{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:6D3SE6YTOM4PA52MFJ2ZI4YE3Z","short_pith_number":"pith:6D3SE6YT","canonical_record":{"source":{"id":"1908.06656","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-19T09:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"eb46150363bc5b1bd585cae9e9e2bfedba664f8c0eb4eaeb35e7b68b3d859dff","abstract_canon_sha256":"20d1a2b4aee1f4a07dfee5b50c0223920321871b87d1021abfcd0c31f0234495"},"schema_version":"1.0"},"canonical_sha256":"f0f7227b137338f0774c2a75947304de4950b7d19424d18cc6d5bd9fec6af58a","source":{"kind":"arxiv","id":"1908.06656","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06656","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06656v3","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06656","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"6D3SE6YTOM4P","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_16","alias_value":"6D3SE6YTOM4PA52M","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_8","alias_value":"6D3SE6YT","created_at":"2026-07-05T03:35:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:6D3SE6YTOM4PA52MFJ2ZI4YE3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06656","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-19T09:21:36Z","cross_cats_sorted":[],"title_canon_sha256":"eb46150363bc5b1bd585cae9e9e2bfedba664f8c0eb4eaeb35e7b68b3d859dff","abstract_canon_sha256":"20d1a2b4aee1f4a07dfee5b50c0223920321871b87d1021abfcd0c31f0234495"},"schema_version":"1.0"},"canonical_sha256":"f0f7227b137338f0774c2a75947304de4950b7d19424d18cc6d5bd9fec6af58a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:35:47.651893Z","signature_b64":"79lFixL5gnR4Dv4CqzoNB4jWs3sZ8WidojV4Dz0wlGlZ49PXNsFdZheh7lxQihImQ7IOgvSGWt9+1A8qcoqAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0f7227b137338f0774c2a75947304de4950b7d19424d18cc6d5bd9fec6af58a","last_reissued_at":"2026-07-05T03:35:47.651436Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:35:47.651436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06656","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":"2026-07-05T03:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5/+OSZYmkBdjE2XJlFd/wkiN/KGHmpApVWl1F7dwRk3Cz2UWuevrU/t/53mPyvStpupek2t5DhVGq5MktZqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:40:04.024691Z"},"content_sha256":"07d92c014d34db1a1de0c8b1e30b44972ab48819f96a2eaccc4eb4bd4d6b9f7f","schema_version":"1.0","event_id":"sha256:07d92c014d34db1a1de0c8b1e30b44972ab48819f96a2eaccc4eb4bd4d6b9f7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:6D3SE6YTOM4PA52MFJ2ZI4YE3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the edge-biclique graph and the iterated edge-biclique operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Leandro Montero, Sylvain Legay","submitted_at":"2019-08-19T09:21:36Z","abstract_excerpt":"A biclique of a graph $G$ is a maximal induced complete bipartite subgraph of $G$. The edge-biclique graph of $G$, $KB_e(G)$, is the edge-intersection graph of the bicliques of $G$. A graph $G$ diverges (resp. converges or is periodic) under an operator $H$ whenever $\\lim_{k \\rightarrow \\infty}|V(H^k(G))|=\\infty$ (resp. $\\lim_{k \\rightarrow \\infty}H^k(G)=H^m(G)$ for some $m$ or $H^k(G)=H^{k+s}(G)$ for some $k$ and $s \\geq 2$). The iterated edge-biclique graph of $G$, $KB_e^k(G)$, is the graph obtained by applying the edge-biclique operator $k$ successive times to $G$. In this paper, we first s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06656","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06656/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":"2026-07-05T03:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLMrQn2Iu8/03OjBsMIv1uzhE36/HEz4F3wC1sUGEsCMrhRG2uKB8EYXFo2XZHmyCvM9hZ3WCbJP9JrTFFJkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:40:04.025739Z"},"content_sha256":"35c599210f51fb1001389458ced5aac648b595ee49561b58f0a12b38fbab123e","schema_version":"1.0","event_id":"sha256:35c599210f51fb1001389458ced5aac648b595ee49561b58f0a12b38fbab123e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/bundle.json","state_url":"https://pith.science/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/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":"2026-08-16T07:40:04Z","links":{"resolver":"https://pith.science/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z","bundle":"https://pith.science/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/bundle.json","state":"https://pith.science/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6D3SE6YTOM4PA52MFJ2ZI4YE3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6D3SE6YTOM4PA52MFJ2ZI4YE3Z","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":"20d1a2b4aee1f4a07dfee5b50c0223920321871b87d1021abfcd0c31f0234495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-19T09:21:36Z","title_canon_sha256":"eb46150363bc5b1bd585cae9e9e2bfedba664f8c0eb4eaeb35e7b68b3d859dff"},"schema_version":"1.0","source":{"id":"1908.06656","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06656","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06656v3","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06656","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"6D3SE6YTOM4P","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_16","alias_value":"6D3SE6YTOM4PA52M","created_at":"2026-07-05T03:35:47Z"},{"alias_kind":"pith_short_8","alias_value":"6D3SE6YT","created_at":"2026-07-05T03:35:47Z"}],"graph_snapshots":[{"event_id":"sha256:35c599210f51fb1001389458ced5aac648b595ee49561b58f0a12b38fbab123e","target":"graph","created_at":"2026-07-05T03:35:47Z","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/1908.06656/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A biclique of a graph $G$ is a maximal induced complete bipartite subgraph of $G$. The edge-biclique graph of $G$, $KB_e(G)$, is the edge-intersection graph of the bicliques of $G$. A graph $G$ diverges (resp. converges or is periodic) under an operator $H$ whenever $\\lim_{k \\rightarrow \\infty}|V(H^k(G))|=\\infty$ (resp. $\\lim_{k \\rightarrow \\infty}H^k(G)=H^m(G)$ for some $m$ or $H^k(G)=H^{k+s}(G)$ for some $k$ and $s \\geq 2$). The iterated edge-biclique graph of $G$, $KB_e^k(G)$, is the graph obtained by applying the edge-biclique operator $k$ successive times to $G$. In this paper, we first s","authors_text":"Leandro Montero, Sylvain Legay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-19T09:21:36Z","title":"On the edge-biclique graph and the iterated edge-biclique operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06656","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":"sha256:07d92c014d34db1a1de0c8b1e30b44972ab48819f96a2eaccc4eb4bd4d6b9f7f","target":"record","created_at":"2026-07-05T03:35:47Z","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":"20d1a2b4aee1f4a07dfee5b50c0223920321871b87d1021abfcd0c31f0234495","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-08-19T09:21:36Z","title_canon_sha256":"eb46150363bc5b1bd585cae9e9e2bfedba664f8c0eb4eaeb35e7b68b3d859dff"},"schema_version":"1.0","source":{"id":"1908.06656","kind":"arxiv","version":3}},"canonical_sha256":"f0f7227b137338f0774c2a75947304de4950b7d19424d18cc6d5bd9fec6af58a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0f7227b137338f0774c2a75947304de4950b7d19424d18cc6d5bd9fec6af58a","first_computed_at":"2026-07-05T03:35:47.651436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:35:47.651436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"79lFixL5gnR4Dv4CqzoNB4jWs3sZ8WidojV4Dz0wlGlZ49PXNsFdZheh7lxQihImQ7IOgvSGWt9+1A8qcoqAAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:35:47.651893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06656","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07d92c014d34db1a1de0c8b1e30b44972ab48819f96a2eaccc4eb4bd4d6b9f7f","sha256:35c599210f51fb1001389458ced5aac648b595ee49561b58f0a12b38fbab123e"],"state_sha256":"9c6783ea1106845abf5ed198ea1cc2db32b7cbdc4591b962dadc5827f983836f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHLqVlzMSzR2WOuzaNiQ2JCZb+9GJFBtjfneNAt77tVMRj6+8/OJP6BD+g3Avx+evmxLupVDtU7etc8tiPpZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:40:04.047872Z","bundle_sha256":"3fdb6e4ddd4fb37a47307c7730627b948fa6a91c18b00db3ff68180142eb338e"}}