{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XWSN74RUQL7J63RAFBB7CKDLWQ","short_pith_number":"pith:XWSN74RU","canonical_record":{"source":{"id":"1405.6160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-23T18:27:27Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"d19047ced259e42afd2f8274ca4bfc7b8bfc4c4143c411d67b42e047b3609949","abstract_canon_sha256":"0594287ae62f6e0f0093e4b3980a80836033b33018c1d32b4a435d5c9f8e7b39"},"schema_version":"1.0"},"canonical_sha256":"bda4dff23482fe9f6e202843f1286bb42d2170f501d825a50f01f587e249d470","source":{"kind":"arxiv","id":"1405.6160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6160","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6160v1","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6160","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"pith_short_12","alias_value":"XWSN74RUQL7J","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XWSN74RUQL7J63RA","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XWSN74RU","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XWSN74RUQL7J63RAFBB7CKDLWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-23T18:27:27Z","cross_cats_sorted":["math-ph","math.CO","math.MP"],"title_canon_sha256":"d19047ced259e42afd2f8274ca4bfc7b8bfc4c4143c411d67b42e047b3609949","abstract_canon_sha256":"0594287ae62f6e0f0093e4b3980a80836033b33018c1d32b4a435d5c9f8e7b39"},"schema_version":"1.0"},"canonical_sha256":"bda4dff23482fe9f6e202843f1286bb42d2170f501d825a50f01f587e249d470","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:13.947424Z","signature_b64":"t6vU7SMimGTsUBhyv1OalyT40n9EJEz7Vho0cAR67Fy2E94ryKUxID+ZsjqE1p8GOQRT/T44vDpE+tXpHCvHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bda4dff23482fe9f6e202843f1286bb42d2170f501d825a50f01f587e249d470","last_reissued_at":"2026-05-18T02:51:13.946989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:13.946989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6160","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":"2026-05-18T02:51:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bHOyiEIi0LNBjXAziE5li9y/FpX7WjNs+M9UC6+Ac5PWkcgCMA6d1ZNj76cb3RCabndvvzhOM1AgrBniv10/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:00:30.260461Z"},"content_sha256":"26e537930b5e96351ae37e6121ad22641bb4a0a32e6a339d39adb79a9846a81c","schema_version":"1.0","event_id":"sha256:26e537930b5e96351ae37e6121ad22641bb4a0a32e6a339d39adb79a9846a81c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XWSN74RUQL7J63RAFBB7CKDLWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decay of Correlations for the Hardcore Model on the $d$-regular Random Graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Allan Sly, Nayantara Bhatnagar, Prasad Tetali","submitted_at":"2014-05-23T18:27:27Z","abstract_excerpt":"A key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs asymptotically until just below its condensation threshold, showing that it converges in probability locally in a strong sense to the free boundary condition Gibbs measure on the tree. As a consequence we show that the reconstruction threshold on the random graph, indicative of the onset of point to set spatial correlations, is equal to the reconstruction threshold on the $d$-regular tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6160","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":"2026-05-18T02:51:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uGj2ID9+zximovLEn6Qy8S9oabTPoJkRie40iUvk6xJDHNj9C6eZw8ZEh+DxQv+vJZRETtvDa+RsSLPZ7gr/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:00:30.260811Z"},"content_sha256":"78c8a30b8c0464da5f93fa2f4027027205346d7d76069faa281543007fa1f92f","schema_version":"1.0","event_id":"sha256:78c8a30b8c0464da5f93fa2f4027027205346d7d76069faa281543007fa1f92f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/bundle.json","state_url":"https://pith.science/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/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":"2026-06-09T16:00:30Z","links":{"resolver":"https://pith.science/pith/XWSN74RUQL7J63RAFBB7CKDLWQ","bundle":"https://pith.science/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/bundle.json","state":"https://pith.science/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWSN74RUQL7J63RAFBB7CKDLWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XWSN74RUQL7J63RAFBB7CKDLWQ","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":"0594287ae62f6e0f0093e4b3980a80836033b33018c1d32b4a435d5c9f8e7b39","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-23T18:27:27Z","title_canon_sha256":"d19047ced259e42afd2f8274ca4bfc7b8bfc4c4143c411d67b42e047b3609949"},"schema_version":"1.0","source":{"id":"1405.6160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6160","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6160v1","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6160","created_at":"2026-05-18T02:51:13Z"},{"alias_kind":"pith_short_12","alias_value":"XWSN74RUQL7J","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XWSN74RUQL7J63RA","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XWSN74RU","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:78c8a30b8c0464da5f93fa2f4027027205346d7d76069faa281543007fa1f92f","target":"graph","created_at":"2026-05-18T02:51:13Z","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 key insight from statistical physics about spin systems on random graphs is the central role played by Gibbs measures on trees. We determine the local weak limit of the hardcore model on random regular graphs asymptotically until just below its condensation threshold, showing that it converges in probability locally in a strong sense to the free boundary condition Gibbs measure on the tree. As a consequence we show that the reconstruction threshold on the random graph, indicative of the onset of point to set spatial correlations, is equal to the reconstruction threshold on the $d$-regular tr","authors_text":"Allan Sly, Nayantara Bhatnagar, Prasad Tetali","cross_cats":["math-ph","math.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-23T18:27:27Z","title":"Decay of Correlations for the Hardcore Model on the $d$-regular Random Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6160","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":"sha256:26e537930b5e96351ae37e6121ad22641bb4a0a32e6a339d39adb79a9846a81c","target":"record","created_at":"2026-05-18T02:51:13Z","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":"0594287ae62f6e0f0093e4b3980a80836033b33018c1d32b4a435d5c9f8e7b39","cross_cats_sorted":["math-ph","math.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-23T18:27:27Z","title_canon_sha256":"d19047ced259e42afd2f8274ca4bfc7b8bfc4c4143c411d67b42e047b3609949"},"schema_version":"1.0","source":{"id":"1405.6160","kind":"arxiv","version":1}},"canonical_sha256":"bda4dff23482fe9f6e202843f1286bb42d2170f501d825a50f01f587e249d470","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bda4dff23482fe9f6e202843f1286bb42d2170f501d825a50f01f587e249d470","first_computed_at":"2026-05-18T02:51:13.946989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:13.946989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t6vU7SMimGTsUBhyv1OalyT40n9EJEz7Vho0cAR67Fy2E94ryKUxID+ZsjqE1p8GOQRT/T44vDpE+tXpHCvHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:13.947424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26e537930b5e96351ae37e6121ad22641bb4a0a32e6a339d39adb79a9846a81c","sha256:78c8a30b8c0464da5f93fa2f4027027205346d7d76069faa281543007fa1f92f"],"state_sha256":"de2699581f2422e88d7b068ce1d50ede96a537cc48f1ed1166611fd57ebfb964"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rERJdnlFv+A5O6jNns+wiX6/8fz3ZtfqVFmuishtwkeihiqhudeunybQgvpP0ZvIrsnowSWf/JpKjEeE7ZscAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:00:30.262797Z","bundle_sha256":"024e8ee69c6368302a1f975fdf50f5224c4445aeabbf599f7e53caac334bda26"}}