{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:MZS4CGH4PKHRUBEY5QWKNWCZQQ","short_pith_number":"pith:MZS4CGH4","canonical_record":{"source":{"id":"cond-mat/9709303","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-26T20:57:17Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"167fdc1b9c9f962215d3d9066f0682c03ced0d9f989e320b50d627cc12ec0e00","abstract_canon_sha256":"f7822b6187dc2ee18ff8afda989a9fd084614d2a3b7acce27f36d86326a63aa7"},"schema_version":"1.0"},"canonical_sha256":"6665c118fc7a8f1a0498ec2ca6d85984229bdfa0855b1fef60e1398ac69d2587","source":{"kind":"arxiv","id":"cond-mat/9709303","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9709303","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9709303v1","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9709303","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"MZS4CGH4PKHR","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MZS4CGH4PKHRUBEY","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MZS4CGH4","created_at":"2026-05-18T12:25:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:MZS4CGH4PKHRUBEY5QWKNWCZQQ","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/9709303","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-26T20:57:17Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"167fdc1b9c9f962215d3d9066f0682c03ced0d9f989e320b50d627cc12ec0e00","abstract_canon_sha256":"f7822b6187dc2ee18ff8afda989a9fd084614d2a3b7acce27f36d86326a63aa7"},"schema_version":"1.0"},"canonical_sha256":"6665c118fc7a8f1a0498ec2ca6d85984229bdfa0855b1fef60e1398ac69d2587","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:33.103172Z","signature_b64":"fW1Kqv4KSfqkhNJK3GqWbBJYyvlQTtOoL3EoB/ZYek8RKiHb+PHqT4KkkLozp9aJXkOgvZkzQ/lyF7Yx7zMwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6665c118fc7a8f1a0498ec2ca6d85984229bdfa0855b1fef60e1398ac69d2587","last_reissued_at":"2026-05-18T01:39:33.102808Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:33.102808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/9709303","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":"2026-05-18T01:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GDq+cVpS8SAjZa/7hjbefjEZrWvSwWc9jUS2K/MRPF4O7N/o/pRcp4tRlu/WLqTJw3yZeXEPxVkyuc11nfUrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:04:06.743373Z"},"content_sha256":"e1e1980efd558348e6dbe55a648b7633ec9d937b3c188a399d5a8eae0d62bd3a","schema_version":"1.0","event_id":"sha256:e1e1980efd558348e6dbe55a648b7633ec9d937b3c188a399d5a8eae0d62bd3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:MZS4CGH4PKHRUBEY5QWKNWCZQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions","license":"","headline":"","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"S. R. Salinas, S. T. R. Pinho, T. A. S. Haddad","submitted_at":"1997-09-26T20:57:17Z","abstract_excerpt":"We write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9709303","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":"2026-05-18T01:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g6PuS/W8efQmHqdNTnu7OUKyxqSMA84sIOkt0GBe397NtN0uj5VLsjQ/TDeH+ebKPuqYdes9Gn+Ph9BEPofoBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:04:06.743968Z"},"content_sha256":"6aba156d7ae2f6e7ef3c713d9577ed530a8341e5892e0d33001c0258afce0bbd","schema_version":"1.0","event_id":"sha256:6aba156d7ae2f6e7ef3c713d9577ed530a8341e5892e0d33001c0258afce0bbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/bundle.json","state_url":"https://pith.science/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/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":"2026-05-30T16:04:06Z","links":{"resolver":"https://pith.science/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ","bundle":"https://pith.science/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/bundle.json","state":"https://pith.science/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZS4CGH4PKHRUBEY5QWKNWCZQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:MZS4CGH4PKHRUBEY5QWKNWCZQQ","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":"f7822b6187dc2ee18ff8afda989a9fd084614d2a3b7acce27f36d86326a63aa7","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-26T20:57:17Z","title_canon_sha256":"167fdc1b9c9f962215d3d9066f0682c03ced0d9f989e320b50d627cc12ec0e00"},"schema_version":"1.0","source":{"id":"cond-mat/9709303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/9709303","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/9709303v1","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/9709303","created_at":"2026-05-18T01:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"MZS4CGH4PKHR","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"MZS4CGH4PKHRUBEY","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"MZS4CGH4","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:6aba156d7ae2f6e7ef3c713d9577ed530a8341e5892e0d33001c0258afce0bbd","target":"graph","created_at":"2026-05-18T01:39:33Z","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 write exact renormalization-group recursion relations for nearest-neighbor ferromagnetic Ising models on Migdal-Kadanoff hierarchical lattices with a distribution of aperiodic exchange interactions according to a class of substitutional sequences. For small geometric fluctuations, the critical behavior is unchanged with respect to the uniform case. For large fluctuations, as in the case of the Rudin-Shapiro sequence, the uniform fixed point in the parameter space cannot be reached from any physical initial conditions. We derive a criterion to check the relevance of the geometric fluctuation","authors_text":"S. R. Salinas, S. T. R. Pinho, T. A. S. Haddad","cross_cats":["cond-mat.dis-nn"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-26T20:57:17Z","title":"Critical behavior of the Ising model on a hierarchical lattice with aperiodic interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9709303","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:e1e1980efd558348e6dbe55a648b7633ec9d937b3c188a399d5a8eae0d62bd3a","target":"record","created_at":"2026-05-18T01:39:33Z","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":"f7822b6187dc2ee18ff8afda989a9fd084614d2a3b7acce27f36d86326a63aa7","cross_cats_sorted":["cond-mat.dis-nn"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"1997-09-26T20:57:17Z","title_canon_sha256":"167fdc1b9c9f962215d3d9066f0682c03ced0d9f989e320b50d627cc12ec0e00"},"schema_version":"1.0","source":{"id":"cond-mat/9709303","kind":"arxiv","version":1}},"canonical_sha256":"6665c118fc7a8f1a0498ec2ca6d85984229bdfa0855b1fef60e1398ac69d2587","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6665c118fc7a8f1a0498ec2ca6d85984229bdfa0855b1fef60e1398ac69d2587","first_computed_at":"2026-05-18T01:39:33.102808Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:33.102808Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fW1Kqv4KSfqkhNJK3GqWbBJYyvlQTtOoL3EoB/ZYek8RKiHb+PHqT4KkkLozp9aJXkOgvZkzQ/lyF7Yx7zMwAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:33.103172Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/9709303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1e1980efd558348e6dbe55a648b7633ec9d937b3c188a399d5a8eae0d62bd3a","sha256:6aba156d7ae2f6e7ef3c713d9577ed530a8341e5892e0d33001c0258afce0bbd"],"state_sha256":"0df02767633bc0a8110b488c0f72cbbe65445f0dafacea3af8ad4a6620d13e54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szIgcKyYMp0b5SoSz4K2DxkeXh/D21rbW25vKRM4/EdgEOeYQ0r17tKNP3uOwBAI/lS3YP59W1Bj7jqbgDUCAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:04:06.746447Z","bundle_sha256":"ee4eb1508b532c2a114dcc5a2eb200ae3a8bcc817f1d07e0650a9908db005f5e"}}