{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HPVDJ6QEAHG2PVMCWDXNVCUOSV","short_pith_number":"pith:HPVDJ6QE","canonical_record":{"source":{"id":"1705.06954","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-19T12:21:38Z","cross_cats_sorted":[],"title_canon_sha256":"44ee9d4aae9caecad96dcebe0afa4c1ee5555bab2719157b99488ceecba5296d","abstract_canon_sha256":"048f2ef315b9128ef8fe02121c7f696309ea9abc8ab169c2c7568f153d5ac079"},"schema_version":"1.0"},"canonical_sha256":"3bea34fa0401cda7d582b0eeda8a8e957d83485b351a650b5bf631bb711ebf4a","source":{"kind":"arxiv","id":"1705.06954","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06954","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06954v2","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06954","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"HPVDJ6QEAHG2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HPVDJ6QEAHG2PVMC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HPVDJ6QE","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HPVDJ6QEAHG2PVMCWDXNVCUOSV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.06954","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-19T12:21:38Z","cross_cats_sorted":[],"title_canon_sha256":"44ee9d4aae9caecad96dcebe0afa4c1ee5555bab2719157b99488ceecba5296d","abstract_canon_sha256":"048f2ef315b9128ef8fe02121c7f696309ea9abc8ab169c2c7568f153d5ac079"},"schema_version":"1.0"},"canonical_sha256":"3bea34fa0401cda7d582b0eeda8a8e957d83485b351a650b5bf631bb711ebf4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:23.822847Z","signature_b64":"4UGijuY+4wpdBBgyM5xhhaIeVgk1JS2fYTnbkdDkU/8F9FL90b4nuz785ESJr+kejx/NdUwQtn9wPTVnxek3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bea34fa0401cda7d582b0eeda8a8e957d83485b351a650b5bf631bb711ebf4a","last_reissued_at":"2026-05-18T00:16:23.822274Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:23.822274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.06954","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":"2026-05-18T00:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7TwFT0vX3KmC0fqx3wRcErptLQH0QwlhAMa+wHnD3H1TlDrtb+NQyyiOUXWWh5vYEOAWdpOgOMRVm3WjBBHKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:19:52.629394Z"},"content_sha256":"9bcb8557b954df3ce1ee78ac5fc403e3a85d07be1b8b8b2ad1e9ae074e533839","schema_version":"1.0","event_id":"sha256:9bcb8557b954df3ce1ee78ac5fc403e3a85d07be1b8b8b2ad1e9ae074e533839"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HPVDJ6QEAHG2PVMCWDXNVCUOSV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion limit for the partner model at the critical value","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anirban Basak, Eric Foxall, Rick Durrett","submitted_at":"2017-05-19T12:21:38Z","abstract_excerpt":"The partner model is an SIS epidemic in a population with random formation and dissolution of partnerships, and with disease transmission only occuring within partnerships. Foxall, Edwards, and van den Driessche found the critical value and studied the subcritical and supercritical regimes. Recently Foxall has shown that (if there are enough initial infecteds $I_0$) the extinction time in the critical model is of order $\\sqrt{N}$. Here we improve that result by proving the convergence of $i_N(t)=I(\\sqrt{N}t)/\\sqrt{N}$ to a limiting diffusion. We do this by showing that within a short time, thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06954","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:16:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yvQ8aGKDJNnSv5LXztElj8I6uREK6tMgcWHqB0hfOkxPBVqeubMkVbEmUbiCoWJx2AmI9vPzhWCr0Q2dvB8wAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T13:19:52.630124Z"},"content_sha256":"4664a29c1498d46ad8f7c7945ccce01a89a38bf9328825e992865e1e4dcc86a7","schema_version":"1.0","event_id":"sha256:4664a29c1498d46ad8f7c7945ccce01a89a38bf9328825e992865e1e4dcc86a7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/bundle.json","state_url":"https://pith.science/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/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":"2026-05-22T13:19:52Z","links":{"resolver":"https://pith.science/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV","bundle":"https://pith.science/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/bundle.json","state":"https://pith.science/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPVDJ6QEAHG2PVMCWDXNVCUOSV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HPVDJ6QEAHG2PVMCWDXNVCUOSV","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":"048f2ef315b9128ef8fe02121c7f696309ea9abc8ab169c2c7568f153d5ac079","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-19T12:21:38Z","title_canon_sha256":"44ee9d4aae9caecad96dcebe0afa4c1ee5555bab2719157b99488ceecba5296d"},"schema_version":"1.0","source":{"id":"1705.06954","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.06954","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1705.06954v2","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.06954","created_at":"2026-05-18T00:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"HPVDJ6QEAHG2","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HPVDJ6QEAHG2PVMC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HPVDJ6QE","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:4664a29c1498d46ad8f7c7945ccce01a89a38bf9328825e992865e1e4dcc86a7","target":"graph","created_at":"2026-05-18T00:16:23Z","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 partner model is an SIS epidemic in a population with random formation and dissolution of partnerships, and with disease transmission only occuring within partnerships. Foxall, Edwards, and van den Driessche found the critical value and studied the subcritical and supercritical regimes. Recently Foxall has shown that (if there are enough initial infecteds $I_0$) the extinction time in the critical model is of order $\\sqrt{N}$. Here we improve that result by proving the convergence of $i_N(t)=I(\\sqrt{N}t)/\\sqrt{N}$ to a limiting diffusion. We do this by showing that within a short time, thi","authors_text":"Anirban Basak, Eric Foxall, Rick Durrett","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-19T12:21:38Z","title":"Diffusion limit for the partner model at the critical value"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06954","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":"sha256:9bcb8557b954df3ce1ee78ac5fc403e3a85d07be1b8b8b2ad1e9ae074e533839","target":"record","created_at":"2026-05-18T00:16:23Z","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":"048f2ef315b9128ef8fe02121c7f696309ea9abc8ab169c2c7568f153d5ac079","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-05-19T12:21:38Z","title_canon_sha256":"44ee9d4aae9caecad96dcebe0afa4c1ee5555bab2719157b99488ceecba5296d"},"schema_version":"1.0","source":{"id":"1705.06954","kind":"arxiv","version":2}},"canonical_sha256":"3bea34fa0401cda7d582b0eeda8a8e957d83485b351a650b5bf631bb711ebf4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bea34fa0401cda7d582b0eeda8a8e957d83485b351a650b5bf631bb711ebf4a","first_computed_at":"2026-05-18T00:16:23.822274Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:23.822274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4UGijuY+4wpdBBgyM5xhhaIeVgk1JS2fYTnbkdDkU/8F9FL90b4nuz785ESJr+kejx/NdUwQtn9wPTVnxek3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:23.822847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.06954","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bcb8557b954df3ce1ee78ac5fc403e3a85d07be1b8b8b2ad1e9ae074e533839","sha256:4664a29c1498d46ad8f7c7945ccce01a89a38bf9328825e992865e1e4dcc86a7"],"state_sha256":"3d56ae9e6765e8fe6414c621f1112fdf56a4597b2ded20f0081cd63a7ac70518"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y0YAsuqA7pOWoJWPta1tSMuuRgaHqAciRYXjd+FmoYNAy2z+F6O96uQF38qU+dQeTYN1cg/gGbhM5nGTLAPVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T13:19:52.634621Z","bundle_sha256":"9019b75e3d58aedb55fc1594153fa916f67ffa52bbec29433c50d110f216d9d6"}}