{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:C6TFV7WRS5NM2JIR6LT6SZRQAP","short_pith_number":"pith:C6TFV7WR","canonical_record":{"source":{"id":"1502.04264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-02-15T01:02:01Z","cross_cats_sorted":["cs.MA","math.OC","math.PR"],"title_canon_sha256":"1d78dfd420fa822051a414acf038a70f016556bcad4c1b32a4ff68bc7812de85","abstract_canon_sha256":"d70dbe9b4169e24a74ffccf88d857b98e3aa55a676eb8bce7f85b8e77fb55c89"},"schema_version":"1.0"},"canonical_sha256":"17a65afed1975acd2511f2e7e9663003dd37b7dace62d62295cde1e405c7a33e","source":{"kind":"arxiv","id":"1502.04264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04264","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04264v1","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04264","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"C6TFV7WRS5NM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C6TFV7WRS5NM2JIR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C6TFV7WR","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:C6TFV7WRS5NM2JIR6LT6SZRQAP","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-02-15T01:02:01Z","cross_cats_sorted":["cs.MA","math.OC","math.PR"],"title_canon_sha256":"1d78dfd420fa822051a414acf038a70f016556bcad4c1b32a4ff68bc7812de85","abstract_canon_sha256":"d70dbe9b4169e24a74ffccf88d857b98e3aa55a676eb8bce7f85b8e77fb55c89"},"schema_version":"1.0"},"canonical_sha256":"17a65afed1975acd2511f2e7e9663003dd37b7dace62d62295cde1e405c7a33e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:00.099923Z","signature_b64":"LtSAqFLVBPqcNL7HrpVNsclHsT9vGzlgQTout791K2r/mXMU4jxctE6JGUX3aeb0tWEupphN76D44qiY20aPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17a65afed1975acd2511f2e7e9663003dd37b7dace62d62295cde1e405c7a33e","last_reissued_at":"2026-05-18T02:27:00.099257Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:00.099257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04264","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":"2026-05-18T02:27:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qD9NDuqBWKvPdn5TPts63ICNMQmJe8gHenbIj/lFDTlOS5Muld2eUYxyLEdkExo9dKSttEZeDJbyfP4EdZE/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:20:24.666080Z"},"content_sha256":"ae65145a173863291860017341cd17fb64f9b72c82a2352991e3c0c59c784148","schema_version":"1.0","event_id":"sha256:ae65145a173863291860017341cd17fb64f9b72c82a2352991e3c0c59c784148"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:C6TFV7WRS5NM2JIR6LT6SZRQAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The robustness of democratic consensus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.MA","math.OC","math.PR"],"primary_cat":"cs.SY","authors_text":"Fabio Fagnani, Jean-Charles Delvenne","submitted_at":"2015-02-15T01:02:01Z","abstract_excerpt":"In linear models of consensus dynamics, the state of the various agents converges to a value which is a convex combination of the agents' initial states. We call it democratic if in the large scale limit (number of agents going to infinity) the vector of convex weights converges to 0 uniformly.\n  Democracy is a relevant property which naturally shows up when we deal with opinion dynamic models and cooperative algorithms such as consensus over a network: it says that each agent's measure/opinion is going to play a negligeable role in the asymptotic behavior of the global system. It can be seen "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04264","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":"2026-05-18T02:27:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+Rbeo+xF/Ma7UtwxMu6kXaPD9a+jS4DRlI13z9X8fHkfKnaueO15kOUCkX7wd7LleKiR5qGYZaZildfFazsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:20:24.666453Z"},"content_sha256":"9bf1b3962e22d32291e4aa4c16bdf93eb0b7072f39448c1d4c61c0ce8b9ff5a6","schema_version":"1.0","event_id":"sha256:9bf1b3962e22d32291e4aa4c16bdf93eb0b7072f39448c1d4c61c0ce8b9ff5a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/bundle.json","state_url":"https://pith.science/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/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":"2026-06-02T16:20:24Z","links":{"resolver":"https://pith.science/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP","bundle":"https://pith.science/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/bundle.json","state":"https://pith.science/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C6TFV7WRS5NM2JIR6LT6SZRQAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:C6TFV7WRS5NM2JIR6LT6SZRQAP","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":"d70dbe9b4169e24a74ffccf88d857b98e3aa55a676eb8bce7f85b8e77fb55c89","cross_cats_sorted":["cs.MA","math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-02-15T01:02:01Z","title_canon_sha256":"1d78dfd420fa822051a414acf038a70f016556bcad4c1b32a4ff68bc7812de85"},"schema_version":"1.0","source":{"id":"1502.04264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04264","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04264v1","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04264","created_at":"2026-05-18T02:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"C6TFV7WRS5NM","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"C6TFV7WRS5NM2JIR","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"C6TFV7WR","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:9bf1b3962e22d32291e4aa4c16bdf93eb0b7072f39448c1d4c61c0ce8b9ff5a6","target":"graph","created_at":"2026-05-18T02:27:00Z","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":"In linear models of consensus dynamics, the state of the various agents converges to a value which is a convex combination of the agents' initial states. We call it democratic if in the large scale limit (number of agents going to infinity) the vector of convex weights converges to 0 uniformly.\n  Democracy is a relevant property which naturally shows up when we deal with opinion dynamic models and cooperative algorithms such as consensus over a network: it says that each agent's measure/opinion is going to play a negligeable role in the asymptotic behavior of the global system. It can be seen ","authors_text":"Fabio Fagnani, Jean-Charles Delvenne","cross_cats":["cs.MA","math.OC","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-02-15T01:02:01Z","title":"The robustness of democratic consensus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04264","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:ae65145a173863291860017341cd17fb64f9b72c82a2352991e3c0c59c784148","target":"record","created_at":"2026-05-18T02:27:00Z","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":"d70dbe9b4169e24a74ffccf88d857b98e3aa55a676eb8bce7f85b8e77fb55c89","cross_cats_sorted":["cs.MA","math.OC","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-02-15T01:02:01Z","title_canon_sha256":"1d78dfd420fa822051a414acf038a70f016556bcad4c1b32a4ff68bc7812de85"},"schema_version":"1.0","source":{"id":"1502.04264","kind":"arxiv","version":1}},"canonical_sha256":"17a65afed1975acd2511f2e7e9663003dd37b7dace62d62295cde1e405c7a33e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17a65afed1975acd2511f2e7e9663003dd37b7dace62d62295cde1e405c7a33e","first_computed_at":"2026-05-18T02:27:00.099257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:00.099257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LtSAqFLVBPqcNL7HrpVNsclHsT9vGzlgQTout791K2r/mXMU4jxctE6JGUX3aeb0tWEupphN76D44qiY20aPAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:00.099923Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae65145a173863291860017341cd17fb64f9b72c82a2352991e3c0c59c784148","sha256:9bf1b3962e22d32291e4aa4c16bdf93eb0b7072f39448c1d4c61c0ce8b9ff5a6"],"state_sha256":"1f3062b18cbec864858514bf689a02b30848d51fbbaa925bb49f2f30044db8d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KhbK7IKbuEmNPkDtLQ6wE5Oxr6P/Jus8uKNig0SVQ+U4icY3/84l28FWR22kse9TpULPfazW4TbgubL5AP9VDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:20:24.668497Z","bundle_sha256":"c1ac955f8c4b518a06a7f9015ddc1e6e534923b3c6b7ff96a468d5460b5d2795"}}