{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:PXWZZIIVJJX6GWWIWPXIRUR42I","short_pith_number":"pith:PXWZZIIV","canonical_record":{"source":{"id":"1005.4556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-25T12:49:43Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"dc92c001f2439d643aa1efe92b656f25e5234c501d638c53397b48694c4d9333","abstract_canon_sha256":"62a835e06ee50e44f76521c88ba77c1d595dc20f49f0e280c6c9057f179e46d2"},"schema_version":"1.0"},"canonical_sha256":"7ded9ca1154a6fe35ac8b3ee88d23cd216c553ea86c8fad53c95249cdd779850","source":{"kind":"arxiv","id":"1005.4556","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4556","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4556v2","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4556","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"PXWZZIIVJJX6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PXWZZIIVJJX6GWWI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PXWZZIIV","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:PXWZZIIVJJX6GWWIWPXIRUR42I","target":"record","payload":{"canonical_record":{"source":{"id":"1005.4556","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-25T12:49:43Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"title_canon_sha256":"dc92c001f2439d643aa1efe92b656f25e5234c501d638c53397b48694c4d9333","abstract_canon_sha256":"62a835e06ee50e44f76521c88ba77c1d595dc20f49f0e280c6c9057f179e46d2"},"schema_version":"1.0"},"canonical_sha256":"7ded9ca1154a6fe35ac8b3ee88d23cd216c553ea86c8fad53c95249cdd779850","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:04.451215Z","signature_b64":"LCx/ecqyohbpV1BxUgVFdZKC1cgYHqwT1JI+nGtwEKzJa+oVJi/Uv1Bo1e6KkUb1UT78K0GzgkbQh1+vhkGBAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ded9ca1154a6fe35ac8b3ee88d23cd216c553ea86c8fad53c95249cdd779850","last_reissued_at":"2026-05-18T04:19:04.450604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:04.450604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.4556","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":"2026-05-18T04:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38J7f5kxeODUANw4MCW9Tqnf+tQgDxUC6xI8lkqMadpeW+cV18Ffv+KXiBr7kQmflNPpo2imblKKdHmD5TUZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:27:11.777948Z"},"content_sha256":"47e09b41a4b8aefc73666aeba77557515dd914b38310e8128d3022caa806d68e","schema_version":"1.0","event_id":"sha256:47e09b41a4b8aefc73666aeba77557515dd914b38310e8128d3022caa806d68e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:PXWZZIIVJJX6GWWIWPXIRUR42I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ising models on power-law random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Cristian Giardin\\`a, Remco van der Hofstad, Sander Dommers","submitted_at":"2010-05-25T12:49:43Z","abstract_excerpt":"We study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\\tau>2$), for which the random graph has a tree-like structure. For this, we adapt and simplify an analysis by Dembo and Montanari, which assumes finite variance degrees ($\\tau>3$). We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4556","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":"2026-05-18T04:19:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C8Di1xH5v8t62s0roBlyrUawRXcNVYgOfjfvkCS9xabPU+aAXPTrSfQM1ZMiY8RRU4zb04upJ8wgBBbbzOCoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:27:11.778527Z"},"content_sha256":"815d9d1a12b1f092371f2b7021a8bd417fa45b3531c37c9ee4544ba7d3e71e15","schema_version":"1.0","event_id":"sha256:815d9d1a12b1f092371f2b7021a8bd417fa45b3531c37c9ee4544ba7d3e71e15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/bundle.json","state_url":"https://pith.science/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/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":"2026-06-23T16:27:11Z","links":{"resolver":"https://pith.science/pith/PXWZZIIVJJX6GWWIWPXIRUR42I","bundle":"https://pith.science/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/bundle.json","state":"https://pith.science/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXWZZIIVJJX6GWWIWPXIRUR42I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PXWZZIIVJJX6GWWIWPXIRUR42I","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":"62a835e06ee50e44f76521c88ba77c1d595dc20f49f0e280c6c9057f179e46d2","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-25T12:49:43Z","title_canon_sha256":"dc92c001f2439d643aa1efe92b656f25e5234c501d638c53397b48694c4d9333"},"schema_version":"1.0","source":{"id":"1005.4556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4556","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4556v2","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4556","created_at":"2026-05-18T04:19:04Z"},{"alias_kind":"pith_short_12","alias_value":"PXWZZIIVJJX6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PXWZZIIVJJX6GWWI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PXWZZIIV","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:815d9d1a12b1f092371f2b7021a8bd417fa45b3531c37c9ee4544ba7d3e71e15","target":"graph","created_at":"2026-05-18T04:19:04Z","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 study a ferromagnetic Ising model on random graphs with a power-law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite (degree exponent $\\tau>2$), for which the random graph has a tree-like structure. For this, we adapt and simplify an analysis by Dembo and Montanari, which assumes finite variance degrees ($\\tau>3$). We further identify the thermodynamic limits of various physical quantities, such as the magnetization and the internal energy.","authors_text":"Cristian Giardin\\`a, Remco van der Hofstad, Sander Dommers","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-25T12:49:43Z","title":"Ising models on power-law random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4556","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":"sha256:47e09b41a4b8aefc73666aeba77557515dd914b38310e8128d3022caa806d68e","target":"record","created_at":"2026-05-18T04:19:04Z","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":"62a835e06ee50e44f76521c88ba77c1d595dc20f49f0e280c6c9057f179e46d2","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-05-25T12:49:43Z","title_canon_sha256":"dc92c001f2439d643aa1efe92b656f25e5234c501d638c53397b48694c4d9333"},"schema_version":"1.0","source":{"id":"1005.4556","kind":"arxiv","version":2}},"canonical_sha256":"7ded9ca1154a6fe35ac8b3ee88d23cd216c553ea86c8fad53c95249cdd779850","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ded9ca1154a6fe35ac8b3ee88d23cd216c553ea86c8fad53c95249cdd779850","first_computed_at":"2026-05-18T04:19:04.450604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:04.450604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LCx/ecqyohbpV1BxUgVFdZKC1cgYHqwT1JI+nGtwEKzJa+oVJi/Uv1Bo1e6KkUb1UT78K0GzgkbQh1+vhkGBAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:04.451215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47e09b41a4b8aefc73666aeba77557515dd914b38310e8128d3022caa806d68e","sha256:815d9d1a12b1f092371f2b7021a8bd417fa45b3531c37c9ee4544ba7d3e71e15"],"state_sha256":"194eb8fcb1fb307475f6f132e4cb081cba0e2308155e33dd7a170ffaf8503bce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpII0syl8MhQhm6aqvPFd5gj9IfdWS1ALpojamnlGQD2tfWsDCjH5Mbjvg3a4BzsL3bpGDYKMRVN/lUeWdOHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:27:11.781400Z","bundle_sha256":"201fecf685a219347d20fabda4bc6b0cdc2b15a7475dd26d5221dde1175b11f5"}}