{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3DHOT62GEAVUXPRWI4X45UL4B3","short_pith_number":"pith:3DHOT62G","canonical_record":{"source":{"id":"1611.03960","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-11-12T06:47:43Z","cross_cats_sorted":[],"title_canon_sha256":"c39b84b08fafe757b03c4d2a56e0f6b992cfc1b49d58bb74834c2244393541d6","abstract_canon_sha256":"e637e41d0dc5b3b287cd7829f67aa73346d7a2df5731559e995afecc0ec73d4c"},"schema_version":"1.0"},"canonical_sha256":"d8cee9fb46202b4bbe36472fced17c0ee4554bbd0f55fbc2657a5f6236ffad6b","source":{"kind":"arxiv","id":"1611.03960","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03960","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03960v4","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03960","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"3DHOT62GEAVU","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DHOT62GEAVUXPRW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DHOT62G","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3DHOT62GEAVUXPRWI4X45UL4B3","target":"record","payload":{"canonical_record":{"source":{"id":"1611.03960","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-11-12T06:47:43Z","cross_cats_sorted":[],"title_canon_sha256":"c39b84b08fafe757b03c4d2a56e0f6b992cfc1b49d58bb74834c2244393541d6","abstract_canon_sha256":"e637e41d0dc5b3b287cd7829f67aa73346d7a2df5731559e995afecc0ec73d4c"},"schema_version":"1.0"},"canonical_sha256":"d8cee9fb46202b4bbe36472fced17c0ee4554bbd0f55fbc2657a5f6236ffad6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:14.519805Z","signature_b64":"622lr6Uz4MCw3YdlgS3OnPomfrdPVF2stpq+vX3y7C5+TUZBZJq96JfqD+/DhuSjJ/Xjz7rkCnHTuVFPcIWHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8cee9fb46202b4bbe36472fced17c0ee4554bbd0f55fbc2657a5f6236ffad6b","last_reissued_at":"2026-05-17T23:40:14.518884Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:14.518884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.03960","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"prdHev1dfGf9twfLAecx6ePI3E0pTjUCW6CL+pID/ncYCVC9FDnAXoRQ/7MtRg5Fs28PbpLbPf7NHgztWfOSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:19:38.779269Z"},"content_sha256":"c7694387a2f05f604d6255f0c129d27649bb7d53db8b37a1113f9501406871b3","schema_version":"1.0","event_id":"sha256:c7694387a2f05f604d6255f0c129d27649bb7d53db8b37a1113f9501406871b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3DHOT62GEAVUXPRWI4X45UL4B3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topology of configuration space of the mean-field phi^4 model by Morse theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Fabrizio Baroni","submitted_at":"2016-11-12T06:47:43Z","abstract_excerpt":"In this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field $\\phi^4$ model with a $\\mathbb{Z}_2$ symmetry. Our purpose is discovering, if any, the relation between the second-order $\\mathbb{Z}_2$-symmetry breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results at the light of two theorems on sufficiency conditions for symmetry breaking "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03960","kind":"arxiv","version":4},"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":"2026-05-17T23:40:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pcZHEJDuHGDLuipl28fdpvxn3oXSFkaCVtwlMrul3UvYEulwuo+6vdn85cqgB3L05GooVORwMEZ/z/pR/tYbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T02:19:38.779616Z"},"content_sha256":"e8878d8ce10976ecdc3bbc2da12bfd8823e3b8e9fab9f00c1dda903717bb39d8","schema_version":"1.0","event_id":"sha256:e8878d8ce10976ecdc3bbc2da12bfd8823e3b8e9fab9f00c1dda903717bb39d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DHOT62GEAVUXPRWI4X45UL4B3/bundle.json","state_url":"https://pith.science/pith/3DHOT62GEAVUXPRWI4X45UL4B3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DHOT62GEAVUXPRWI4X45UL4B3/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":"2026-07-03T02:19:38Z","links":{"resolver":"https://pith.science/pith/3DHOT62GEAVUXPRWI4X45UL4B3","bundle":"https://pith.science/pith/3DHOT62GEAVUXPRWI4X45UL4B3/bundle.json","state":"https://pith.science/pith/3DHOT62GEAVUXPRWI4X45UL4B3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DHOT62GEAVUXPRWI4X45UL4B3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3DHOT62GEAVUXPRWI4X45UL4B3","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":"e637e41d0dc5b3b287cd7829f67aa73346d7a2df5731559e995afecc0ec73d4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-11-12T06:47:43Z","title_canon_sha256":"c39b84b08fafe757b03c4d2a56e0f6b992cfc1b49d58bb74834c2244393541d6"},"schema_version":"1.0","source":{"id":"1611.03960","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03960","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03960v4","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03960","created_at":"2026-05-17T23:40:14Z"},{"alias_kind":"pith_short_12","alias_value":"3DHOT62GEAVU","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DHOT62GEAVUXPRW","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DHOT62G","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:e8878d8ce10976ecdc3bbc2da12bfd8823e3b8e9fab9f00c1dda903717bb39d8","target":"graph","created_at":"2026-05-17T23:40:14Z","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 this paper we present the study of the topology of the equipotential hypersurfaces of configuration space of the mean-field $\\phi^4$ model with a $\\mathbb{Z}_2$ symmetry. Our purpose is discovering, if any, the relation between the second-order $\\mathbb{Z}_2$-symmetry breaking phase transition and the geometric entities mentioned above. The mean-field interaction allows us to solve analytically either the thermodynamic in the canonical ensemble or the topology by means of Morse theory. We have analyzed the results at the light of two theorems on sufficiency conditions for symmetry breaking ","authors_text":"Fabrizio Baroni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-11-12T06:47:43Z","title":"Topology of configuration space of the mean-field phi^4 model by Morse theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03960","kind":"arxiv","version":4},"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:c7694387a2f05f604d6255f0c129d27649bb7d53db8b37a1113f9501406871b3","target":"record","created_at":"2026-05-17T23:40:14Z","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":"e637e41d0dc5b3b287cd7829f67aa73346d7a2df5731559e995afecc0ec73d4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-11-12T06:47:43Z","title_canon_sha256":"c39b84b08fafe757b03c4d2a56e0f6b992cfc1b49d58bb74834c2244393541d6"},"schema_version":"1.0","source":{"id":"1611.03960","kind":"arxiv","version":4}},"canonical_sha256":"d8cee9fb46202b4bbe36472fced17c0ee4554bbd0f55fbc2657a5f6236ffad6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8cee9fb46202b4bbe36472fced17c0ee4554bbd0f55fbc2657a5f6236ffad6b","first_computed_at":"2026-05-17T23:40:14.518884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:14.518884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"622lr6Uz4MCw3YdlgS3OnPomfrdPVF2stpq+vX3y7C5+TUZBZJq96JfqD+/DhuSjJ/Xjz7rkCnHTuVFPcIWHCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:14.519805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03960","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7694387a2f05f604d6255f0c129d27649bb7d53db8b37a1113f9501406871b3","sha256:e8878d8ce10976ecdc3bbc2da12bfd8823e3b8e9fab9f00c1dda903717bb39d8"],"state_sha256":"5fa61f18d54ad603508c126cfe9a9cef34bdb761668330433cbd07865af8d58b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZ7+Cw1ISh0lb4NdBL3CLMvav1i8fuQBWcjR8CXWt7mqAdKKfOquHDDCA/ziiKC9Bhdo1b2y/kqVcXPNKBzjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T02:19:38.781647Z","bundle_sha256":"33e4cc50f1f39fbf81b162c947158ffd731f24a3ec9f68959441e63a11815b33"}}