{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:SECPK6TZT2RN3T2HY347DQ7O7Q","short_pith_number":"pith:SECPK6TZ","canonical_record":{"source":{"id":"cond-mat/0509136","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-09-06T08:27:04Z","cross_cats_sorted":[],"title_canon_sha256":"d3ff270e56a6d46625cbd564c1e4e5a8207acd160c3c0c43833875247d015a35","abstract_canon_sha256":"7165bbb9652b26efd44259791f121c6eb86ca54bd10da01ce4132742729ab151"},"schema_version":"1.0"},"canonical_sha256":"9104f57a799ea2ddcf47c6f9f1c3eefc1bc8d3a7df18f30357b3be5de5ce2fc6","source":{"kind":"arxiv","id":"cond-mat/0509136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0509136","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0509136v1","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0509136","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"SECPK6TZT2RN","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"SECPK6TZT2RN3T2H","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"SECPK6TZ","created_at":"2026-07-04T15:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:SECPK6TZT2RN3T2HY347DQ7O7Q","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0509136","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-09-06T08:27:04Z","cross_cats_sorted":[],"title_canon_sha256":"d3ff270e56a6d46625cbd564c1e4e5a8207acd160c3c0c43833875247d015a35","abstract_canon_sha256":"7165bbb9652b26efd44259791f121c6eb86ca54bd10da01ce4132742729ab151"},"schema_version":"1.0"},"canonical_sha256":"9104f57a799ea2ddcf47c6f9f1c3eefc1bc8d3a7df18f30357b3be5de5ce2fc6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:25:57.611496Z","signature_b64":"hs0lHnoV1i/AXIIRKAJcf1M0PPiCH91IIU4042rQ/lZczg58H4v/VY2LbDrZPZF4yUj59nUXNKj9dW6542taAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9104f57a799ea2ddcf47c6f9f1c3eefc1bc8d3a7df18f30357b3be5de5ce2fc6","last_reissued_at":"2026-07-04T15:25:57.611072Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:25:57.611072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0509136","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":"2026-07-04T15:25:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XlprAZIG0RTYDEVzv1NPH+M7Pcbe3+epdOqJ6WJi725pmN2MHlQfvgEWIelq5L26Gwz9yVp0M+0EH9T0q4q2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:26:41.409172Z"},"content_sha256":"e8a571b3e1769ae29110b4460fd0ffe774f2eadca7d70f868c74bca4844766ab","schema_version":"1.0","event_id":"sha256:e8a571b3e1769ae29110b4460fd0ffe774f2eadca7d70f868c74bca4844766ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:SECPK6TZT2RN3T2HY347DQ7O7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When topology triggers a phase transition","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Michael Kastner","submitted_at":"2005-09-06T08:27:04Z","abstract_excerpt":"Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by a such topology change are discussed. The first one is a model with long-range interactions, namely the mean-field phi^4-model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0509136","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/cond-mat/0509136/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:25:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kWnDcRvClDpyZUiPLmxoYctmS21HZmddt0soYV/IUROmyE+eYp7OPMRvt40wq0nuCc+r7NsHToBh59kzFsDUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:26:41.409564Z"},"content_sha256":"299723dd9992ba87c9832f2ca28689e034386706de0203511d772b45230ddbb4","schema_version":"1.0","event_id":"sha256:299723dd9992ba87c9832f2ca28689e034386706de0203511d772b45230ddbb4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/bundle.json","state_url":"https://pith.science/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/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":"2026-07-04T23:26:41Z","links":{"resolver":"https://pith.science/pith/SECPK6TZT2RN3T2HY347DQ7O7Q","bundle":"https://pith.science/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/bundle.json","state":"https://pith.science/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SECPK6TZT2RN3T2HY347DQ7O7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SECPK6TZT2RN3T2HY347DQ7O7Q","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":"7165bbb9652b26efd44259791f121c6eb86ca54bd10da01ce4132742729ab151","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-09-06T08:27:04Z","title_canon_sha256":"d3ff270e56a6d46625cbd564c1e4e5a8207acd160c3c0c43833875247d015a35"},"schema_version":"1.0","source":{"id":"cond-mat/0509136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0509136","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0509136v1","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0509136","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"SECPK6TZT2RN","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"SECPK6TZT2RN3T2H","created_at":"2026-07-04T15:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"SECPK6TZ","created_at":"2026-07-04T15:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:299723dd9992ba87c9832f2ca28689e034386706de0203511d772b45230ddbb4","target":"graph","created_at":"2026-07-04T15:25:57Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/cond-mat/0509136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Two mathematical mechanisms, responsible for the generation of a thermodynamic singularity, are individuated. For a class of short-range, confining potentials, a topology change in some family of configuration space submanifolds is the only possible such mechanism. Two examples of systems in which the phase transition is not accompanied by a such topology change are discussed. The first one is a model with long-range interactions, namely the mean-field phi^4-model, the second example is a one-dimensional system with a non-confining potential energy function. For both these systems, the thermod","authors_text":"Michael Kastner","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-09-06T08:27:04Z","title":"When topology triggers a phase transition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0509136","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:e8a571b3e1769ae29110b4460fd0ffe774f2eadca7d70f868c74bca4844766ab","target":"record","created_at":"2026-07-04T15:25:57Z","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":"7165bbb9652b26efd44259791f121c6eb86ca54bd10da01ce4132742729ab151","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2005-09-06T08:27:04Z","title_canon_sha256":"d3ff270e56a6d46625cbd564c1e4e5a8207acd160c3c0c43833875247d015a35"},"schema_version":"1.0","source":{"id":"cond-mat/0509136","kind":"arxiv","version":1}},"canonical_sha256":"9104f57a799ea2ddcf47c6f9f1c3eefc1bc8d3a7df18f30357b3be5de5ce2fc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9104f57a799ea2ddcf47c6f9f1c3eefc1bc8d3a7df18f30357b3be5de5ce2fc6","first_computed_at":"2026-07-04T15:25:57.611072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:25:57.611072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hs0lHnoV1i/AXIIRKAJcf1M0PPiCH91IIU4042rQ/lZczg58H4v/VY2LbDrZPZF4yUj59nUXNKj9dW6542taAA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:25:57.611496Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0509136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8a571b3e1769ae29110b4460fd0ffe774f2eadca7d70f868c74bca4844766ab","sha256:299723dd9992ba87c9832f2ca28689e034386706de0203511d772b45230ddbb4"],"state_sha256":"035a51b59f37c754abfb8a0be6c312f3b3d3cda7cb24a96e31dd635cb0cd3638"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h2YOY4wlF2rGc7aIdk0bBjV35A2Z71KDOY25A0j1q20b+HYQB9F1SyinRxGA77gqsaHQp4CX8vplCU/B1bdZCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:26:41.411494Z","bundle_sha256":"8dca97bc11a2623d5bb0ace2f96e9e8451c560470560fcc6f8d7bffdb1b917a1"}}