{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:REXHK3IZTE7G45TGUAY62ZEHLC","short_pith_number":"pith:REXHK3IZ","schema_version":"1.0","canonical_sha256":"892e756d19993e6e7666a031ed648758adb5c38950d2ae99a67bbf89fd15fab8","source":{"kind":"arxiv","id":"1202.2910","version":2},"attestation_state":"computed","paper":{"title":"Revolutionaries and spies: Spy-good and spy-bad graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Daniel W. Cranston, Douglas B. West, Gregory J. Puleo, Jane V. Butterfield, Reza Zamani","submitted_at":"2012-02-14T02:02:35Z","abstract_excerpt":"We study a game on a graph $G$ played by $r$ {\\it revolutionaries} and $s$ {\\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever.\n  Let $\\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume $|V(G)|\\ge r-m+1\\ge\\floor{r/m}\\ge 1$. The easy bounds are then $\\floor{r/"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1202.2910","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-02-14T02:02:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"a4639e75edf62db75015f51a597fc97380953c31782355d3f91fb20df5ef40d7","abstract_canon_sha256":"bd03a0062622b6b376cdd0571a4f0f2c67b325606fa2c58497d316989c19b61a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:53.070545Z","signature_b64":"ENFX/0F7mtLpcHPBXMnp39FCnq6oIFwxZoyXxUQAm+iLI4h6ARw+0UAkSYWEEUQlUKK3ZiDhY2ekzn9oSeJUDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"892e756d19993e6e7666a031ed648758adb5c38950d2ae99a67bbf89fd15fab8","last_reissued_at":"2026-05-18T01:35:53.069857Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:53.069857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revolutionaries and spies: Spy-good and spy-bad graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Daniel W. Cranston, Douglas B. West, Gregory J. Puleo, Jane V. Butterfield, Reza Zamani","submitted_at":"2012-02-14T02:02:35Z","abstract_excerpt":"We study a game on a graph $G$ played by $r$ {\\it revolutionaries} and $s$ {\\it spies}. Initially, revolutionaries and then spies occupy vertices. In each subsequent round, each revolutionary may move to a neighboring vertex or not move, and then each spy has the same option. The revolutionaries win if $m$ of them meet at some vertex having no spy (at the end of a round); the spies win if they can avoid this forever.\n  Let $\\sigma(G,m,r)$ denote the minimum number of spies needed to win. To avoid degenerate cases, assume $|V(G)|\\ge r-m+1\\ge\\floor{r/m}\\ge 1$. The easy bounds are then $\\floor{r/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.2910","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1202.2910","created_at":"2026-05-18T01:35:53.069973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1202.2910v2","created_at":"2026-05-18T01:35:53.069973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.2910","created_at":"2026-05-18T01:35:53.069973+00:00"},{"alias_kind":"pith_short_12","alias_value":"REXHK3IZTE7G","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"REXHK3IZTE7G45TG","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"REXHK3IZ","created_at":"2026-05-18T12:27:20.899486+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC","json":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC.json","graph_json":"https://pith.science/api/pith-number/REXHK3IZTE7G45TGUAY62ZEHLC/graph.json","events_json":"https://pith.science/api/pith-number/REXHK3IZTE7G45TGUAY62ZEHLC/events.json","paper":"https://pith.science/paper/REXHK3IZ"},"agent_actions":{"view_html":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC","download_json":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC.json","view_paper":"https://pith.science/paper/REXHK3IZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1202.2910&json=true","fetch_graph":"https://pith.science/api/pith-number/REXHK3IZTE7G45TGUAY62ZEHLC/graph.json","fetch_events":"https://pith.science/api/pith-number/REXHK3IZTE7G45TGUAY62ZEHLC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC/action/storage_attestation","attest_author":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC/action/author_attestation","sign_citation":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC/action/citation_signature","submit_replication":"https://pith.science/pith/REXHK3IZTE7G45TGUAY62ZEHLC/action/replication_record"}},"created_at":"2026-05-18T01:35:53.069973+00:00","updated_at":"2026-05-18T01:35:53.069973+00:00"}