{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RIHSV3ORLHPYYXCLFBXT3G3P6R","short_pith_number":"pith:RIHSV3OR","canonical_record":{"source":{"id":"1401.6733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-01-27T03:48:04Z","cross_cats_sorted":["cs.SI","physics.data-an"],"title_canon_sha256":"803ed001e96260f15c8509765a6e378fd1ff18ddc07124c7e9764646581265b7","abstract_canon_sha256":"e51fab7f3476f921c93a17c8e3b02cc72f88ed47a817638d5b0dbf809e66d0af"},"schema_version":"1.0"},"canonical_sha256":"8a0f2aedd159df8c5c4b286f3d9b6ff47fd14381f32885755c2af8212df2bd2a","source":{"kind":"arxiv","id":"1401.6733","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6733","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6733v1","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6733","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"RIHSV3ORLHPY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RIHSV3ORLHPYYXCL","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RIHSV3OR","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RIHSV3ORLHPYYXCLFBXT3G3P6R","target":"record","payload":{"canonical_record":{"source":{"id":"1401.6733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-01-27T03:48:04Z","cross_cats_sorted":["cs.SI","physics.data-an"],"title_canon_sha256":"803ed001e96260f15c8509765a6e378fd1ff18ddc07124c7e9764646581265b7","abstract_canon_sha256":"e51fab7f3476f921c93a17c8e3b02cc72f88ed47a817638d5b0dbf809e66d0af"},"schema_version":"1.0"},"canonical_sha256":"8a0f2aedd159df8c5c4b286f3d9b6ff47fd14381f32885755c2af8212df2bd2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.699269Z","signature_b64":"fl7/i6yQSuL6G3sxl0VuWT22LRZoLGEp4JoTnBbmyBlV5DkHQBH3c3w0iwP5I/JaPo2hJcPcFO6tn1MO+PiEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a0f2aedd159df8c5c4b286f3d9b6ff47fd14381f32885755c2af8212df2bd2a","last_reissued_at":"2026-05-18T00:31:00.698602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.698602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.6733","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7lCkaCYpfm2oTyWHpm2Kyqr3pKB7bIg8SJjaH5B1Dbd5u1wXp0kDqtE04UI2EwAeawiuC2LZnRMLgS6C5vDkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:31:29.398658Z"},"content_sha256":"029cf0e22c39aebb1519f57667c2d92702226fb6d6916cbd60b25c170bad03d5","schema_version":"1.0","event_id":"sha256:029cf0e22c39aebb1519f57667c2d92702226fb6d6916cbd60b25c170bad03d5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RIHSV3ORLHPYYXCLFBXT3G3P6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Walk modularity and community structure in networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"Amy Strosser, Anthony Harkin, David Mehrle","submitted_at":"2014-01-27T03:48:04Z","abstract_excerpt":"Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically expect to find based on random chance. We present a natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which we call walk-modulari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6733","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZhpvTgvjjzbEnENOOa08H+XTLOjs/ZhxEgOEZLLvxhrw0LeuYojZUCqwNPGW8JM8mOpXbbcNm7BKIgPUfq6SBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T18:31:29.399004Z"},"content_sha256":"4e07b772067128382d23d0ebbe198e8b30a9f62d0599468d2305760dff6c1057","schema_version":"1.0","event_id":"sha256:4e07b772067128382d23d0ebbe198e8b30a9f62d0599468d2305760dff6c1057"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/bundle.json","state_url":"https://pith.science/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/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":"2026-07-03T18:31:29Z","links":{"resolver":"https://pith.science/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R","bundle":"https://pith.science/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/bundle.json","state":"https://pith.science/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIHSV3ORLHPYYXCLFBXT3G3P6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RIHSV3ORLHPYYXCLFBXT3G3P6R","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":"e51fab7f3476f921c93a17c8e3b02cc72f88ed47a817638d5b0dbf809e66d0af","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-01-27T03:48:04Z","title_canon_sha256":"803ed001e96260f15c8509765a6e378fd1ff18ddc07124c7e9764646581265b7"},"schema_version":"1.0","source":{"id":"1401.6733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6733","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6733v1","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6733","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"RIHSV3ORLHPY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RIHSV3ORLHPYYXCL","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RIHSV3OR","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:4e07b772067128382d23d0ebbe198e8b30a9f62d0599468d2305760dff6c1057","target":"graph","created_at":"2026-05-18T00:31:00Z","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":"Modularity maximization has been one of the most widely used approaches in the last decade for discovering community structure in networks of practical interest in biology, computing, social science, statistical mechanics, and more. Modularity is a quality function that measures the difference between the number of edges found within clusters minus the number of edges one would statistically expect to find based on random chance. We present a natural generalization of modularity based on the difference between the actual and expected number of walks within clusters, which we call walk-modulari","authors_text":"Amy Strosser, Anthony Harkin, David Mehrle","cross_cats":["cs.SI","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-01-27T03:48:04Z","title":"Walk modularity and community structure in networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6733","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":"sha256:029cf0e22c39aebb1519f57667c2d92702226fb6d6916cbd60b25c170bad03d5","target":"record","created_at":"2026-05-18T00:31:00Z","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":"e51fab7f3476f921c93a17c8e3b02cc72f88ed47a817638d5b0dbf809e66d0af","cross_cats_sorted":["cs.SI","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2014-01-27T03:48:04Z","title_canon_sha256":"803ed001e96260f15c8509765a6e378fd1ff18ddc07124c7e9764646581265b7"},"schema_version":"1.0","source":{"id":"1401.6733","kind":"arxiv","version":1}},"canonical_sha256":"8a0f2aedd159df8c5c4b286f3d9b6ff47fd14381f32885755c2af8212df2bd2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a0f2aedd159df8c5c4b286f3d9b6ff47fd14381f32885755c2af8212df2bd2a","first_computed_at":"2026-05-18T00:31:00.698602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:00.698602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fl7/i6yQSuL6G3sxl0VuWT22LRZoLGEp4JoTnBbmyBlV5DkHQBH3c3w0iwP5I/JaPo2hJcPcFO6tn1MO+PiEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:00.699269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:029cf0e22c39aebb1519f57667c2d92702226fb6d6916cbd60b25c170bad03d5","sha256:4e07b772067128382d23d0ebbe198e8b30a9f62d0599468d2305760dff6c1057"],"state_sha256":"9f73c7a2b843681bd6af3dae479ba5cb8eddb8c645bd6b4273344081f6498656"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EuPPdqVCZ9vaouApww1W8Aszobrm28/usFWt0AylCe4kQdrtsg++feZ3oRjPepeHsGQJAExH/VgFR9mDgL0zCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T18:31:29.400930Z","bundle_sha256":"a07d1d89c1969499c57ecbfb00cb6ff5dbfd5f5e1fc6da3d2d5e9ec67313b8a7"}}