{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:L54GUGXMXKNNRMAZ7RVKOFA5O7","short_pith_number":"pith:L54GUGXM","canonical_record":{"source":{"id":"1411.1726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-06T20:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"1aa91ca8151dbf4d876e0babe15fc29815ead11b738679e584f718344f55429d","abstract_canon_sha256":"4174afc3171c94f1373d2d5a1a5a8ac2acca222218a87cdcd159df4ff4a2d4ef"},"schema_version":"1.0"},"canonical_sha256":"5f786a1aecba9ad8b019fc6aa7141d77e213dc233986de661560fee845d6905a","source":{"kind":"arxiv","id":"1411.1726","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1726","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1726v2","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1726","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"L54GUGXMXKNN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L54GUGXMXKNNRMAZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L54GUGXM","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:L54GUGXMXKNNRMAZ7RVKOFA5O7","target":"record","payload":{"canonical_record":{"source":{"id":"1411.1726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-06T20:11:25Z","cross_cats_sorted":[],"title_canon_sha256":"1aa91ca8151dbf4d876e0babe15fc29815ead11b738679e584f718344f55429d","abstract_canon_sha256":"4174afc3171c94f1373d2d5a1a5a8ac2acca222218a87cdcd159df4ff4a2d4ef"},"schema_version":"1.0"},"canonical_sha256":"5f786a1aecba9ad8b019fc6aa7141d77e213dc233986de661560fee845d6905a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:56.858275Z","signature_b64":"PVQDQpp4Eb2nsrQsAqwbmB+9mdN763L4oet+of9xOvANICPGiDjpdLFGD/AKTmDvrH0QgWyF9evX34mHyzhZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f786a1aecba9ad8b019fc6aa7141d77e213dc233986de661560fee845d6905a","last_reissued_at":"2026-05-18T02:27:56.857709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:56.857709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.1726","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WiPmOnVUhMZRpEUd6MKogPK2hfFnOAMPi/2A1AbBTG65Z3zmfXewlxfoGqKh6nzuyKqpwE0Rd6q45LdlXsQMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:41:26.619222Z"},"content_sha256":"775cd8cf59fab414d585c883431f2c5be47b3c4d32935ff107d04b2433fb45df","schema_version":"1.0","event_id":"sha256:775cd8cf59fab414d585c883431f2c5be47b3c4d32935ff107d04b2433fb45df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:L54GUGXMXKNNRMAZ7RVKOFA5O7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The large connectivity limit of bootstrap percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Giorgio Parisi, Mauro Sellitto","submitted_at":"2014-11-06T20:11:25Z","abstract_excerpt":"Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation probability of a site depends on the state of its neighbours through a certain threshold parameter. In this paper we investigate the phase behavior of the bootstrap percolation on the regular random graph in the limit in which the threshold parameter and lattice connectivity become both increasingly large while their ratio $\\alpha$ is held constant. We find t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1726","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":"2026-05-18T02:27:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vA/KnypdhguqlnpGYZ2dqIc4fZx3U7bUc11jMHfJ/GRL4sIBdXgjw/OG3tStUVds7L9JLGu+yIfEHEeYW8yXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:41:26.619650Z"},"content_sha256":"e66b54a412371e26f035fea0f504c70a46c8af1114b3fc04780ebd8554dfbff9","schema_version":"1.0","event_id":"sha256:e66b54a412371e26f035fea0f504c70a46c8af1114b3fc04780ebd8554dfbff9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/bundle.json","state_url":"https://pith.science/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/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":"2026-05-31T09:41:26Z","links":{"resolver":"https://pith.science/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7","bundle":"https://pith.science/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/bundle.json","state":"https://pith.science/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L54GUGXMXKNNRMAZ7RVKOFA5O7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:L54GUGXMXKNNRMAZ7RVKOFA5O7","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":"4174afc3171c94f1373d2d5a1a5a8ac2acca222218a87cdcd159df4ff4a2d4ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-06T20:11:25Z","title_canon_sha256":"1aa91ca8151dbf4d876e0babe15fc29815ead11b738679e584f718344f55429d"},"schema_version":"1.0","source":{"id":"1411.1726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1726","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1726v2","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1726","created_at":"2026-05-18T02:27:56Z"},{"alias_kind":"pith_short_12","alias_value":"L54GUGXMXKNN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"L54GUGXMXKNNRMAZ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"L54GUGXM","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:e66b54a412371e26f035fea0f504c70a46c8af1114b3fc04780ebd8554dfbff9","target":"graph","created_at":"2026-05-18T02:27:56Z","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":"Bootstrap percolation provides an emblematic instance of phase behavior characterised by an abrupt transition with diverging critical fluctuations. This unusual hybrid situation generally occurs in particle systems in which the occupation probability of a site depends on the state of its neighbours through a certain threshold parameter. In this paper we investigate the phase behavior of the bootstrap percolation on the regular random graph in the limit in which the threshold parameter and lattice connectivity become both increasingly large while their ratio $\\alpha$ is held constant. We find t","authors_text":"Giorgio Parisi, Mauro Sellitto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-06T20:11:25Z","title":"The large connectivity limit of bootstrap percolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1726","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":"sha256:775cd8cf59fab414d585c883431f2c5be47b3c4d32935ff107d04b2433fb45df","target":"record","created_at":"2026-05-18T02:27:56Z","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":"4174afc3171c94f1373d2d5a1a5a8ac2acca222218a87cdcd159df4ff4a2d4ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-11-06T20:11:25Z","title_canon_sha256":"1aa91ca8151dbf4d876e0babe15fc29815ead11b738679e584f718344f55429d"},"schema_version":"1.0","source":{"id":"1411.1726","kind":"arxiv","version":2}},"canonical_sha256":"5f786a1aecba9ad8b019fc6aa7141d77e213dc233986de661560fee845d6905a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f786a1aecba9ad8b019fc6aa7141d77e213dc233986de661560fee845d6905a","first_computed_at":"2026-05-18T02:27:56.857709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:56.857709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVQDQpp4Eb2nsrQsAqwbmB+9mdN763L4oet+of9xOvANICPGiDjpdLFGD/AKTmDvrH0QgWyF9evX34mHyzhZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:56.858275Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:775cd8cf59fab414d585c883431f2c5be47b3c4d32935ff107d04b2433fb45df","sha256:e66b54a412371e26f035fea0f504c70a46c8af1114b3fc04780ebd8554dfbff9"],"state_sha256":"7a10841c37ba48c08e68c773ce65fb9ad62beb0f02d32d4f041fa64f738d2d36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DUj0oMK0XRwOjuk4tun72KlohKhByfDhiIBbpO+0xFvHiCrxWyTZruiUoCJFzAAaeeBevC7gZ7+H/7gcJAZ8Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:41:26.622612Z","bundle_sha256":"c62009643bd93856755b9d05bada10aa6a71af2cc271dc0b2e6e251aa569c9b0"}}