{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZVTXLKFPWDK4364MHMYUXIWW7T","short_pith_number":"pith:ZVTXLKFP","canonical_record":{"source":{"id":"1606.08266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-06-27T13:30:32Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"938317f7ad333d5e4ef8c2a363e18fac24040712e9156f68b061d7acefbd7ec8","abstract_canon_sha256":"b3cddd30d3ee8c4d1934e063aa9a6daffbadd7d3fcf91d49924de2a40e9de14a"},"schema_version":"1.0"},"canonical_sha256":"cd6775a8afb0d5cdfb8c3b314ba2d6fcf8c0e18541e5ae39302a0f6b47d61b22","source":{"kind":"arxiv","id":"1606.08266","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08266","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08266v2","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08266","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZVTXLKFPWDK4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZVTXLKFPWDK4364M","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZVTXLKFP","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZVTXLKFPWDK4364MHMYUXIWW7T","target":"record","payload":{"canonical_record":{"source":{"id":"1606.08266","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-06-27T13:30:32Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"938317f7ad333d5e4ef8c2a363e18fac24040712e9156f68b061d7acefbd7ec8","abstract_canon_sha256":"b3cddd30d3ee8c4d1934e063aa9a6daffbadd7d3fcf91d49924de2a40e9de14a"},"schema_version":"1.0"},"canonical_sha256":"cd6775a8afb0d5cdfb8c3b314ba2d6fcf8c0e18541e5ae39302a0f6b47d61b22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:15.098241Z","signature_b64":"UR8KgMQqGkkQCDA9fw04lySlgiWLV2JG6lWshcdhEN4hXvjK/sGXQU7lt3GWZIwk+iM0170Fby87fgXGR2QOCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd6775a8afb0d5cdfb8c3b314ba2d6fcf8c0e18541e5ae39302a0f6b47d61b22","last_reissued_at":"2026-05-18T00:32:15.097735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:15.097735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.08266","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZGmGe27mPnxqf0g4c+hpAsmtClDHUgYlhPKbOOnra3guoKmLdOvBuSi0FwxmYHXEfO0qJdApgdi5mqlrl+rAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:37:59.901777Z"},"content_sha256":"7be39938491717fbd4b5397e8011021c9b2e085cdd7244beb86a8671055991c6","schema_version":"1.0","event_id":"sha256:7be39938491717fbd4b5397e8011021c9b2e085cdd7244beb86a8671055991c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZVTXLKFPWDK4364MHMYUXIWW7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Magnetic Eigenmaps for the Visualization of Directed Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"\\'Angela Fern\\'andez, Carlos M. Ala\\'iz, Johan A. K. Suykens, Micha\\\"el Fanuel","submitted_at":"2016-06-27T13:30:32Z","abstract_excerpt":"We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08266","kind":"arxiv","version":2},"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":"2026-05-18T00:32:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gFud7MAaeHNmxS6M/5F4EK8dvdMT4aaXf0jst3zWhNN30sguB/ikB4a0EGyu418ga4KeWzENdng9Q5TEZMx0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:37:59.902266Z"},"content_sha256":"d7c6f7956d44422249fba3ef216c23f877422ea189ddacdbe5aae7146d8f8d96","schema_version":"1.0","event_id":"sha256:d7c6f7956d44422249fba3ef216c23f877422ea189ddacdbe5aae7146d8f8d96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/bundle.json","state_url":"https://pith.science/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/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":"2026-05-27T12:37:59Z","links":{"resolver":"https://pith.science/pith/ZVTXLKFPWDK4364MHMYUXIWW7T","bundle":"https://pith.science/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/bundle.json","state":"https://pith.science/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZVTXLKFPWDK4364MHMYUXIWW7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZVTXLKFPWDK4364MHMYUXIWW7T","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":"b3cddd30d3ee8c4d1934e063aa9a6daffbadd7d3fcf91d49924de2a40e9de14a","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-06-27T13:30:32Z","title_canon_sha256":"938317f7ad333d5e4ef8c2a363e18fac24040712e9156f68b061d7acefbd7ec8"},"schema_version":"1.0","source":{"id":"1606.08266","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08266","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08266v2","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08266","created_at":"2026-05-18T00:32:15Z"},{"alias_kind":"pith_short_12","alias_value":"ZVTXLKFPWDK4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZVTXLKFPWDK4364M","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZVTXLKFP","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:d7c6f7956d44422249fba3ef216c23f877422ea189ddacdbe5aae7146d8f8d96","target":"graph","created_at":"2026-05-18T00:32:15Z","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":"We propose a framework for the visualization of directed networks relying on the eigenfunctions of the magnetic Laplacian, called here Magnetic Eigenmaps. The magnetic Laplacian is a complex deformation of the well-known combinatorial Laplacian. Features such as density of links and directionality patterns are revealed by plotting the phases of the first magnetic eigenvectors. An interpretation of the magnetic eigenvectors is given in connection with the angular synchronization problem. Illustrations of our method are given for both artificial and real networks.","authors_text":"\\'Angela Fern\\'andez, Carlos M. Ala\\'iz, Johan A. K. Suykens, Micha\\\"el Fanuel","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-06-27T13:30:32Z","title":"Magnetic Eigenmaps for the Visualization of Directed Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08266","kind":"arxiv","version":2},"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":"sha256:7be39938491717fbd4b5397e8011021c9b2e085cdd7244beb86a8671055991c6","target":"record","created_at":"2026-05-18T00:32:15Z","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":"b3cddd30d3ee8c4d1934e063aa9a6daffbadd7d3fcf91d49924de2a40e9de14a","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-06-27T13:30:32Z","title_canon_sha256":"938317f7ad333d5e4ef8c2a363e18fac24040712e9156f68b061d7acefbd7ec8"},"schema_version":"1.0","source":{"id":"1606.08266","kind":"arxiv","version":2}},"canonical_sha256":"cd6775a8afb0d5cdfb8c3b314ba2d6fcf8c0e18541e5ae39302a0f6b47d61b22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd6775a8afb0d5cdfb8c3b314ba2d6fcf8c0e18541e5ae39302a0f6b47d61b22","first_computed_at":"2026-05-18T00:32:15.097735Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:15.097735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UR8KgMQqGkkQCDA9fw04lySlgiWLV2JG6lWshcdhEN4hXvjK/sGXQU7lt3GWZIwk+iM0170Fby87fgXGR2QOCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:15.098241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08266","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7be39938491717fbd4b5397e8011021c9b2e085cdd7244beb86a8671055991c6","sha256:d7c6f7956d44422249fba3ef216c23f877422ea189ddacdbe5aae7146d8f8d96"],"state_sha256":"c0d7ca78e89c7f53c7c3afc3e02bb5c7a16c43265dfd34e0b151ed907ca15bde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"afMhiVq3tQHxW6y/p57ZgNiA70MB6zq47iE+eMBF+cxmByia0PuPqnHuDkGakLNE0sn+CVPEFSzzmT217ZYwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:37:59.904783Z","bundle_sha256":"3bd1567b012ee07e756695602753af410cf072393f2e9f9f0d1f45cd7097feb0"}}