{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:EFSXHIN3DBBSOWN47DIVKZJADH","short_pith_number":"pith:EFSXHIN3","canonical_record":{"source":{"id":"2502.14593","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T14:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"59f7ea4d544343c4eb701899321d2b895eda06e2c1cb1248fbd1076645d5532d","abstract_canon_sha256":"c95ceb127b8f574d09e2ca641f66835eee67a65497a0328b6926da21d1e72e8c"},"schema_version":"1.0"},"canonical_sha256":"216573a1bb18432759bcf8d155652019d0d9b20545acc96c54ce1b4b11933a77","source":{"kind":"arxiv","id":"2502.14593","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.14593","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.14593v2","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.14593","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"EFSXHIN3DBBS","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_16","alias_value":"EFSXHIN3DBBSOWN4","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_8","alias_value":"EFSXHIN3","created_at":"2026-07-05T10:20:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:EFSXHIN3DBBSOWN47DIVKZJADH","target":"record","payload":{"canonical_record":{"source":{"id":"2502.14593","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T14:27:38Z","cross_cats_sorted":[],"title_canon_sha256":"59f7ea4d544343c4eb701899321d2b895eda06e2c1cb1248fbd1076645d5532d","abstract_canon_sha256":"c95ceb127b8f574d09e2ca641f66835eee67a65497a0328b6926da21d1e72e8c"},"schema_version":"1.0"},"canonical_sha256":"216573a1bb18432759bcf8d155652019d0d9b20545acc96c54ce1b4b11933a77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:20:44.459978Z","signature_b64":"+IB0u6C9LysV3Jw4h3FvQWIczzL6qhyTk0EPPYzKC/M7WTPkYQvNmTpoQxz4WfjAouiyjXIaNIYUmf8/HOWGBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"216573a1bb18432759bcf8d155652019d0d9b20545acc96c54ce1b4b11933a77","last_reissued_at":"2026-07-05T10:20:44.459358Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:20:44.459358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.14593","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":"2026-07-05T10:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h1x4Q+qCkWDWnT+5Xds4qbbGMg+J8zdp9G80Mtcf0yg1aUJ0o/C8vjSEMumt9ua15AYvA45aNofIovZA49VDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:37:51.622045Z"},"content_sha256":"b2daae1f8b2cda87f863188dfe2527eacff99e99fab45807fa53db88364d35d1","schema_version":"1.0","event_id":"sha256:b2daae1f8b2cda87f863188dfe2527eacff99e99fab45807fa53db88364d35d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:EFSXHIN3DBBSOWN47DIVKZJADH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Alternative set-theoretical algorithms for efficient computations of cliques in Vietoris-Rips complexes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Danillo Barros de Souza, Fernando A. N. Santos, Jonatas Teodomiro, Mathieu Desroches, Serafim Rodrigues","submitted_at":"2025-02-20T14:27:38Z","abstract_excerpt":"Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage, implemented across diverse programming languages. Yet, the inherent NP-completeness of the problem continues to hinder performance on large-scale networks, often resulting in memory leaks and slow computations. In the present study, we critically evaluate classic algorithms to pinpoint computational bottlenecks and introduce novel set-theoretical approaches tailor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.14593","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.14593/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:20:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MgS1Yd6mih73O+eq33zXqZzFq7nWDvfX+pSFqkWmAHiyMBBW5fapwfUKTyvnUaZJQw395TYj8wgkcDS1GYoZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:37:51.622441Z"},"content_sha256":"242bec25c697934e418103876d1324b0e64e9726946731243cc92ad5cb9e1cf5","schema_version":"1.0","event_id":"sha256:242bec25c697934e418103876d1324b0e64e9726946731243cc92ad5cb9e1cf5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EFSXHIN3DBBSOWN47DIVKZJADH/bundle.json","state_url":"https://pith.science/pith/EFSXHIN3DBBSOWN47DIVKZJADH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EFSXHIN3DBBSOWN47DIVKZJADH/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":"2026-07-06T18:37:51Z","links":{"resolver":"https://pith.science/pith/EFSXHIN3DBBSOWN47DIVKZJADH","bundle":"https://pith.science/pith/EFSXHIN3DBBSOWN47DIVKZJADH/bundle.json","state":"https://pith.science/pith/EFSXHIN3DBBSOWN47DIVKZJADH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EFSXHIN3DBBSOWN47DIVKZJADH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EFSXHIN3DBBSOWN47DIVKZJADH","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":"c95ceb127b8f574d09e2ca641f66835eee67a65497a0328b6926da21d1e72e8c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T14:27:38Z","title_canon_sha256":"59f7ea4d544343c4eb701899321d2b895eda06e2c1cb1248fbd1076645d5532d"},"schema_version":"1.0","source":{"id":"2502.14593","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.14593","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"arxiv_version","alias_value":"2502.14593v2","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.14593","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_12","alias_value":"EFSXHIN3DBBS","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_16","alias_value":"EFSXHIN3DBBSOWN4","created_at":"2026-07-05T10:20:44Z"},{"alias_kind":"pith_short_8","alias_value":"EFSXHIN3","created_at":"2026-07-05T10:20:44Z"}],"graph_snapshots":[{"event_id":"sha256:242bec25c697934e418103876d1324b0e64e9726946731243cc92ad5cb9e1cf5","target":"graph","created_at":"2026-07-05T10:20:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.14593/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Identifying cliques in dense networks remains a formidable challenge, even with significant advances in computational power and methodologies. To tackle this, numerous algorithms have been developed to optimize time and memory usage, implemented across diverse programming languages. Yet, the inherent NP-completeness of the problem continues to hinder performance on large-scale networks, often resulting in memory leaks and slow computations. In the present study, we critically evaluate classic algorithms to pinpoint computational bottlenecks and introduce novel set-theoretical approaches tailor","authors_text":"Danillo Barros de Souza, Fernando A. N. Santos, Jonatas Teodomiro, Mathieu Desroches, Serafim Rodrigues","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T14:27:38Z","title":"Alternative set-theoretical algorithms for efficient computations of cliques in Vietoris-Rips complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.14593","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:b2daae1f8b2cda87f863188dfe2527eacff99e99fab45807fa53db88364d35d1","target":"record","created_at":"2026-07-05T10:20:44Z","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":"c95ceb127b8f574d09e2ca641f66835eee67a65497a0328b6926da21d1e72e8c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-02-20T14:27:38Z","title_canon_sha256":"59f7ea4d544343c4eb701899321d2b895eda06e2c1cb1248fbd1076645d5532d"},"schema_version":"1.0","source":{"id":"2502.14593","kind":"arxiv","version":2}},"canonical_sha256":"216573a1bb18432759bcf8d155652019d0d9b20545acc96c54ce1b4b11933a77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216573a1bb18432759bcf8d155652019d0d9b20545acc96c54ce1b4b11933a77","first_computed_at":"2026-07-05T10:20:44.459358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:20:44.459358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+IB0u6C9LysV3Jw4h3FvQWIczzL6qhyTk0EPPYzKC/M7WTPkYQvNmTpoQxz4WfjAouiyjXIaNIYUmf8/HOWGBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:20:44.459978Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.14593","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2daae1f8b2cda87f863188dfe2527eacff99e99fab45807fa53db88364d35d1","sha256:242bec25c697934e418103876d1324b0e64e9726946731243cc92ad5cb9e1cf5"],"state_sha256":"f0ccebaecc23188fa7c8dbe45af305e47aaa5a50932f88e1a423bcab291791db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxZMMmfrunnwQDg8hbYEE50ulOrBqFoIuvQ+Tl9dagQ4REC8h+y5JsIw2A2/PB5DdBlh/nHCXBzLWte8ln8rDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:37:51.624689Z","bundle_sha256":"31b18500d7168eb7fc84c2969255696677e43e4a05b2cf7a48746d4be95180f5"}}