{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EIR6SRJ2NUU7RJCFYZ3RLZVAQ2","short_pith_number":"pith:EIR6SRJ2","canonical_record":{"source":{"id":"1704.01043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-04-04T14:58:59Z","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"title_canon_sha256":"622cb5f66b877887f5057c9bf28270fd67bab46efe50aa71d298634ca7eb6951","abstract_canon_sha256":"9ec120a0193519a06100be85068090e8a940016a63638ee31345d8ed5e420c42"},"schema_version":"1.0"},"canonical_sha256":"2223e9453a6d29f8a445c67715e6a086a3e6a1ab24c58a0ead325a323347105c","source":{"kind":"arxiv","id":"1704.01043","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01043","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01043v1","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01043","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"EIR6SRJ2NUU7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EIR6SRJ2NUU7RJCF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EIR6SRJ2","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EIR6SRJ2NUU7RJCFYZ3RLZVAQ2","target":"record","payload":{"canonical_record":{"source":{"id":"1704.01043","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-04-04T14:58:59Z","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"title_canon_sha256":"622cb5f66b877887f5057c9bf28270fd67bab46efe50aa71d298634ca7eb6951","abstract_canon_sha256":"9ec120a0193519a06100be85068090e8a940016a63638ee31345d8ed5e420c42"},"schema_version":"1.0"},"canonical_sha256":"2223e9453a6d29f8a445c67715e6a086a3e6a1ab24c58a0ead325a323347105c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:14.422422Z","signature_b64":"liR1QhtXj8L+KyKNl3uAq0Zpfun+bvnwVtY0xM13XVwXY5WuRh22VcdzAwRNYRGtZsLtJbNRuzaHS7EZodQFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2223e9453a6d29f8a445c67715e6a086a3e6a1ab24c58a0ead325a323347105c","last_reissued_at":"2026-05-18T00:21:14.421909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:14.421909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.01043","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":"2026-05-18T00:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8XtXqG1R3sFh6zQpq1wcFqMmLmB+5oaTyYlVe/0fDaXVt1JUc6RabDOtALtoifkzYSJDscLhV3dhcOWTPPNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:38:35.863288Z"},"content_sha256":"5b80105a523a4e01a0cab1f6dc0be6a49dca80f83f2161dfeaa203b6e712ef6c","schema_version":"1.0","event_id":"sha256:5b80105a523a4e01a0cab1f6dc0be6a49dca80f83f2161dfeaa203b6e712ef6c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EIR6SRJ2NUU7RJCFYZ3RLZVAQ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Charting the replica symmetric phase","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"primary_cat":"cs.DM","authors_text":"Amin Coja-Oghlan, Charilaos Efthymiou, Mihyun Kang, Nor Jaafari, Tobias Kapetanopoulos","submitted_at":"2017-04-04T14:58:59Z","abstract_excerpt":"Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous `cavity method', physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01043","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":"2026-05-18T00:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5m23HrB1VyLhP5Mh8sRFdT396ICkb2LWGsSRUAtK57sG/eLCMFzaTnM29SLvhFkLhzLFQCPkJVHz5ADmrfe5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:38:35.863656Z"},"content_sha256":"f637816aa30e9a272f30d3c3b2827d1ea98a163519df20fe400c83afcaebd464","schema_version":"1.0","event_id":"sha256:f637816aa30e9a272f30d3c3b2827d1ea98a163519df20fe400c83afcaebd464"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/bundle.json","state_url":"https://pith.science/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/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":"2026-06-01T08:38:35Z","links":{"resolver":"https://pith.science/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2","bundle":"https://pith.science/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/bundle.json","state":"https://pith.science/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIR6SRJ2NUU7RJCFYZ3RLZVAQ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EIR6SRJ2NUU7RJCFYZ3RLZVAQ2","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":"9ec120a0193519a06100be85068090e8a940016a63638ee31345d8ed5e420c42","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-04-04T14:58:59Z","title_canon_sha256":"622cb5f66b877887f5057c9bf28270fd67bab46efe50aa71d298634ca7eb6951"},"schema_version":"1.0","source":{"id":"1704.01043","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01043","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01043v1","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01043","created_at":"2026-05-18T00:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"EIR6SRJ2NUU7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EIR6SRJ2NUU7RJCF","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EIR6SRJ2","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f637816aa30e9a272f30d3c3b2827d1ea98a163519df20fe400c83afcaebd464","target":"graph","created_at":"2026-05-18T00:21:14Z","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":"Diluted mean-field models are spin systems whose geometry of interactions is induced by a sparse random graph or hypergraph. Such models play an eminent role in the statistical mechanics of disordered systems as well as in combinatorics and computer science. In a path-breaking paper based on the non-rigorous `cavity method', physicists predicted not only the existence of a replica symmetry breaking phase transition in such models but also sketched a detailed picture of the evolution of the Gibbs measure within the replica symmetric phase and its impact on important problems in combinatorics, c","authors_text":"Amin Coja-Oghlan, Charilaos Efthymiou, Mihyun Kang, Nor Jaafari, Tobias Kapetanopoulos","cross_cats":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-04-04T14:58:59Z","title":"Charting the replica symmetric phase"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01043","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":"sha256:5b80105a523a4e01a0cab1f6dc0be6a49dca80f83f2161dfeaa203b6e712ef6c","target":"record","created_at":"2026-05-18T00:21:14Z","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":"9ec120a0193519a06100be85068090e8a940016a63638ee31345d8ed5e420c42","cross_cats_sorted":["cond-mat.dis-nn","math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-04-04T14:58:59Z","title_canon_sha256":"622cb5f66b877887f5057c9bf28270fd67bab46efe50aa71d298634ca7eb6951"},"schema_version":"1.0","source":{"id":"1704.01043","kind":"arxiv","version":1}},"canonical_sha256":"2223e9453a6d29f8a445c67715e6a086a3e6a1ab24c58a0ead325a323347105c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2223e9453a6d29f8a445c67715e6a086a3e6a1ab24c58a0ead325a323347105c","first_computed_at":"2026-05-18T00:21:14.421909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:14.421909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"liR1QhtXj8L+KyKNl3uAq0Zpfun+bvnwVtY0xM13XVwXY5WuRh22VcdzAwRNYRGtZsLtJbNRuzaHS7EZodQFBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:14.422422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01043","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b80105a523a4e01a0cab1f6dc0be6a49dca80f83f2161dfeaa203b6e712ef6c","sha256:f637816aa30e9a272f30d3c3b2827d1ea98a163519df20fe400c83afcaebd464"],"state_sha256":"fde7d71e61ae89bdf56e030d89f043d98f564538e5b9405b5bcb24d6d20df25c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvX+0AuI9memCSV9/uyhIG3a+8K+hLrk9QOCnHObk8SAm3k7H3gfCFDz9SMuCe882MHszysXNkKDPtn8uFSRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:38:35.865643Z","bundle_sha256":"ffd887d939f406f485ee5743be42c9d08c54ae105e2cf219e6d1f5e6db33f52a"}}