{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6HFUQQF3THGL6N5ZUVEZLPRKAY","short_pith_number":"pith:6HFUQQF3","canonical_record":{"source":{"id":"1605.06322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-05-20T12:28:49Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"ab9ebb47664e2ae415642a431b57c70931d17e13a515c3b04a931f3a9a63ba6d","abstract_canon_sha256":"2d09d25e3441c9a7312df606306ece1f85c52f9e37816546ba9703ec3e641275"},"schema_version":"1.0"},"canonical_sha256":"f1cb4840bb99ccbf37b9a54995be2a062a0af49747905c1f96e2e45b2785869d","source":{"kind":"arxiv","id":"1605.06322","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06322","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06322v1","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06322","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"6HFUQQF3THGL","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6HFUQQF3THGL6N5Z","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6HFUQQF3","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6HFUQQF3THGL6N5ZUVEZLPRKAY","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06322","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-05-20T12:28:49Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"ab9ebb47664e2ae415642a431b57c70931d17e13a515c3b04a931f3a9a63ba6d","abstract_canon_sha256":"2d09d25e3441c9a7312df606306ece1f85c52f9e37816546ba9703ec3e641275"},"schema_version":"1.0"},"canonical_sha256":"f1cb4840bb99ccbf37b9a54995be2a062a0af49747905c1f96e2e45b2785869d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:19.252919Z","signature_b64":"DOfn+vAEmg0nO3kt6Bmhqqkf0EZ5jjS+To8cD84gVNw3pN2A17arRcJzRKCOdiCsqEgNJNCEZDSC9K/ZXd0pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1cb4840bb99ccbf37b9a54995be2a062a0af49747905c1f96e2e45b2785869d","last_reissued_at":"2026-05-18T01:14:19.252360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:19.252360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06322","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":"2026-05-18T01:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PjNdwapxriZy0vakwQF7on3mv3lyYDwV7e6H3ndSNxSdgeO5txiQWLxsXL8CQMfHqbJyEZwRmFOlE+rU+BosBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:53:29.163782Z"},"content_sha256":"1cfa5984df849c38f84f926e0103e9174eb6ef95ebe42c5c3a4174e46e1b1598","schema_version":"1.0","event_id":"sha256:1cfa5984df849c38f84f926e0103e9174eb6ef95ebe42c5c3a4174e46e1b1598"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6HFUQQF3THGL6N5ZUVEZLPRKAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic analysis of threshold models for social networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cs.SI","authors_text":"Andrea Garulli, Antonio Giannitrapani","submitted_at":"2016-05-20T12:28:49Z","abstract_excerpt":"A class of dynamic threshold models is proposed, for describing the upset of collective actions in social networks. The agents of the network have to decide whether to undertake a certain action or not. They make their decision by comparing the activity level of their neighbors with a time-varying threshold, evolving according to a time-invariant opinion dynamic model. Key features of the model are a parameter representing the degree of self-confidence of the agents, and the mechanism adopted by the agents to evaluate the activity level of their neighbors. The case in which a radical agent, in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06322","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":"2026-05-18T01:14:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2H+F4m6ZIl+hp4l7G4OVvLkojQCLUxpLTVjVPIAwjzozNjW93waIG6SFI38uqjFqolRdX3Ole1XA/f8zGWfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:53:29.164411Z"},"content_sha256":"314f9ff85b16fcbd018650b67ab48924887e200c5db8ddd23b11702325603f76","schema_version":"1.0","event_id":"sha256:314f9ff85b16fcbd018650b67ab48924887e200c5db8ddd23b11702325603f76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/bundle.json","state_url":"https://pith.science/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/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":"2026-06-07T17:53:29Z","links":{"resolver":"https://pith.science/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY","bundle":"https://pith.science/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/bundle.json","state":"https://pith.science/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6HFUQQF3THGL6N5ZUVEZLPRKAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6HFUQQF3THGL6N5ZUVEZLPRKAY","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":"2d09d25e3441c9a7312df606306ece1f85c52f9e37816546ba9703ec3e641275","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-05-20T12:28:49Z","title_canon_sha256":"ab9ebb47664e2ae415642a431b57c70931d17e13a515c3b04a931f3a9a63ba6d"},"schema_version":"1.0","source":{"id":"1605.06322","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06322","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06322v1","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06322","created_at":"2026-05-18T01:14:19Z"},{"alias_kind":"pith_short_12","alias_value":"6HFUQQF3THGL","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6HFUQQF3THGL6N5Z","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6HFUQQF3","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:314f9ff85b16fcbd018650b67ab48924887e200c5db8ddd23b11702325603f76","target":"graph","created_at":"2026-05-18T01:14:19Z","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":"A class of dynamic threshold models is proposed, for describing the upset of collective actions in social networks. The agents of the network have to decide whether to undertake a certain action or not. They make their decision by comparing the activity level of their neighbors with a time-varying threshold, evolving according to a time-invariant opinion dynamic model. Key features of the model are a parameter representing the degree of self-confidence of the agents, and the mechanism adopted by the agents to evaluate the activity level of their neighbors. The case in which a radical agent, in","authors_text":"Andrea Garulli, Antonio Giannitrapani","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-05-20T12:28:49Z","title":"Asymptotic analysis of threshold models for social networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06322","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":"sha256:1cfa5984df849c38f84f926e0103e9174eb6ef95ebe42c5c3a4174e46e1b1598","target":"record","created_at":"2026-05-18T01:14:19Z","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":"2d09d25e3441c9a7312df606306ece1f85c52f9e37816546ba9703ec3e641275","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2016-05-20T12:28:49Z","title_canon_sha256":"ab9ebb47664e2ae415642a431b57c70931d17e13a515c3b04a931f3a9a63ba6d"},"schema_version":"1.0","source":{"id":"1605.06322","kind":"arxiv","version":1}},"canonical_sha256":"f1cb4840bb99ccbf37b9a54995be2a062a0af49747905c1f96e2e45b2785869d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1cb4840bb99ccbf37b9a54995be2a062a0af49747905c1f96e2e45b2785869d","first_computed_at":"2026-05-18T01:14:19.252360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:19.252360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DOfn+vAEmg0nO3kt6Bmhqqkf0EZ5jjS+To8cD84gVNw3pN2A17arRcJzRKCOdiCsqEgNJNCEZDSC9K/ZXd0pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:19.252919Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06322","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cfa5984df849c38f84f926e0103e9174eb6ef95ebe42c5c3a4174e46e1b1598","sha256:314f9ff85b16fcbd018650b67ab48924887e200c5db8ddd23b11702325603f76"],"state_sha256":"77bd2d68886fecbc7429cdafca5989010ea72ba2114d5d35e3391bde69a67432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cXTi9bS9ycsO9dnICD8Z4ZeMiusgckySD+sOR9mkJQnEqPnZpJcT2nKiKsTGqQrwhRTZTd6TrcOHFB1nVYoYCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:53:29.168180Z","bundle_sha256":"004214bb5f64cf6a3ecfdf0af31456fda0a6873c0974341c7bb0309f5eb390d7"}}