{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NYGKGDAJOPIGRZOOVOSP2VQYVU","short_pith_number":"pith:NYGKGDAJ","canonical_record":{"source":{"id":"1206.5062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-22T06:13:16Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"bd4f340aad1e66964086f36f6e94c08755cbefd9e45eeef13ac734b43cee157c","abstract_canon_sha256":"710862e421b6dc90120a9ff30d9c5cb72aa6bf0cdeacd898c3a7e273b9eaafd6"},"schema_version":"1.0"},"canonical_sha256":"6e0ca30c0973d068e5ceaba4fd5618ad1a836cbd93de8df9df6b11e3ab8f7ac2","source":{"kind":"arxiv","id":"1206.5062","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5062","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5062v2","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5062","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"NYGKGDAJOPIG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NYGKGDAJOPIGRZOO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NYGKGDAJ","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NYGKGDAJOPIGRZOOVOSP2VQYVU","target":"record","payload":{"canonical_record":{"source":{"id":"1206.5062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-22T06:13:16Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"bd4f340aad1e66964086f36f6e94c08755cbefd9e45eeef13ac734b43cee157c","abstract_canon_sha256":"710862e421b6dc90120a9ff30d9c5cb72aa6bf0cdeacd898c3a7e273b9eaafd6"},"schema_version":"1.0"},"canonical_sha256":"6e0ca30c0973d068e5ceaba4fd5618ad1a836cbd93de8df9df6b11e3ab8f7ac2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:36.116561Z","signature_b64":"sChTWkxRnfbtjyiv+Y7MiZr5X5HtkFJ1hbDIgqt/E7uzZSjEV7DcQYRXdB9Vh+AaeW3IYl6x9NrI3apK+T4sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e0ca30c0973d068e5ceaba4fd5618ad1a836cbd93de8df9df6b11e3ab8f7ac2","last_reissued_at":"2026-05-18T02:57:36.115959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:36.115959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.5062","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":"2026-05-18T02:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nhi/m5OHopa21i81PW/GDaix5E3c/56SYX81s9MlK7CyB1tPLsuCLRqkNv86K2ZLMkDIiB0hod+VQG0d0V04Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:05:03.496463Z"},"content_sha256":"571aac1489a8aee3a63029e4b04ed7ddaa35606c8c25c2ddc0ec041ab179c8b2","schema_version":"1.0","event_id":"sha256:571aac1489a8aee3a63029e4b04ed7ddaa35606c8c25c2ddc0ec041ab179c8b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NYGKGDAJOPIGRZOOVOSP2VQYVU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Koji Nemoto, Takehisa Hasegawa, Tomoaki Nogawa","submitted_at":"2012-06-22T06:13:16Z","abstract_excerpt":"We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5062","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":"2026-05-18T02:57:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72P15FMV6H6Y9fYNhRyKsHLipv/IXt8w/twnZ7a/88zUYPt9vfzlvzWxMYi9NeUHfUrFH3cC3llx0JhLCNQ2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T18:05:03.496849Z"},"content_sha256":"22a29eaa10179e75f3760e1dbb208d4000460180ec1dfe270dfc1f399454eb96","schema_version":"1.0","event_id":"sha256:22a29eaa10179e75f3760e1dbb208d4000460180ec1dfe270dfc1f399454eb96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/bundle.json","state_url":"https://pith.science/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/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":"2026-05-26T18:05:03Z","links":{"resolver":"https://pith.science/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU","bundle":"https://pith.science/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/bundle.json","state":"https://pith.science/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NYGKGDAJOPIGRZOOVOSP2VQYVU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NYGKGDAJOPIGRZOOVOSP2VQYVU","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":"710862e421b6dc90120a9ff30d9c5cb72aa6bf0cdeacd898c3a7e273b9eaafd6","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-22T06:13:16Z","title_canon_sha256":"bd4f340aad1e66964086f36f6e94c08755cbefd9e45eeef13ac734b43cee157c"},"schema_version":"1.0","source":{"id":"1206.5062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5062","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5062v2","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5062","created_at":"2026-05-18T02:57:36Z"},{"alias_kind":"pith_short_12","alias_value":"NYGKGDAJOPIG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NYGKGDAJOPIGRZOO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NYGKGDAJ","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:22a29eaa10179e75f3760e1dbb208d4000460180ec1dfe270dfc1f399454eb96","target":"graph","created_at":"2026-05-18T02:57:36Z","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 propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical network, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.","authors_text":"Koji Nemoto, Takehisa Hasegawa, Tomoaki Nogawa","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-22T06:13:16Z","title":"Generalized scaling theory for critical phenomena including essential singularity and infinite dimensionality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5062","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":"sha256:571aac1489a8aee3a63029e4b04ed7ddaa35606c8c25c2ddc0ec041ab179c8b2","target":"record","created_at":"2026-05-18T02:57:36Z","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":"710862e421b6dc90120a9ff30d9c5cb72aa6bf0cdeacd898c3a7e273b9eaafd6","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2012-06-22T06:13:16Z","title_canon_sha256":"bd4f340aad1e66964086f36f6e94c08755cbefd9e45eeef13ac734b43cee157c"},"schema_version":"1.0","source":{"id":"1206.5062","kind":"arxiv","version":2}},"canonical_sha256":"6e0ca30c0973d068e5ceaba4fd5618ad1a836cbd93de8df9df6b11e3ab8f7ac2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e0ca30c0973d068e5ceaba4fd5618ad1a836cbd93de8df9df6b11e3ab8f7ac2","first_computed_at":"2026-05-18T02:57:36.115959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:36.115959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sChTWkxRnfbtjyiv+Y7MiZr5X5HtkFJ1hbDIgqt/E7uzZSjEV7DcQYRXdB9Vh+AaeW3IYl6x9NrI3apK+T4sCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:36.116561Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571aac1489a8aee3a63029e4b04ed7ddaa35606c8c25c2ddc0ec041ab179c8b2","sha256:22a29eaa10179e75f3760e1dbb208d4000460180ec1dfe270dfc1f399454eb96"],"state_sha256":"5aff9566c0fdc3917f4075360fd9cb5c38b9d7f96ca3cb310147657fce74dba3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wMqu2tdawAQyU8qb62GOcEHC0bUFHmJAWRfCpQyIBKhT/56EtaQoA4r6jFDFSkyAn5tazpfpDgXG4+MG7QPOAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T18:05:03.499653Z","bundle_sha256":"801b1d7cd7e6f94db6db41409a78f94a865da2af9a6787bc17de566c57f1a02b"}}