{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:NSKB7XN36MGSDRZKF65PKSKOKC","short_pith_number":"pith:NSKB7XN3","canonical_record":{"source":{"id":"1802.00615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-02T09:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"d42403bcfb796f756648c265b395f89b5dc8aa12ff3465e209eae3cf8149a45a","abstract_canon_sha256":"31bdc2519d4b4d8c4895c6bd905d2759682fdb4e6217274eee1ec63963fd662f"},"schema_version":"1.0"},"canonical_sha256":"6c941fddbbf30d21c72a2fbaf5494e508b70b89ab654e3cdc3fd2111b410c4f3","source":{"kind":"arxiv","id":"1802.00615","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00615","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00615v1","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00615","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"NSKB7XN36MGS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NSKB7XN36MGSDRZK","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NSKB7XN3","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:NSKB7XN36MGSDRZKF65PKSKOKC","target":"record","payload":{"canonical_record":{"source":{"id":"1802.00615","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-02T09:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"d42403bcfb796f756648c265b395f89b5dc8aa12ff3465e209eae3cf8149a45a","abstract_canon_sha256":"31bdc2519d4b4d8c4895c6bd905d2759682fdb4e6217274eee1ec63963fd662f"},"schema_version":"1.0"},"canonical_sha256":"6c941fddbbf30d21c72a2fbaf5494e508b70b89ab654e3cdc3fd2111b410c4f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:32.748399Z","signature_b64":"89XvQHEcEbwF+TVxCYc4EwgfyImhTqMTax/juSLCcc1X9YJnyMC41fJ+0soQ591jZkmDNesFpkvn/Pipyx5tBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c941fddbbf30d21c72a2fbaf5494e508b70b89ab654e3cdc3fd2111b410c4f3","last_reissued_at":"2026-05-18T00:24:32.747886Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:32.747886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.00615","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":"2026-05-18T00:24:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Os2S0ADAuwu441VWHiBg5Q6aIkrFawg2K2GUA514tmPqaFEDRarbOrCpB7XlRuf/RAMkcp5t11LwfL/OpbLbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:10:37.707279Z"},"content_sha256":"75803128e2d5437647563026e7e123f9b0bbc15598a3f8da55309f136c21e24e","schema_version":"1.0","event_id":"sha256:75803128e2d5437647563026e7e123f9b0bbc15598a3f8da55309f136c21e24e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:NSKB7XN36MGSDRZKF65PKSKOKC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse control of Hegselmann-Krause models: Black hole and declustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benedetto Piccoli, Emmanuel Tr\\'elat, Nastassia Pouradier Duteil","submitted_at":"2018-02-02T09:40:28Z","abstract_excerpt":"This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting consensus. In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, we introduce an entropy-type functional that is adapted to measuring pairwise distances between agents. We then focus on a Hegselmann-Krause-type system and design declustering sparse controls both in finite-dimensional and k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00615","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":"2026-05-18T00:24:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Chg10AVW5FN/yWHkZM24g2ZZcxyy1VlvbwCgyYy0t+f5WnyNHMi/FImRMgPiefP6hsuAAV0ypVRqFszQvYmtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:10:37.707634Z"},"content_sha256":"80ae667442a209d5ff45203e9e44559952dbd6a8e65291dadc171493e3892269","schema_version":"1.0","event_id":"sha256:80ae667442a209d5ff45203e9e44559952dbd6a8e65291dadc171493e3892269"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSKB7XN36MGSDRZKF65PKSKOKC/bundle.json","state_url":"https://pith.science/pith/NSKB7XN36MGSDRZKF65PKSKOKC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSKB7XN36MGSDRZKF65PKSKOKC/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":"2026-06-04T20:10:37Z","links":{"resolver":"https://pith.science/pith/NSKB7XN36MGSDRZKF65PKSKOKC","bundle":"https://pith.science/pith/NSKB7XN36MGSDRZKF65PKSKOKC/bundle.json","state":"https://pith.science/pith/NSKB7XN36MGSDRZKF65PKSKOKC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSKB7XN36MGSDRZKF65PKSKOKC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:NSKB7XN36MGSDRZKF65PKSKOKC","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":"31bdc2519d4b4d8c4895c6bd905d2759682fdb4e6217274eee1ec63963fd662f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-02T09:40:28Z","title_canon_sha256":"d42403bcfb796f756648c265b395f89b5dc8aa12ff3465e209eae3cf8149a45a"},"schema_version":"1.0","source":{"id":"1802.00615","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.00615","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"arxiv_version","alias_value":"1802.00615v1","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.00615","created_at":"2026-05-18T00:24:32Z"},{"alias_kind":"pith_short_12","alias_value":"NSKB7XN36MGS","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"NSKB7XN36MGSDRZK","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"NSKB7XN3","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:80ae667442a209d5ff45203e9e44559952dbd6a8e65291dadc171493e3892269","target":"graph","created_at":"2026-05-18T00:24:32Z","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":"This paper elaborates control strategies to prevent clustering effects in opinion formation models. This is the exact opposite of numerous situations encountered in the literature where, on the contrary, one seeks controls promoting consensus. In order to promote declustering, instead of using the classical variance that does not capture well the phenomenon of dispersion, we introduce an entropy-type functional that is adapted to measuring pairwise distances between agents. We then focus on a Hegselmann-Krause-type system and design declustering sparse controls both in finite-dimensional and k","authors_text":"Benedetto Piccoli, Emmanuel Tr\\'elat, Nastassia Pouradier Duteil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-02T09:40:28Z","title":"Sparse control of Hegselmann-Krause models: Black hole and declustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00615","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":"sha256:75803128e2d5437647563026e7e123f9b0bbc15598a3f8da55309f136c21e24e","target":"record","created_at":"2026-05-18T00:24:32Z","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":"31bdc2519d4b4d8c4895c6bd905d2759682fdb4e6217274eee1ec63963fd662f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-02T09:40:28Z","title_canon_sha256":"d42403bcfb796f756648c265b395f89b5dc8aa12ff3465e209eae3cf8149a45a"},"schema_version":"1.0","source":{"id":"1802.00615","kind":"arxiv","version":1}},"canonical_sha256":"6c941fddbbf30d21c72a2fbaf5494e508b70b89ab654e3cdc3fd2111b410c4f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c941fddbbf30d21c72a2fbaf5494e508b70b89ab654e3cdc3fd2111b410c4f3","first_computed_at":"2026-05-18T00:24:32.747886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:32.747886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"89XvQHEcEbwF+TVxCYc4EwgfyImhTqMTax/juSLCcc1X9YJnyMC41fJ+0soQ591jZkmDNesFpkvn/Pipyx5tBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:32.748399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.00615","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75803128e2d5437647563026e7e123f9b0bbc15598a3f8da55309f136c21e24e","sha256:80ae667442a209d5ff45203e9e44559952dbd6a8e65291dadc171493e3892269"],"state_sha256":"16f23ec063e100b9ccb13028b287c364b62e8dd66fb5ed9b231dd8d9f22985f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"htVrChGzugDoNlbJD8GzIi5Ive3zk93EOX4e5NMXQ47LojI7sxCcC5l53qPL1eqzRLzxolC9wH5mhVseFIfwAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:10:37.709470Z","bundle_sha256":"acc9a1240b2e79924dbf3eb118e89f35a01c10c6e7aa83a55a0a7084f1acb5c8"}}