9884c797544faa84031e0dcbbd549beeb1b55a8cd06f5023e"},"schema_version":"1.0"},"canonical_sha256":"64d43e7710f028a1ce586ba35631f1ee9d6f87ac440523c2e8462e80e8704db8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:50.599042Z","signature_b64":"fIx3z/iU501hSNSX7TRWDY18k7fdIKZiWYlAtY3dVjDPs9yZKOpUyq6Cow8wuHrQzQ5vg0A8TQsK6z6wLwWXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64d43e7710f028a1ce586ba35631f1ee9d6f87ac440523c2e8462e80e8704db8","last_reissued_at":"2026-05-18T01:04:50.598650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:50.598650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.01688","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NGLNaxqhU71ULf2rfN9o6FTwc1cFAbt42mgTDcTH5tdb9VI05MPt66heEUETwY6R+gn7KK+Eqt+9PGYKM2XdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:02.940350Z"},"content_sha256":"25dccb01ef3145536ec913462e64861e55f64b02b6f34cd5a3076cef1578edbf","schema_version":"1.0","event_id":"sha256:25dccb01ef3145536ec913462e64861e55f64b02b6f34cd5a3076cef1578edbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MTKD45YQ6AUKDTSYNORVMMPR52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two distinct transitions in spatially embedded multiplex networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"Louis M. Shekhtman, Michael M. Danziger, Shlomo Havlin, Yehiel Berezin","submitted_at":"2015-05-07T12:54:11Z","abstract_excerpt":"Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we model such systems as a multiplex network composed of two or more layers, each with links of characteristic geographic length, embedded in 2-dimensional space. This is equivalent to a system of interdependent spatially embedded networks in two dimensions in which the connectivity links are constrained in length but varied while the length of the dependency li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01688","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkgZ4+OwRZO0aecVwkaFBfneGfIiw6fTeYcqRptwogknXZT5ZiINebZ77ZJYapgECMhjXsg4Njm1x520ZfehDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:52:02.940792Z"},"content_sha256":"d7e2275c8ec03a7cb220bdf3bd31694e156d571da13523dde52c9c2a6d485ed8","schema_version":"1.0","event_id":"sha256:d7e2275c8ec03a7cb220bdf3bd31694e156d571da13523dde52c9c2a6d485ed8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MTKD45YQ6AUKDTSYNORVMMPR52/bundle.json","state_url":"https://pith.science/pith/MTKD45YQ6AUKDTSYNORVMMPR52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MTKD45YQ6AUKDTSYNORVMMPR52/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T15:52:02Z","links":{"resolver":"https://pith.science/pith/MTKD45YQ6AUKDTSYNORVMMPR52","bundle":"https://pith.science/pith/MTKD45YQ6AUKDTSYNORVMMPR52/bundle.json","state":"https://pith.science/pith/MTKD45YQ6AUKDTSYNORVMMPR52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MTKD45YQ6AUKDTSYNORVMMPR52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MTKD45YQ6AUKDTSYNORVMMPR52","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b42a46308de267d9884c797544faa84031e0dcbbd549beeb1b55a8cd06f5023e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-07T12:54:11Z","title_canon_sha256":"6ece35e292498a3de2756b380a70a92bed36a3ff23fa79e21be5140253370bc1"},"schema_version":"1.0","source":{"id":"1505.01688","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.01688","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1505.01688v1","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01688","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"MTKD45YQ6AUK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MTKD45YQ6AUKDTSY","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MTKD45YQ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d7e2275c8ec03a7cb220bdf3bd31694e156d571da13523dde52c9c2a6d485ed8","target":"graph","created_at":"2026-05-18T01:04:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we model such systems as a multiplex network composed of two or more layers, each with links of characteristic geographic length, embedded in 2-dimensional space. This is equivalent to a system of interdependent spatially embedded networks in two dimensions in which the connectivity links are constrained in length but varied while the length of the dependency li","authors_text":"Louis M. Shekhtman, Michael M. Danziger, Shlomo Havlin, Yehiel Berezin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-07T12:54:11Z","title":"Two distinct transitions in spatially embedded multiplex networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01688","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:25dccb01ef3145536ec913462e64861e55f64b02b6f34cd5a3076cef1578edbf","target":"record","created_at":"2026-05-18T01:04:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b42a46308de267d9884c797544faa84031e0dcbbd549beeb1b55a8cd06f5023e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-05-07T12:54:11Z","title_canon_sha256":"6ece35e292498a3de2756b380a70a92bed36a3ff23fa79e21be5140253370bc1"},"schema_version":"1.0","source":{"id":"1505.01688","kind":"arxiv","version":1}},"canonical_sha256":"64d43e7710f028a1ce586ba35631f1ee9d6f87ac440523c2e8462e80e8704db8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64d43e7710f028a1ce586ba35631f1ee9d6f87ac440523c2e8462e80e8704db8","first_computed_at":"2026-05-18T01:04:50.598650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.598650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fIx3z/iU501hSNSX7TRWDY18k7fdIKZiWYlAtY3dVjDPs9yZKOpUyq6Cow8wuHrQzQ5vg0A8TQsK6z6wLwWXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.599042Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.01688","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25dccb01ef3145536ec913462e64861e55f64b02b6f34cd5a3076cef1578edbf","sha256:d7e2275c8ec03a7cb220bdf3bd31694e156d571da13523dde52c9c2a6d485ed8"],"state_sha256":"e73ba11dd4ac70acdb308ef5e1b30e031f349a9951e77f8fd7c026ba2aa2c7ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oug4AvMJIW/jsR6F2ZeOTGeBARI6O/wxNZty5+OtRomJjKhdEoPROJikzhKlDFazblVSJW3lrH7NqZnmr+MKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:52:02.943996Z","bundle_sha256":"a7705cecde8fe4282fb19b276b91cb79189523d45e217ca16b3a15c01b595ba8"}}