{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LOEANYHEQNCXODINO67ON3CZBA","short_pith_number":"pith:LOEANYHE","canonical_record":{"source":{"id":"1509.08572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-29T02:58:55Z","cross_cats_sorted":["cs.MA","math.OC"],"title_canon_sha256":"9e07a555b4f3a6e46db55a1a47f586aa7205b8ce21dc74c484df8598818926c7","abstract_canon_sha256":"5abfa9300526f148f514adf77b65c94f97c4d42dc2564db9d96fb3ed17c7d84c"},"schema_version":"1.0"},"canonical_sha256":"5b8806e0e48345770d0d77bee6ec5908007cfc47c4838bc4d4dfe1d7005ddfa1","source":{"kind":"arxiv","id":"1509.08572","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08572","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08572v2","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08572","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"LOEANYHEQNCX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOEANYHEQNCXODIN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOEANYHE","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LOEANYHEQNCXODINO67ON3CZBA","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-29T02:58:55Z","cross_cats_sorted":["cs.MA","math.OC"],"title_canon_sha256":"9e07a555b4f3a6e46db55a1a47f586aa7205b8ce21dc74c484df8598818926c7","abstract_canon_sha256":"5abfa9300526f148f514adf77b65c94f97c4d42dc2564db9d96fb3ed17c7d84c"},"schema_version":"1.0"},"canonical_sha256":"5b8806e0e48345770d0d77bee6ec5908007cfc47c4838bc4d4dfe1d7005ddfa1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:40.612570Z","signature_b64":"8xX1rgK/8XRwE7tWFXJecL3mvEut2+l77zRVSwoBC+GXB8NyouMPie4heeAyjFHUbrKv1o5Dpax6uJ/Hz9h5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b8806e0e48345770d0d77bee6ec5908007cfc47c4838bc4d4dfe1d7005ddfa1","last_reissued_at":"2026-05-18T01:19:40.611950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:40.611950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08572","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":"2026-05-18T01:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOjqB5GsxGcZ6GvTFUjijZzhzlzUhRtfd9kcTs1NT1Jsmmj2qACgL7k+mJ6yScDkoCBuGbhAMxe+ORwzxHICAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:39:49.549373Z"},"content_sha256":"4d0f29d5aa72782a3b130ccdf6afd3421865a1a8244f37e413d4b38e5f43df59","schema_version":"1.0","event_id":"sha256:4d0f29d5aa72782a3b130ccdf6afd3421865a1a8244f37e413d4b38e5f43df59"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LOEANYHEQNCXODINO67ON3CZBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From local averaging to emergent global behaviors: the fundamental role of network interconnections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","math.OC"],"primary_cat":"cs.SY","authors_text":"Fabio Fagnani, Giacomo Como","submitted_at":"2015-09-29T02:58:55Z","abstract_excerpt":"Distributed averaging is one of the simplest and most studied network dynamics. Its applications range from cooperative inference in sensor networks, to robot formation, to opinion dynamics. A number of fundamental results and examples scattered through the literature are gathered here and originally presented, emphasizing the deep interplay between the network interconnection structure and the emergent global behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08572","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":"2026-05-18T01:19:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yc0l2Pvjix0jFuDCG2OXsD8MGEJD4FcMYLf8p01aL8874QxW4OLUG4naAM1Zai3+ZwPR8gfCAzQAqryI/uZ3Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T03:39:49.549721Z"},"content_sha256":"88615c177a9c7731d90cdd060ccd8a74c5d75389bc85faa5bcc456e4d89b3b8b","schema_version":"1.0","event_id":"sha256:88615c177a9c7731d90cdd060ccd8a74c5d75389bc85faa5bcc456e4d89b3b8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOEANYHEQNCXODINO67ON3CZBA/bundle.json","state_url":"https://pith.science/pith/LOEANYHEQNCXODINO67ON3CZBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOEANYHEQNCXODINO67ON3CZBA/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":"2026-06-03T03:39:49Z","links":{"resolver":"https://pith.science/pith/LOEANYHEQNCXODINO67ON3CZBA","bundle":"https://pith.science/pith/LOEANYHEQNCXODINO67ON3CZBA/bundle.json","state":"https://pith.science/pith/LOEANYHEQNCXODINO67ON3CZBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOEANYHEQNCXODINO67ON3CZBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LOEANYHEQNCXODINO67ON3CZBA","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":"5abfa9300526f148f514adf77b65c94f97c4d42dc2564db9d96fb3ed17c7d84c","cross_cats_sorted":["cs.MA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-29T02:58:55Z","title_canon_sha256":"9e07a555b4f3a6e46db55a1a47f586aa7205b8ce21dc74c484df8598818926c7"},"schema_version":"1.0","source":{"id":"1509.08572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08572","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08572v2","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08572","created_at":"2026-05-18T01:19:40Z"},{"alias_kind":"pith_short_12","alias_value":"LOEANYHEQNCX","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOEANYHEQNCXODIN","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOEANYHE","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:88615c177a9c7731d90cdd060ccd8a74c5d75389bc85faa5bcc456e4d89b3b8b","target":"graph","created_at":"2026-05-18T01:19:40Z","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":"Distributed averaging is one of the simplest and most studied network dynamics. Its applications range from cooperative inference in sensor networks, to robot formation, to opinion dynamics. A number of fundamental results and examples scattered through the literature are gathered here and originally presented, emphasizing the deep interplay between the network interconnection structure and the emergent global behavior.","authors_text":"Fabio Fagnani, Giacomo Como","cross_cats":["cs.MA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-29T02:58:55Z","title":"From local averaging to emergent global behaviors: the fundamental role of network interconnections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08572","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":"sha256:4d0f29d5aa72782a3b130ccdf6afd3421865a1a8244f37e413d4b38e5f43df59","target":"record","created_at":"2026-05-18T01:19:40Z","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":"5abfa9300526f148f514adf77b65c94f97c4d42dc2564db9d96fb3ed17c7d84c","cross_cats_sorted":["cs.MA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-29T02:58:55Z","title_canon_sha256":"9e07a555b4f3a6e46db55a1a47f586aa7205b8ce21dc74c484df8598818926c7"},"schema_version":"1.0","source":{"id":"1509.08572","kind":"arxiv","version":2}},"canonical_sha256":"5b8806e0e48345770d0d77bee6ec5908007cfc47c4838bc4d4dfe1d7005ddfa1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b8806e0e48345770d0d77bee6ec5908007cfc47c4838bc4d4dfe1d7005ddfa1","first_computed_at":"2026-05-18T01:19:40.611950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:40.611950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8xX1rgK/8XRwE7tWFXJecL3mvEut2+l77zRVSwoBC+GXB8NyouMPie4heeAyjFHUbrKv1o5Dpax6uJ/Hz9h5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:40.612570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d0f29d5aa72782a3b130ccdf6afd3421865a1a8244f37e413d4b38e5f43df59","sha256:88615c177a9c7731d90cdd060ccd8a74c5d75389bc85faa5bcc456e4d89b3b8b"],"state_sha256":"656512a4efc368542e9cd71272a2839a334cc19eb56ded3dc86109395314c2e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MDK9c0WWd/vDUH69YmqUmxJhAA+cNK1sVZxwy3fitTyQ3wQiOmsUyeWk8mBnkkvYHFYKkWQTgrriHALJ06JBCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T03:39:49.551644Z","bundle_sha256":"fbffad34120624c5424c49c44596f45f25d60f4aff58440b8410611e3d9fdfa4"}}