{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4RQ2T3JVO267RGTGXONTECQHQ6","short_pith_number":"pith:4RQ2T3JV","canonical_record":{"source":{"id":"1501.06614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-01-26T22:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"4cb3386fe9293478be9325d64341336f34071327daff9d79d6495e8e82dd6c36","abstract_canon_sha256":"bfefe18cec5dd2dee9cbafcd052b7560a4d8a9e5e8b884e1cb6a9287a3ef9f86"},"schema_version":"1.0"},"canonical_sha256":"e461a9ed3576bdf89a66bb9b320a0787bee09005098965c025ba94b3ea99d1b0","source":{"kind":"arxiv","id":"1501.06614","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06614","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06614v1","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06614","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"pith_short_12","alias_value":"4RQ2T3JVO267","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4RQ2T3JVO267RGTG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4RQ2T3JV","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4RQ2T3JVO267RGTGXONTECQHQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-01-26T22:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"4cb3386fe9293478be9325d64341336f34071327daff9d79d6495e8e82dd6c36","abstract_canon_sha256":"bfefe18cec5dd2dee9cbafcd052b7560a4d8a9e5e8b884e1cb6a9287a3ef9f86"},"schema_version":"1.0"},"canonical_sha256":"e461a9ed3576bdf89a66bb9b320a0787bee09005098965c025ba94b3ea99d1b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:39.502393Z","signature_b64":"j4JK6vJBpulmfNr4IBAT+qdYNcjx7X9Yi4Y9TJKoNGSySAeXLHskx7Awx4w7nj5xjz7f2XogFj6O1dV+wcSuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e461a9ed3576bdf89a66bb9b320a0787bee09005098965c025ba94b3ea99d1b0","last_reissued_at":"2026-05-18T02:28:39.501796Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:39.501796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06614","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":"2026-05-18T02:28:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y89WBol2EAZzhHD1AQJECnGtws27kSEE+/t5ofowH2cjnrrSzsP1y9kmgNnFN+Y97pWlsqs/XuBQtUOVIdloAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:13:43.411424Z"},"content_sha256":"a6867afc29d9899fb2a190993f624a39d098cb943bfcd80fe03f64fbfe0cb814","schema_version":"1.0","event_id":"sha256:a6867afc29d9899fb2a190993f624a39d098cb943bfcd80fe03f64fbfe0cb814"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4RQ2T3JVO267RGTGXONTECQHQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximation Algorithms for Reducing the Spectral Radius to Control Epidemic Spread","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"Abhijin Adiga, Anil Kumar S. Vullikanti, B. Aditya Prakash, Sudip Saha","submitted_at":"2015-01-26T22:38:39Z","abstract_excerpt":"The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the `flu-like' SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motivates a strategy to control epidemic spread by reducing the spectral radius of the underlying network.\n  In this paper, we develop a suite of provable approximation algorithms for reducing the spectral rad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06614","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":"2026-05-18T02:28:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gb6W13TPV+HZf+cD/V22e8+b8PnU3Xl+rVwgOqi791dzVZ/YQYzNk9mqLgdMlox5Wz2RQOWrCQRjdly1cPV7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:13:43.411775Z"},"content_sha256":"2430f14be0de9546c8a881fe2687b7a13be8b9b93a4e35a2a2a77efd6dfbc550","schema_version":"1.0","event_id":"sha256:2430f14be0de9546c8a881fe2687b7a13be8b9b93a4e35a2a2a77efd6dfbc550"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4RQ2T3JVO267RGTGXONTECQHQ6/bundle.json","state_url":"https://pith.science/pith/4RQ2T3JVO267RGTGXONTECQHQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4RQ2T3JVO267RGTGXONTECQHQ6/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":"2026-05-28T13:13:43Z","links":{"resolver":"https://pith.science/pith/4RQ2T3JVO267RGTGXONTECQHQ6","bundle":"https://pith.science/pith/4RQ2T3JVO267RGTGXONTECQHQ6/bundle.json","state":"https://pith.science/pith/4RQ2T3JVO267RGTGXONTECQHQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4RQ2T3JVO267RGTGXONTECQHQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4RQ2T3JVO267RGTGXONTECQHQ6","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":"bfefe18cec5dd2dee9cbafcd052b7560a4d8a9e5e8b884e1cb6a9287a3ef9f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-01-26T22:38:39Z","title_canon_sha256":"4cb3386fe9293478be9325d64341336f34071327daff9d79d6495e8e82dd6c36"},"schema_version":"1.0","source":{"id":"1501.06614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06614","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06614v1","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06614","created_at":"2026-05-18T02:28:39Z"},{"alias_kind":"pith_short_12","alias_value":"4RQ2T3JVO267","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4RQ2T3JVO267RGTG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4RQ2T3JV","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:2430f14be0de9546c8a881fe2687b7a13be8b9b93a4e35a2a2a77efd6dfbc550","target":"graph","created_at":"2026-05-18T02:28:39Z","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":"The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the `flu-like' SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motivates a strategy to control epidemic spread by reducing the spectral radius of the underlying network.\n  In this paper, we develop a suite of provable approximation algorithms for reducing the spectral rad","authors_text":"Abhijin Adiga, Anil Kumar S. Vullikanti, B. Aditya Prakash, Sudip Saha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-01-26T22:38:39Z","title":"Approximation Algorithms for Reducing the Spectral Radius to Control Epidemic Spread"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06614","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:a6867afc29d9899fb2a190993f624a39d098cb943bfcd80fe03f64fbfe0cb814","target":"record","created_at":"2026-05-18T02:28:39Z","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":"bfefe18cec5dd2dee9cbafcd052b7560a4d8a9e5e8b884e1cb6a9287a3ef9f86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2015-01-26T22:38:39Z","title_canon_sha256":"4cb3386fe9293478be9325d64341336f34071327daff9d79d6495e8e82dd6c36"},"schema_version":"1.0","source":{"id":"1501.06614","kind":"arxiv","version":1}},"canonical_sha256":"e461a9ed3576bdf89a66bb9b320a0787bee09005098965c025ba94b3ea99d1b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e461a9ed3576bdf89a66bb9b320a0787bee09005098965c025ba94b3ea99d1b0","first_computed_at":"2026-05-18T02:28:39.501796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:39.501796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j4JK6vJBpulmfNr4IBAT+qdYNcjx7X9Yi4Y9TJKoNGSySAeXLHskx7Awx4w7nj5xjz7f2XogFj6O1dV+wcSuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:39.502393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6867afc29d9899fb2a190993f624a39d098cb943bfcd80fe03f64fbfe0cb814","sha256:2430f14be0de9546c8a881fe2687b7a13be8b9b93a4e35a2a2a77efd6dfbc550"],"state_sha256":"f68de45f7de0994c175cf6383bb741a6c9949749e6090ff10319a6e715e849f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wzua3Ub5YEbtOcTBMsfEuqYCCNnqvKTI9MtbgEnRLnxkGb4ALdKnOmCQuj9otZrINNbT9YlcCEeaWg/zt1mlBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:13:43.413709Z","bundle_sha256":"bf8cd25f90863f6f1a552a3ed9b66dc7f8a7138099c96715914072b1eb45f969"}}