{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:26EP64DTM574SUPMDWPNDMOPNS","short_pith_number":"pith:26EP64DT","canonical_record":{"source":{"id":"1904.11027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-24T19:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"0fa614f6cdbc2209116c970ff10810d5955c23684e7a9bf67ad88a3c65a7a38a","abstract_canon_sha256":"077f0f720838d9dcd0c4f9911dbb3d484f49d27e62419a1a3b02b8d71d81eca2"},"schema_version":"1.0"},"canonical_sha256":"d788ff7073677fc951ec1d9ed1b1cf6c8fc194e50d89bf628d11636be70f580c","source":{"kind":"arxiv","id":"1904.11027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11027","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11027v1","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11027","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"pith_short_12","alias_value":"26EP64DTM574","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"26EP64DTM574SUPM","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"26EP64DT","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:26EP64DTM574SUPMDWPNDMOPNS","target":"record","payload":{"canonical_record":{"source":{"id":"1904.11027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-24T19:16:25Z","cross_cats_sorted":[],"title_canon_sha256":"0fa614f6cdbc2209116c970ff10810d5955c23684e7a9bf67ad88a3c65a7a38a","abstract_canon_sha256":"077f0f720838d9dcd0c4f9911dbb3d484f49d27e62419a1a3b02b8d71d81eca2"},"schema_version":"1.0"},"canonical_sha256":"d788ff7073677fc951ec1d9ed1b1cf6c8fc194e50d89bf628d11636be70f580c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:47.843510Z","signature_b64":"2jMnIyc/W7oG6KuIuet89UMMycZhuZZGAuaBph1TVyqflzSgMi637c3wKDcff8QnGKC9FhS3/x53IA03Z+LmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d788ff7073677fc951ec1d9ed1b1cf6c8fc194e50d89bf628d11636be70f580c","last_reissued_at":"2026-05-17T23:47:47.842890Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:47.842890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.11027","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":"2026-05-17T23:47:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DDxP4ckXc1prv6LfOSQUq2CUXyLJzCdpIe1y/MASmK3oqCPLG5mJu3zK2fXz3EzeAZ0nOvWUmBf1YH0BHtq9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:00.933243Z"},"content_sha256":"a290576f6e35206a2e298bcacf66a6197ef70576ea01027d001b705f735544d5","schema_version":"1.0","event_id":"sha256:a290576f6e35206a2e298bcacf66a6197ef70576ea01027d001b705f735544d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:26EP64DTM574SUPMDWPNDMOPNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Modularity Embedding: a General Framework for Network Embedding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Cheng-Shang Chang, Chia-Tai Chang, Ching-Chu Huang, Duan-Shin Lee, Ping-En Lu","submitted_at":"2019-04-24T19:16:25Z","abstract_excerpt":"The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general considered as an ill-posed problem, and its solution may depend on a person's view on this problem. In this book chapter, we adopt the framework of sampled graphs that treat a person's view as a sampling method for a network. The modularity for a sampled graph, called the generalized modularity in the book chapter, is a similarity matrix that has a specific probabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11027","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":"2026-05-17T23:47:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ipRUS8Bh/peHM0rRFbeIPIODljKiN4aF3gOtESQ+3xz6Y3rz3hYh0Loopt1q0QxCsclMzZbzZFYC8OJ0MHQDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:00.933983Z"},"content_sha256":"0586bc6254a1a7bc2e9778fcbcfdc91d893d7a9080b0bd50eff006b40ab57732","schema_version":"1.0","event_id":"sha256:0586bc6254a1a7bc2e9778fcbcfdc91d893d7a9080b0bd50eff006b40ab57732"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26EP64DTM574SUPMDWPNDMOPNS/bundle.json","state_url":"https://pith.science/pith/26EP64DTM574SUPMDWPNDMOPNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26EP64DTM574SUPMDWPNDMOPNS/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":"2026-06-09T19:05:00Z","links":{"resolver":"https://pith.science/pith/26EP64DTM574SUPMDWPNDMOPNS","bundle":"https://pith.science/pith/26EP64DTM574SUPMDWPNDMOPNS/bundle.json","state":"https://pith.science/pith/26EP64DTM574SUPMDWPNDMOPNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26EP64DTM574SUPMDWPNDMOPNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:26EP64DTM574SUPMDWPNDMOPNS","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":"077f0f720838d9dcd0c4f9911dbb3d484f49d27e62419a1a3b02b8d71d81eca2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-24T19:16:25Z","title_canon_sha256":"0fa614f6cdbc2209116c970ff10810d5955c23684e7a9bf67ad88a3c65a7a38a"},"schema_version":"1.0","source":{"id":"1904.11027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.11027","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"arxiv_version","alias_value":"1904.11027v1","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.11027","created_at":"2026-05-17T23:47:47Z"},{"alias_kind":"pith_short_12","alias_value":"26EP64DTM574","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"26EP64DTM574SUPM","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"26EP64DT","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:0586bc6254a1a7bc2e9778fcbcfdc91d893d7a9080b0bd50eff006b40ab57732","target":"graph","created_at":"2026-05-17T23:47:47Z","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":"The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general considered as an ill-posed problem, and its solution may depend on a person's view on this problem. In this book chapter, we adopt the framework of sampled graphs that treat a person's view as a sampling method for a network. The modularity for a sampled graph, called the generalized modularity in the book chapter, is a similarity matrix that has a specific probabi","authors_text":"Cheng-Shang Chang, Chia-Tai Chang, Ching-Chu Huang, Duan-Shin Lee, Ping-En Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-24T19:16:25Z","title":"Generalized Modularity Embedding: a General Framework for Network Embedding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.11027","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:a290576f6e35206a2e298bcacf66a6197ef70576ea01027d001b705f735544d5","target":"record","created_at":"2026-05-17T23:47:47Z","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":"077f0f720838d9dcd0c4f9911dbb3d484f49d27e62419a1a3b02b8d71d81eca2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2019-04-24T19:16:25Z","title_canon_sha256":"0fa614f6cdbc2209116c970ff10810d5955c23684e7a9bf67ad88a3c65a7a38a"},"schema_version":"1.0","source":{"id":"1904.11027","kind":"arxiv","version":1}},"canonical_sha256":"d788ff7073677fc951ec1d9ed1b1cf6c8fc194e50d89bf628d11636be70f580c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d788ff7073677fc951ec1d9ed1b1cf6c8fc194e50d89bf628d11636be70f580c","first_computed_at":"2026-05-17T23:47:47.842890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:47.842890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2jMnIyc/W7oG6KuIuet89UMMycZhuZZGAuaBph1TVyqflzSgMi637c3wKDcff8QnGKC9FhS3/x53IA03Z+LmBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:47.843510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.11027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a290576f6e35206a2e298bcacf66a6197ef70576ea01027d001b705f735544d5","sha256:0586bc6254a1a7bc2e9778fcbcfdc91d893d7a9080b0bd50eff006b40ab57732"],"state_sha256":"b5202f162669f44652eca8a80bee9f4e5f8da8d8e1b69b3a76b8ef428be295bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"To0myaD90mfW/QJ8pK1jKzzIaSiBaunWsg0efPiZtZoIDbUNlBlK4HP+Vhjf04gnHv40gWYgQAJUlnsryTRrAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:05:00.938486Z","bundle_sha256":"8df304a2059792bfd77e2873512818d42e2c4a18bc60d8ef31d31309a707943b"}}