{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:NANGRC2XSZZQTKBNUIUWVB3A3H","short_pith_number":"pith:NANGRC2X","canonical_record":{"source":{"id":"1412.3349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-10T15:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"dafc0afb17b88be74df9083e4d319aa959903783d52b28e1e61832296252f41f","abstract_canon_sha256":"b0e3d42a9c7105eac798697ea4404bb8ecce839eb4bbab7d7c9bc0330240d60a"},"schema_version":"1.0"},"canonical_sha256":"681a688b57967309a82da2296a8760d9d3cf32e991844e96330f1486daa293f1","source":{"kind":"arxiv","id":"1412.3349","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3349","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3349v2","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3349","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"NANGRC2XSZZQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NANGRC2XSZZQTKBN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NANGRC2X","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:NANGRC2XSZZQTKBNUIUWVB3A3H","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3349","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-10T15:59:52Z","cross_cats_sorted":[],"title_canon_sha256":"dafc0afb17b88be74df9083e4d319aa959903783d52b28e1e61832296252f41f","abstract_canon_sha256":"b0e3d42a9c7105eac798697ea4404bb8ecce839eb4bbab7d7c9bc0330240d60a"},"schema_version":"1.0"},"canonical_sha256":"681a688b57967309a82da2296a8760d9d3cf32e991844e96330f1486daa293f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:01.900987Z","signature_b64":"9ITVN/zGBJjC1aT5NRLl8U0KDUWsAR6TdhAOd48zrsXei+i5/7ajZ8o05VMhstyOdxoOKGuPUkSP8Iqdv5kmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"681a688b57967309a82da2296a8760d9d3cf32e991844e96330f1486daa293f1","last_reissued_at":"2026-05-18T01:12:01.900664Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:01.900664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3349","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":"2026-05-18T01:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iawhh6+UUFCRZXp4cJp7MChGhlsWl4lOEYYzEeiGFB1JllRGsZhnm6+a8VTCZCYzmlcQHscxxXW4ymEYMwo/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:03:23.155384Z"},"content_sha256":"00aa7dd21ea578226483a17b639cf854dc632a1076de3c226f12e3c26bb12d48","schema_version":"1.0","event_id":"sha256:00aa7dd21ea578226483a17b639cf854dc632a1076de3c226f12e3c26bb12d48"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:NANGRC2XSZZQTKBNUIUWVB3A3H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Social contact processes and the partner model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Foxall, P. van den Driessche, Roderick Edwards","submitted_at":"2014-12-10T15:59:52Z","abstract_excerpt":"We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_0$ with the property that if $R_0<1$ the infection dies out by time $O(\\log N)$, while if $R_0>1$ the infection survives for an amount of time $e^{\\gamma N}$ for some $\\gamma>0$ and hovers around a uniquely determined metastable proportion of infectiou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3349","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":"2026-05-18T01:12:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+EVSKeowb52Vq9hAJdeVOZ8nLAy8bXWXgcQrnNAXYWIPP/WeU5qn2iWRAVTZq2IXf5dQ7AWBV0eD33iovEuDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T07:03:23.156080Z"},"content_sha256":"f855611570a5022e66c26ae2c4bac56f2a96ec098dfd568cb52b7bc9861e95bf","schema_version":"1.0","event_id":"sha256:f855611570a5022e66c26ae2c4bac56f2a96ec098dfd568cb52b7bc9861e95bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/bundle.json","state_url":"https://pith.science/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/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":"2026-05-22T07:03:23Z","links":{"resolver":"https://pith.science/pith/NANGRC2XSZZQTKBNUIUWVB3A3H","bundle":"https://pith.science/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/bundle.json","state":"https://pith.science/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NANGRC2XSZZQTKBNUIUWVB3A3H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NANGRC2XSZZQTKBNUIUWVB3A3H","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":"b0e3d42a9c7105eac798697ea4404bb8ecce839eb4bbab7d7c9bc0330240d60a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-10T15:59:52Z","title_canon_sha256":"dafc0afb17b88be74df9083e4d319aa959903783d52b28e1e61832296252f41f"},"schema_version":"1.0","source":{"id":"1412.3349","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3349","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3349v2","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3349","created_at":"2026-05-18T01:12:01Z"},{"alias_kind":"pith_short_12","alias_value":"NANGRC2XSZZQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NANGRC2XSZZQTKBN","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NANGRC2X","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:f855611570a5022e66c26ae2c4bac56f2a96ec098dfd568cb52b7bc9861e95bf","target":"graph","created_at":"2026-05-18T01:12:01Z","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":"We consider a stochastic model of infection spread on the complete graph on $N$ vertices incorporating dynamic partnerships, which we assume to be monogamous. This can be seen as a variation on the contact process in which some form of edge dynamics determines the set of contacts at each moment in time. We identify a basic reproduction number $R_0$ with the property that if $R_0<1$ the infection dies out by time $O(\\log N)$, while if $R_0>1$ the infection survives for an amount of time $e^{\\gamma N}$ for some $\\gamma>0$ and hovers around a uniquely determined metastable proportion of infectiou","authors_text":"Eric Foxall, P. van den Driessche, Roderick Edwards","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-10T15:59:52Z","title":"Social contact processes and the partner model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3349","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":"sha256:00aa7dd21ea578226483a17b639cf854dc632a1076de3c226f12e3c26bb12d48","target":"record","created_at":"2026-05-18T01:12:01Z","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":"b0e3d42a9c7105eac798697ea4404bb8ecce839eb4bbab7d7c9bc0330240d60a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-10T15:59:52Z","title_canon_sha256":"dafc0afb17b88be74df9083e4d319aa959903783d52b28e1e61832296252f41f"},"schema_version":"1.0","source":{"id":"1412.3349","kind":"arxiv","version":2}},"canonical_sha256":"681a688b57967309a82da2296a8760d9d3cf32e991844e96330f1486daa293f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"681a688b57967309a82da2296a8760d9d3cf32e991844e96330f1486daa293f1","first_computed_at":"2026-05-18T01:12:01.900664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:01.900664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ITVN/zGBJjC1aT5NRLl8U0KDUWsAR6TdhAOd48zrsXei+i5/7ajZ8o05VMhstyOdxoOKGuPUkSP8Iqdv5kmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:01.900987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3349","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00aa7dd21ea578226483a17b639cf854dc632a1076de3c226f12e3c26bb12d48","sha256:f855611570a5022e66c26ae2c4bac56f2a96ec098dfd568cb52b7bc9861e95bf"],"state_sha256":"199000b9e00f4c060ba96484f0bbc3fadfeb2ae940e71fade2301beabfdf7a63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7sJsI/g6qDMGacBmyRR+M0dTFF9jr95NnnW/c+gXgDDtnGNT88EGe2Y9hpYoUUxbLRbOuVHgnL4N8x55AHfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T07:03:23.159790Z","bundle_sha256":"d0e175d45afcb9f45a1fa258e24c2234cc9ce2da552ecea28101197c9f795109"}}