{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:VZBHPEZQPIF55N2RGIYKYHGULY","short_pith_number":"pith:VZBHPEZQ","canonical_record":{"source":{"id":"0905.3679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-05-22T13:42:52Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"11fb376b1fefe3057e3108646db5c2b88c1bf7882055e83acbf005f73ebd621a","abstract_canon_sha256":"ea18488a2193e75f260dd7b34a15b414230c39fa35bfd5030006f8d343ffb4a6"},"schema_version":"1.0"},"canonical_sha256":"ae427793307a0bdeb7513230ac1cd45e0cad9033695d3a9dcb000ac1effbf4b2","source":{"kind":"arxiv","id":"0905.3679","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3679","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3679v1","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3679","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZBHPEZQPIF5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VZBHPEZQPIF55N2R","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VZBHPEZQ","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:VZBHPEZQPIF55N2RGIYKYHGULY","target":"record","payload":{"canonical_record":{"source":{"id":"0905.3679","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-05-22T13:42:52Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"11fb376b1fefe3057e3108646db5c2b88c1bf7882055e83acbf005f73ebd621a","abstract_canon_sha256":"ea18488a2193e75f260dd7b34a15b414230c39fa35bfd5030006f8d343ffb4a6"},"schema_version":"1.0"},"canonical_sha256":"ae427793307a0bdeb7513230ac1cd45e0cad9033695d3a9dcb000ac1effbf4b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:06.248246Z","signature_b64":"INbePE2ClFJ3Mek6zHP7HRo+ENm8f5MtpgdKy27ek8ddP3y9yp7C4V2jQMDUSZCyZWavTSoJrbspxinF4Q7ECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae427793307a0bdeb7513230ac1cd45e0cad9033695d3a9dcb000ac1effbf4b2","last_reissued_at":"2026-05-18T03:24:06.247499Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:06.247499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.3679","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":"2026-05-18T03:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5GJsFPhrhvDKSCfVztDXbQMxGY/XPvYcbnjZ6xcfrJwWU95NTgh19crnur4a1TTxVaN5a4AZ8K4s3f8qCVnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:04:30.606522Z"},"content_sha256":"44b7870e89151a92aadb610bb31671dc59ae41896411563ae9b6625fbb0e1abe","schema_version":"1.0","event_id":"sha256:44b7870e89151a92aadb610bb31671dc59ae41896411563ae9b6625fbb0e1abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:VZBHPEZQPIF55N2RGIYKYHGULY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equilibrium properties of disordered spin models with two scale interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"David Saad, Jack Raymond","submitted_at":"2009-05-22T13:42:52Z","abstract_excerpt":"Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdos-Renyi graph structures above the percolation threshold, and to Bethe lattices when appropriate boundary conditions apply. In this paper we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3679","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":"2026-05-18T03:24:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MIFSCPIzZuVz382bMEMGNBD6lvBATR9l7AAcDabdlkssHPcuIdwin8ZO9/kSsf6tJHydTMHCEphE4KRyVmBTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:04:30.606871Z"},"content_sha256":"3d7867e746deadf3757218b1344f25200b711a3709a06fce8e07ce69164b0079","schema_version":"1.0","event_id":"sha256:3d7867e746deadf3757218b1344f25200b711a3709a06fce8e07ce69164b0079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZBHPEZQPIF55N2RGIYKYHGULY/bundle.json","state_url":"https://pith.science/pith/VZBHPEZQPIF55N2RGIYKYHGULY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZBHPEZQPIF55N2RGIYKYHGULY/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":"2026-06-11T10:04:30Z","links":{"resolver":"https://pith.science/pith/VZBHPEZQPIF55N2RGIYKYHGULY","bundle":"https://pith.science/pith/VZBHPEZQPIF55N2RGIYKYHGULY/bundle.json","state":"https://pith.science/pith/VZBHPEZQPIF55N2RGIYKYHGULY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZBHPEZQPIF55N2RGIYKYHGULY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:VZBHPEZQPIF55N2RGIYKYHGULY","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":"ea18488a2193e75f260dd7b34a15b414230c39fa35bfd5030006f8d343ffb4a6","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-05-22T13:42:52Z","title_canon_sha256":"11fb376b1fefe3057e3108646db5c2b88c1bf7882055e83acbf005f73ebd621a"},"schema_version":"1.0","source":{"id":"0905.3679","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3679","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3679v1","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3679","created_at":"2026-05-18T03:24:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZBHPEZQPIF5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"VZBHPEZQPIF55N2R","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"VZBHPEZQ","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:3d7867e746deadf3757218b1344f25200b711a3709a06fce8e07ce69164b0079","target":"graph","created_at":"2026-05-18T03:24:06Z","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":"Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdos-Renyi graph structures above the percolation threshold, and to Bethe lattices when appropriate boundary conditions apply. In this paper we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model.","authors_text":"David Saad, Jack Raymond","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-05-22T13:42:52Z","title":"Equilibrium properties of disordered spin models with two scale interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3679","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":"sha256:44b7870e89151a92aadb610bb31671dc59ae41896411563ae9b6625fbb0e1abe","target":"record","created_at":"2026-05-18T03:24:06Z","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":"ea18488a2193e75f260dd7b34a15b414230c39fa35bfd5030006f8d343ffb4a6","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2009-05-22T13:42:52Z","title_canon_sha256":"11fb376b1fefe3057e3108646db5c2b88c1bf7882055e83acbf005f73ebd621a"},"schema_version":"1.0","source":{"id":"0905.3679","kind":"arxiv","version":1}},"canonical_sha256":"ae427793307a0bdeb7513230ac1cd45e0cad9033695d3a9dcb000ac1effbf4b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae427793307a0bdeb7513230ac1cd45e0cad9033695d3a9dcb000ac1effbf4b2","first_computed_at":"2026-05-18T03:24:06.247499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:06.247499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"INbePE2ClFJ3Mek6zHP7HRo+ENm8f5MtpgdKy27ek8ddP3y9yp7C4V2jQMDUSZCyZWavTSoJrbspxinF4Q7ECA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:06.248246Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3679","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:44b7870e89151a92aadb610bb31671dc59ae41896411563ae9b6625fbb0e1abe","sha256:3d7867e746deadf3757218b1344f25200b711a3709a06fce8e07ce69164b0079"],"state_sha256":"2f60ff7115d2b7cdc34d3694ff5902424500374910e37db2f49acf0d7d57fb8e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nvPA69WuOghIdXw+dBTEHq+hQD+8O7YaCOsfi/iMTi6593Q9mfV7noPybQXY0Kut6LOrRJ9YTe0eKPSmoS5VCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:04:30.608791Z","bundle_sha256":"79cd1a0286fedbb6db1bf797c09c655dd201ab8f8ae01c60ba12da66dd7d08d5"}}