{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WRNBL6TAODOSCCMI733EU6WWBC","short_pith_number":"pith:WRNBL6TA","canonical_record":{"source":{"id":"1011.2945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T15:26:35Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"title_canon_sha256":"c713143a111a17817b0f07f47f09400465c8255c9539cb7cbd85f03618420954","abstract_canon_sha256":"438b91aba57ec2e2531b42ce838101ad0b6636a35bbb7c8cc90c639dc3587816"},"schema_version":"1.0"},"canonical_sha256":"b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100","source":{"kind":"arxiv","id":"1011.2945","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2945","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2945v1","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2945","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"WRNBL6TAODOS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WRNBL6TAODOSCCMI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WRNBL6TA","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WRNBL6TAODOSCCMI733EU6WWBC","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T15:26:35Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"title_canon_sha256":"c713143a111a17817b0f07f47f09400465c8255c9539cb7cbd85f03618420954","abstract_canon_sha256":"438b91aba57ec2e2531b42ce838101ad0b6636a35bbb7c8cc90c639dc3587816"},"schema_version":"1.0"},"canonical_sha256":"b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:48.284991Z","signature_b64":"pg+rBnAd4wU6UdY4mMw7ij9qYbe7OO7yATUoOSAoJuUlNieHPNRbfk+syczxRALhXhwoni6GVY98NLQ2b6X6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100","last_reissued_at":"2026-05-18T02:04:48.284414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:48.284414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2945","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":"2026-05-18T02:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yJ4k+hGvreFHckj8THRqEbp12g5eB93sHMoPkWio02wRVxlMR1g5jqOGpmv96/bV4tkspol3kwsJnUa9COaaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:24:31.032343Z"},"content_sha256":"f327e33456936bd792e61c66f0f44a3ccf763165ddfc4d111b1fd09c49e7d00b","schema_version":"1.0","event_id":"sha256:f327e33456936bd792e61c66f0f44a3ccf763165ddfc4d111b1fd09c49e7d00b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WRNBL6TAODOSCCMI733EU6WWBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Phase transitions for the cavity approach to the clique problem on random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"primary_cat":"math.PR","authors_text":"Alexandre Gaudilliere, Benedetto Scoppola, Elisabetta Scoppola, Massimiliano Viale","submitted_at":"2010-11-12T15:26:35Z","abstract_excerpt":"We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2945","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":"2026-05-18T02:04:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y771JOaTF8ac8+taUOqtjQiDtQtzQM9YfplkcNyugFO8Mpq1nIinR4BIHkqsaL97l0rCVYFbHUhf/2/rOqNzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:24:31.032742Z"},"content_sha256":"79eeb1ec00eb3e09d320e038decada4074b1a5271235ab2c8527cb9a6c42c273","schema_version":"1.0","event_id":"sha256:79eeb1ec00eb3e09d320e038decada4074b1a5271235ab2c8527cb9a6c42c273"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WRNBL6TAODOSCCMI733EU6WWBC/bundle.json","state_url":"https://pith.science/pith/WRNBL6TAODOSCCMI733EU6WWBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WRNBL6TAODOSCCMI733EU6WWBC/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":"2026-05-27T18:24:31Z","links":{"resolver":"https://pith.science/pith/WRNBL6TAODOSCCMI733EU6WWBC","bundle":"https://pith.science/pith/WRNBL6TAODOSCCMI733EU6WWBC/bundle.json","state":"https://pith.science/pith/WRNBL6TAODOSCCMI733EU6WWBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WRNBL6TAODOSCCMI733EU6WWBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WRNBL6TAODOSCCMI733EU6WWBC","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":"438b91aba57ec2e2531b42ce838101ad0b6636a35bbb7c8cc90c639dc3587816","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T15:26:35Z","title_canon_sha256":"c713143a111a17817b0f07f47f09400465c8255c9539cb7cbd85f03618420954"},"schema_version":"1.0","source":{"id":"1011.2945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2945","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2945v1","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2945","created_at":"2026-05-18T02:04:48Z"},{"alias_kind":"pith_short_12","alias_value":"WRNBL6TAODOS","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WRNBL6TAODOSCCMI","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WRNBL6TA","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:79eeb1ec00eb3e09d320e038decada4074b1a5271235ab2c8527cb9a6c42c273","target":"graph","created_at":"2026-05-18T02:04:48Z","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":"We give a rigorous proof of two phase transitions for a disordered system designed to find large cliques inside Erdos random graphs. Such a system is associated with a conservative probabilistic cellular automaton inspired by the cavity method originally introduced in spin glass theory.","authors_text":"Alexandre Gaudilliere, Benedetto Scoppola, Elisabetta Scoppola, Massimiliano Viale","cross_cats":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T15:26:35Z","title":"Phase transitions for the cavity approach to the clique problem on random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2945","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:f327e33456936bd792e61c66f0f44a3ccf763165ddfc4d111b1fd09c49e7d00b","target":"record","created_at":"2026-05-18T02:04:48Z","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":"438b91aba57ec2e2531b42ce838101ad0b6636a35bbb7c8cc90c639dc3587816","cross_cats_sorted":["cond-mat.stat-mech","cs.SI","physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-12T15:26:35Z","title_canon_sha256":"c713143a111a17817b0f07f47f09400465c8255c9539cb7cbd85f03618420954"},"schema_version":"1.0","source":{"id":"1011.2945","kind":"arxiv","version":1}},"canonical_sha256":"b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b45a15fa6070dd210988fef64a7ad6088530f8174d35e623a879f522e0ecb100","first_computed_at":"2026-05-18T02:04:48.284414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:48.284414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pg+rBnAd4wU6UdY4mMw7ij9qYbe7OO7yATUoOSAoJuUlNieHPNRbfk+syczxRALhXhwoni6GVY98NLQ2b6X6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:48.284991Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f327e33456936bd792e61c66f0f44a3ccf763165ddfc4d111b1fd09c49e7d00b","sha256:79eeb1ec00eb3e09d320e038decada4074b1a5271235ab2c8527cb9a6c42c273"],"state_sha256":"9691cba218e0d7debffcf5566f7034f24c76591cefb1d240f576acf0194ca2df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+TX/xr1/66AFEHkSazo6zJehg02AJcFqQ3lH+ElrOdFrqNmrTF12Pacjy5lsSI64VJwAfkiHJ7P+VJM+96PpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:24:31.035107Z","bundle_sha256":"3fce81dc1a77ce75beaa47f8e674c833f5608ed77f83899f90ae2bc72aa6faff"}}