{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N7CKK63J732B45YEOA6YCMHLA2","short_pith_number":"pith:N7CKK63J","canonical_record":{"source":{"id":"1405.1477","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-07T00:28:23Z","cross_cats_sorted":["cs.DM","cs.SI"],"title_canon_sha256":"90954462a150a46c4fccaece9536bed4627414d52de76ea9cedaa4895ef40cff","abstract_canon_sha256":"8d4557f5e1e332fc01c8661cd15c41adfd3b99cd1d3abc28a6fc20e38f6ef757"},"schema_version":"1.0"},"canonical_sha256":"6fc4a57b69fef41e7704703d8130eb0696ed93ae2e9860d90cf3089c2465ba7d","source":{"kind":"arxiv","id":"1405.1477","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1477","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1477v3","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1477","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"N7CKK63J732B","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7CKK63J732B45YE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7CKK63J","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N7CKK63J732B45YEOA6YCMHLA2","target":"record","payload":{"canonical_record":{"source":{"id":"1405.1477","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-07T00:28:23Z","cross_cats_sorted":["cs.DM","cs.SI"],"title_canon_sha256":"90954462a150a46c4fccaece9536bed4627414d52de76ea9cedaa4895ef40cff","abstract_canon_sha256":"8d4557f5e1e332fc01c8661cd15c41adfd3b99cd1d3abc28a6fc20e38f6ef757"},"schema_version":"1.0"},"canonical_sha256":"6fc4a57b69fef41e7704703d8130eb0696ed93ae2e9860d90cf3089c2465ba7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:24.807308Z","signature_b64":"DrcXFuQlTwOrHOhmzqsfHmvStS1r9qBgqRLGd/TYmPPWwLfndTcrRbL0N/4IUphjmjpHsvoprixdET5LpRgLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fc4a57b69fef41e7704703d8130eb0696ed93ae2e9860d90cf3089c2465ba7d","last_reissued_at":"2026-05-18T02:51:24.806602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:24.806602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.1477","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NesN1Z7Vo4LrADvtCyx4x7zydVS8UQBe5MuuBk9hk/sJhgTovWIC1gfjODGL/m2tz0fNTr/foDE0V/lv5m32BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:24:11.390260Z"},"content_sha256":"9183f76e197726679a8ef54927a161b5af117048c436f9fd2b0af4b7ef2b8388","schema_version":"1.0","event_id":"sha256:9183f76e197726679a8ef54927a161b5af117048c436f9fd2b0af4b7ef2b8388"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N7CKK63J732B45YEOA6YCMHLA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.SI"],"primary_cat":"cs.DS","authors_text":"Charalampos E. Tsourakakis","submitted_at":"2014-05-07T00:28:23Z","abstract_excerpt":"Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes the average degree over all subgraphs is solvable in polynomial time but for many networks fails to find subgraphs which are near-cliques. On the other hand, formulations that are geared towards finding near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem.\n  In this work, we propose a formulation which co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1477","kind":"arxiv","version":3},"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":"2026-05-18T02:51:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jm74uhxfOa82PGs8j1LYQaSSOLJPRD+UqC6S6OiNy1Du+qT3CEAu5v8v40Q2Ja6WeKDFAO8+jad8N8hRNYGUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:24:11.390637Z"},"content_sha256":"dab44606d164ce7ab75a6fa393b2d3715f3e695e6e9b0f89991ac9498606a135","schema_version":"1.0","event_id":"sha256:dab44606d164ce7ab75a6fa393b2d3715f3e695e6e9b0f89991ac9498606a135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7CKK63J732B45YEOA6YCMHLA2/bundle.json","state_url":"https://pith.science/pith/N7CKK63J732B45YEOA6YCMHLA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7CKK63J732B45YEOA6YCMHLA2/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":"2026-06-20T04:24:11Z","links":{"resolver":"https://pith.science/pith/N7CKK63J732B45YEOA6YCMHLA2","bundle":"https://pith.science/pith/N7CKK63J732B45YEOA6YCMHLA2/bundle.json","state":"https://pith.science/pith/N7CKK63J732B45YEOA6YCMHLA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7CKK63J732B45YEOA6YCMHLA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N7CKK63J732B45YEOA6YCMHLA2","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":"8d4557f5e1e332fc01c8661cd15c41adfd3b99cd1d3abc28a6fc20e38f6ef757","cross_cats_sorted":["cs.DM","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-07T00:28:23Z","title_canon_sha256":"90954462a150a46c4fccaece9536bed4627414d52de76ea9cedaa4895ef40cff"},"schema_version":"1.0","source":{"id":"1405.1477","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.1477","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"arxiv_version","alias_value":"1405.1477v3","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.1477","created_at":"2026-05-18T02:51:24Z"},{"alias_kind":"pith_short_12","alias_value":"N7CKK63J732B","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N7CKK63J732B45YE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N7CKK63J","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:dab44606d164ce7ab75a6fa393b2d3715f3e695e6e9b0f89991ac9498606a135","target":"graph","created_at":"2026-05-18T02:51:24Z","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":"Many graph mining applications rely on detecting subgraphs which are near-cliques. There exists a dichotomy between the results in the existing work related to this problem: on the one hand the densest subgraph problem (DSP) which maximizes the average degree over all subgraphs is solvable in polynomial time but for many networks fails to find subgraphs which are near-cliques. On the other hand, formulations that are geared towards finding near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem.\n  In this work, we propose a formulation which co","authors_text":"Charalampos E. Tsourakakis","cross_cats":["cs.DM","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-07T00:28:23Z","title":"A Novel Approach to Finding Near-Cliques: The Triangle-Densest Subgraph Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1477","kind":"arxiv","version":3},"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":"sha256:9183f76e197726679a8ef54927a161b5af117048c436f9fd2b0af4b7ef2b8388","target":"record","created_at":"2026-05-18T02:51:24Z","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":"8d4557f5e1e332fc01c8661cd15c41adfd3b99cd1d3abc28a6fc20e38f6ef757","cross_cats_sorted":["cs.DM","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-05-07T00:28:23Z","title_canon_sha256":"90954462a150a46c4fccaece9536bed4627414d52de76ea9cedaa4895ef40cff"},"schema_version":"1.0","source":{"id":"1405.1477","kind":"arxiv","version":3}},"canonical_sha256":"6fc4a57b69fef41e7704703d8130eb0696ed93ae2e9860d90cf3089c2465ba7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fc4a57b69fef41e7704703d8130eb0696ed93ae2e9860d90cf3089c2465ba7d","first_computed_at":"2026-05-18T02:51:24.806602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:24.806602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DrcXFuQlTwOrHOhmzqsfHmvStS1r9qBgqRLGd/TYmPPWwLfndTcrRbL0N/4IUphjmjpHsvoprixdET5LpRgLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:24.807308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.1477","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9183f76e197726679a8ef54927a161b5af117048c436f9fd2b0af4b7ef2b8388","sha256:dab44606d164ce7ab75a6fa393b2d3715f3e695e6e9b0f89991ac9498606a135"],"state_sha256":"d52bf9a0bd4c0371e159ad14a893ba35b9d754b27ee07d6c78aee30c236c01af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3tYy0lhhKA/ckiiPPd1Ypa5fCH1iK0n70R4+Wkl8fM+4oUiD8ffJpiA6SVnPR+7EA8kQyBvZgFha9lACSnr1Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:24:11.392585Z","bundle_sha256":"a24dadb1d74ca837a462ea6f66f62db31591fc36901d91768a15c89c3482b4d8"}}