{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:PVAJC67XWIYUOMWS4H2HDVVKNI","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":"34e8f1dad5377eeab60d5a096b90edecfbfc9ded72636cbf3a71cbfc7212c7d2","cross_cats_sorted":["hep-lat"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-27T22:22:57Z","title_canon_sha256":"b9e6d7d4457567d2dd3244352a5de6f4a60d9ffdb570cd4af737b9d5883ddb7d"},"schema_version":"1.0","source":{"id":"cond-mat/0612655","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0612655","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0612655v2","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0612655","created_at":"2026-05-18T00:57:06Z"},{"alias_kind":"pith_short_12","alias_value":"PVAJC67XWIYU","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"PVAJC67XWIYUOMWS","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"PVAJC67X","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:bc859163b760d4463ccfa1835010c1ebb92ce49e6080661bca7c5d1f593216ba","target":"graph","created_at":"2026-05-18T00:57:06Z","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":"In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models. This expansion, known as the hopping expansion in the context of lattice field theory, yields a geometric description of the phase transition in these models, with the thermal critical exponents being determined by the fractal structure of the high-temperature graphs. The graphs percolate at the thermal critical point and can be studied using purely geometrica","authors_text":"Adriaan M. J. Schakel, Wolfhard Janke","cross_cats":["hep-lat"],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-27T22:22:57Z","title":"Spacetime Approach to Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0612655","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":"sha256:6a07320901b3905d6d90331d5d28a31120c475ad4c40c372f2887200674e4246","target":"record","created_at":"2026-05-18T00:57:06Z","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":"34e8f1dad5377eeab60d5a096b90edecfbfc9ded72636cbf3a71cbfc7212c7d2","cross_cats_sorted":["hep-lat"],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-12-27T22:22:57Z","title_canon_sha256":"b9e6d7d4457567d2dd3244352a5de6f4a60d9ffdb570cd4af737b9d5883ddb7d"},"schema_version":"1.0","source":{"id":"cond-mat/0612655","kind":"arxiv","version":2}},"canonical_sha256":"7d40917bf7b2314732d2e1f471d6aa6a04f942451120015ff5ba5a960bc25a46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d40917bf7b2314732d2e1f471d6aa6a04f942451120015ff5ba5a960bc25a46","first_computed_at":"2026-05-18T00:57:06.443922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:06.443922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TLypXF8Duz5NRwTaLRbNyVZRkwgXMPgHLn0GkHZopJ6YW5LfhyOwuC1xPIO4/F2Y6BACl34d7xT5FNqE+IqSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:06.444597Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0612655","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a07320901b3905d6d90331d5d28a31120c475ad4c40c372f2887200674e4246","sha256:bc859163b760d4463ccfa1835010c1ebb92ce49e6080661bca7c5d1f593216ba"],"state_sha256":"88ab0cbc4377502ec5d8304333d7dffbc67ddbc2d25ee06f10bd1bf50cdfe596"}