{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WNSX2ICXHI5CQ3KQGKA25Q3ZUS","short_pith_number":"pith:WNSX2ICX","canonical_record":{"source":{"id":"1309.7983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-30T19:45:34Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"dadb11ccd8f6102d8e4fa7362ea8442b220d6625e470de7e1c1d5ab1e4049587","abstract_canon_sha256":"5ad99a67b9bbe0da61da99e169d769f5bae9a98173ee6040782da89abd20d235"},"schema_version":"1.0"},"canonical_sha256":"b3657d20573a3a286d503281aec379a4b69e21bf9bc916f4a390b1a2a3af66a5","source":{"kind":"arxiv","id":"1309.7983","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7983","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7983v2","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7983","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"WNSX2ICXHI5C","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WNSX2ICXHI5CQ3KQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WNSX2ICX","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WNSX2ICXHI5CQ3KQGKA25Q3ZUS","target":"record","payload":{"canonical_record":{"source":{"id":"1309.7983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-30T19:45:34Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"dadb11ccd8f6102d8e4fa7362ea8442b220d6625e470de7e1c1d5ab1e4049587","abstract_canon_sha256":"5ad99a67b9bbe0da61da99e169d769f5bae9a98173ee6040782da89abd20d235"},"schema_version":"1.0"},"canonical_sha256":"b3657d20573a3a286d503281aec379a4b69e21bf9bc916f4a390b1a2a3af66a5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:59:34.475055Z","signature_b64":"9vaAa4QYUl7ZfqsSZNXS5nuf/az8XMHxvi+B7W2uRu6rneOvIRRNPWgPV9d6ZnTFnCPWb5bAvtMjYIYJQWLJCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3657d20573a3a286d503281aec379a4b69e21bf9bc916f4a390b1a2a3af66a5","last_reissued_at":"2026-05-18T02:59:34.474260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:59:34.474260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.7983","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":"2026-05-18T02:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dA/sO5NsAXA4rKVJAg/J9ylzzRviQkqVnvd/mvvj/lxqiGOuZ0Hu/qUR3wAk8GZoMh84fdchFYXCvWcoB76TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:29:45.770415Z"},"content_sha256":"43dd0a07a5b4f391aaf5f2eea29fc48b846400101c0f47c690a717365b5a6c28","schema_version":"1.0","event_id":"sha256:43dd0a07a5b4f391aaf5f2eea29fc48b846400101c0f47c690a717365b5a6c28"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WNSX2ICXHI5CQ3KQGKA25Q3ZUS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coexistence of phases and the observability of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Antoine Allard, Jean-Gabriel Young, Laurent H\\'ebert-Dufresne, Louis J. Dub\\'e","submitted_at":"2013-09-30T19:45:34Z","abstract_excerpt":"In a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-L percolation---where the state of nodes up to a distance L of monitored nodes is known---can be mapped unto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a non-trivial coexistence of an obser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7983","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":"2026-05-18T02:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lLo8ceeLQFGvOvIaOTsvrgC3P7/SMEkx8Q6CIxSWMUQtD4dZgwdhcj4DDwcsJzqFCLs8ryaqkOEbkprrVXvdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:29:45.771133Z"},"content_sha256":"9fd68e2da3792eea4b9372247c86374485ff3293025e2ad3e8eb88b6202f398c","schema_version":"1.0","event_id":"sha256:9fd68e2da3792eea4b9372247c86374485ff3293025e2ad3e8eb88b6202f398c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/bundle.json","state_url":"https://pith.science/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/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":"2026-05-29T18:29:45Z","links":{"resolver":"https://pith.science/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS","bundle":"https://pith.science/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/bundle.json","state":"https://pith.science/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNSX2ICXHI5CQ3KQGKA25Q3ZUS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WNSX2ICXHI5CQ3KQGKA25Q3ZUS","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":"5ad99a67b9bbe0da61da99e169d769f5bae9a98173ee6040782da89abd20d235","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-30T19:45:34Z","title_canon_sha256":"dadb11ccd8f6102d8e4fa7362ea8442b220d6625e470de7e1c1d5ab1e4049587"},"schema_version":"1.0","source":{"id":"1309.7983","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7983","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7983v2","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7983","created_at":"2026-05-18T02:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"WNSX2ICXHI5C","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WNSX2ICXHI5CQ3KQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WNSX2ICX","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:9fd68e2da3792eea4b9372247c86374485ff3293025e2ad3e8eb88b6202f398c","target":"graph","created_at":"2026-05-18T02:59:34Z","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 a recent Letter, Yang et al. [Phys. Rev. Lett. 109, 258701 (2012)] introduced the concept of observability transitions: the percolation-like emergence of a macroscopic observable component in graphs in which the state of a fraction of the nodes, and of their first neighbors, is monitored. We show how their concept of depth-L percolation---where the state of nodes up to a distance L of monitored nodes is known---can be mapped unto multitype random graphs, and use this mapping to exactly solve the observability problem for arbitrary L. We then demonstrate a non-trivial coexistence of an obser","authors_text":"Antoine Allard, Jean-Gabriel Young, Laurent H\\'ebert-Dufresne, Louis J. Dub\\'e","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-30T19:45:34Z","title":"Coexistence of phases and the observability of random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7983","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":"sha256:43dd0a07a5b4f391aaf5f2eea29fc48b846400101c0f47c690a717365b5a6c28","target":"record","created_at":"2026-05-18T02:59:34Z","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":"5ad99a67b9bbe0da61da99e169d769f5bae9a98173ee6040782da89abd20d235","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-09-30T19:45:34Z","title_canon_sha256":"dadb11ccd8f6102d8e4fa7362ea8442b220d6625e470de7e1c1d5ab1e4049587"},"schema_version":"1.0","source":{"id":"1309.7983","kind":"arxiv","version":2}},"canonical_sha256":"b3657d20573a3a286d503281aec379a4b69e21bf9bc916f4a390b1a2a3af66a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3657d20573a3a286d503281aec379a4b69e21bf9bc916f4a390b1a2a3af66a5","first_computed_at":"2026-05-18T02:59:34.474260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:59:34.474260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vaAa4QYUl7ZfqsSZNXS5nuf/az8XMHxvi+B7W2uRu6rneOvIRRNPWgPV9d6ZnTFnCPWb5bAvtMjYIYJQWLJCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:59:34.475055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7983","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43dd0a07a5b4f391aaf5f2eea29fc48b846400101c0f47c690a717365b5a6c28","sha256:9fd68e2da3792eea4b9372247c86374485ff3293025e2ad3e8eb88b6202f398c"],"state_sha256":"76c467976cdc64399451b4f1fc02827a026906eaa0949e99174fee8269ce090d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rvVNHmCMyp6Flw/3Qofd4W0kENP+vamUAqlRV3sS0BG9+3qt+/YYcypmPUUXQv5z9lDOkKE6bl/lAwjNyY6aBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:29:45.774907Z","bundle_sha256":"80fdd1e3fc9467fa1ce2ab1c507c74958b829b5432b7615722e9edc87108b0a7"}}