{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G2HBAUJK4C7ZU5O3RXL3COPL24","short_pith_number":"pith:G2HBAUJK","canonical_record":{"source":{"id":"1407.6071","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-22T23:39:48Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"ba3c63b8c4b6021bb9baf86e1bc27dd08020344b9a90704506dcd1d0f5ac874c","abstract_canon_sha256":"83173787f8866eed47084c44654c74e56518ecec81fbdceadb93a2aca83be423"},"schema_version":"1.0"},"canonical_sha256":"368e10512ae0bf9a75db8dd7b139ebd70cfa5cfb802680bffb2a9484cda5833b","source":{"kind":"arxiv","id":"1407.6071","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6071","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6071v5","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6071","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"G2HBAUJK4C7Z","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2HBAUJK4C7ZU5O3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2HBAUJK","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G2HBAUJK4C7ZU5O3RXL3COPL24","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6071","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-22T23:39:48Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"ba3c63b8c4b6021bb9baf86e1bc27dd08020344b9a90704506dcd1d0f5ac874c","abstract_canon_sha256":"83173787f8866eed47084c44654c74e56518ecec81fbdceadb93a2aca83be423"},"schema_version":"1.0"},"canonical_sha256":"368e10512ae0bf9a75db8dd7b139ebd70cfa5cfb802680bffb2a9484cda5833b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:05.517976Z","signature_b64":"28ia6cjxF7vuFX2cVZy2/qrjfURnUAotgYz2OEFWc2aEiEs+HpooDVrphO4jDFDf0pEs1J6ZIJtHu1Wcr0caAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"368e10512ae0bf9a75db8dd7b139ebd70cfa5cfb802680bffb2a9484cda5833b","last_reissued_at":"2026-05-18T01:29:05.517304Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:05.517304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6071","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hIDmjhfnbNrHEvM4m62AppjRJp39IcqQTfTbGBTGkcTCB7mpxGGvWbVeU1KzKgYMSBh/p67HEW7KZM6478UDAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:55:50.236266Z"},"content_sha256":"8ec35307d296395bb71e168d697d7513449c753cecc1b9fec9c1e2a71207eff9","schema_version":"1.0","event_id":"sha256:8ec35307d296395bb71e168d697d7513449c753cecc1b9fec9c1e2a71207eff9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G2HBAUJK4C7ZU5O3RXL3COPL24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deep Community Detection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Alfred O. Hero, Pin-Yu Chen","submitted_at":"2014-07-22T23:39:48Z","abstract_excerpt":"A deep community in a graph is a connected component that can only be seen after removal of nodes or edges from the rest of the graph. This paper formulates the problem of detecting deep communities as multi-stage node removal that maximizes a new centrality measure, called the local Fiedler vector centrality (LFVC), at each stage. The LFVC is associated with the sensitivity of algebraic connectivity to node or edge removals. We prove that a greedy node/edge removal strategy, based on successive maximization of LFVC, has bounded performance loss relative to the optimal, but intractable, combin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6071","kind":"arxiv","version":5},"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":"2026-05-18T01:29:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LIrA/iTA9iY8kyQ0y9NE17QBsv9GuVIGCqBWEPYk3TP2HIEmh6PbsM/WXYkEULVtJvtgZdCF6nhXuLc6JtB4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T13:55:50.236983Z"},"content_sha256":"baf29ea860778554ba1f4794602d1c43b7fb817c60791e458180c748900b5551","schema_version":"1.0","event_id":"sha256:baf29ea860778554ba1f4794602d1c43b7fb817c60791e458180c748900b5551"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/bundle.json","state_url":"https://pith.science/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/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":"2026-05-30T13:55:50Z","links":{"resolver":"https://pith.science/pith/G2HBAUJK4C7ZU5O3RXL3COPL24","bundle":"https://pith.science/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/bundle.json","state":"https://pith.science/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G2HBAUJK4C7ZU5O3RXL3COPL24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G2HBAUJK4C7ZU5O3RXL3COPL24","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":"83173787f8866eed47084c44654c74e56518ecec81fbdceadb93a2aca83be423","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-22T23:39:48Z","title_canon_sha256":"ba3c63b8c4b6021bb9baf86e1bc27dd08020344b9a90704506dcd1d0f5ac874c"},"schema_version":"1.0","source":{"id":"1407.6071","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6071","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6071v5","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6071","created_at":"2026-05-18T01:29:05Z"},{"alias_kind":"pith_short_12","alias_value":"G2HBAUJK4C7Z","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G2HBAUJK4C7ZU5O3","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G2HBAUJK","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:baf29ea860778554ba1f4794602d1c43b7fb817c60791e458180c748900b5551","target":"graph","created_at":"2026-05-18T01:29:05Z","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":"A deep community in a graph is a connected component that can only be seen after removal of nodes or edges from the rest of the graph. This paper formulates the problem of detecting deep communities as multi-stage node removal that maximizes a new centrality measure, called the local Fiedler vector centrality (LFVC), at each stage. The LFVC is associated with the sensitivity of algebraic connectivity to node or edge removals. We prove that a greedy node/edge removal strategy, based on successive maximization of LFVC, has bounded performance loss relative to the optimal, but intractable, combin","authors_text":"Alfred O. Hero, Pin-Yu Chen","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-22T23:39:48Z","title":"Deep Community Detection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6071","kind":"arxiv","version":5},"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":"sha256:8ec35307d296395bb71e168d697d7513449c753cecc1b9fec9c1e2a71207eff9","target":"record","created_at":"2026-05-18T01:29:05Z","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":"83173787f8866eed47084c44654c74e56518ecec81fbdceadb93a2aca83be423","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2014-07-22T23:39:48Z","title_canon_sha256":"ba3c63b8c4b6021bb9baf86e1bc27dd08020344b9a90704506dcd1d0f5ac874c"},"schema_version":"1.0","source":{"id":"1407.6071","kind":"arxiv","version":5}},"canonical_sha256":"368e10512ae0bf9a75db8dd7b139ebd70cfa5cfb802680bffb2a9484cda5833b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"368e10512ae0bf9a75db8dd7b139ebd70cfa5cfb802680bffb2a9484cda5833b","first_computed_at":"2026-05-18T01:29:05.517304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:05.517304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"28ia6cjxF7vuFX2cVZy2/qrjfURnUAotgYz2OEFWc2aEiEs+HpooDVrphO4jDFDf0pEs1J6ZIJtHu1Wcr0caAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:05.517976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6071","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ec35307d296395bb71e168d697d7513449c753cecc1b9fec9c1e2a71207eff9","sha256:baf29ea860778554ba1f4794602d1c43b7fb817c60791e458180c748900b5551"],"state_sha256":"bf5a5701e32a1ce1af6ad696d9e0a866320de19c885e4b96a12f4ac84da31c17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J853Yno5SuOgbP6kOl7MktVQedLSxX0KUfy68MAfXP/rcZ7ofeG814ZlHyd1xe+NFup4XNxkuOMC8r+XcZWQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T13:55:50.241581Z","bundle_sha256":"60de17b462898675315e59e97ac103e53ae45063230e8ed5ce1a9c6b91d879d4"}}