{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TN52D5BPHTICDA27MBJ7OWOEIU","short_pith_number":"pith:TN52D5BP","canonical_record":{"source":{"id":"1509.07672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-25T10:59:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"889942b42ce0cc731c35120cfcec5598dd1dde0047b507b14d0acfd86a1f5f22","abstract_canon_sha256":"393b72937de01bf1366a7b00e2da1a813f63f09957b4c16d77159136b851ee02"},"schema_version":"1.0"},"canonical_sha256":"9b7ba1f42f3cd021835f6053f759c44500ec5a2f353bca5bbcd54aa417c74cf2","source":{"kind":"arxiv","id":"1509.07672","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07672","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07672v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07672","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"TN52D5BPHTIC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TN52D5BPHTICDA27","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TN52D5BP","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TN52D5BPHTICDA27MBJ7OWOEIU","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07672","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-25T10:59:42Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"889942b42ce0cc731c35120cfcec5598dd1dde0047b507b14d0acfd86a1f5f22","abstract_canon_sha256":"393b72937de01bf1366a7b00e2da1a813f63f09957b4c16d77159136b851ee02"},"schema_version":"1.0"},"canonical_sha256":"9b7ba1f42f3cd021835f6053f759c44500ec5a2f353bca5bbcd54aa417c74cf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:04.193958Z","signature_b64":"Q7ggvgf1XkUJ+2dlruRlBBkDODR1iK5wgNeeSSWcSQa02g3obQvPCdE8dTgPNYeH2UsCyD5cU5Oms3DwRGHeBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b7ba1f42f3cd021835f6053f759c44500ec5a2f353bca5bbcd54aa417c74cf2","last_reissued_at":"2026-05-18T01:04:04.193428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:04.193428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07672","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RO2FpvFkXYnzhrr2bSRexBPi+gYZFi84UO1eqUe1zdJ0m3o1nqpNflRQOSnzsb1U3Ieswja/xJMf7VxPP0x0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:43:42.015001Z"},"content_sha256":"c4a7ec82f1d86622cd694691adcec5f42dddca293cc2e4fec2fc7029ae3af9c3","schema_version":"1.0","event_id":"sha256:c4a7ec82f1d86622cd694691adcec5f42dddca293cc2e4fec2fc7029ae3af9c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TN52D5BPHTICDA27MBJ7OWOEIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Condensation and symmetry-breaking in the zero-range process with weak site disorder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"C\\'ecile Mailler, Daniel Ueltschi, Peter M\\\"orters","submitted_at":"2015-09-25T10:59:42Z","abstract_excerpt":"Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godr\\`eche and Luck by showing, for a zero range process with weak site disorder, that there exists a phase where condensation occurs with an intermediate type of symmetry-breaki"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07672","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":"2026-05-18T01:04:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQrTM7lQn4wnyFsiaf58qdOZ+Ek7bWrLRWfleyoMW14FnYWez7Nf+x50rRMs9DsoHgF5vmtjwLQ4st9bz4qWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:43:42.015398Z"},"content_sha256":"957b7fcd5c606da756c068115cc3d6203c53c1d7fe0177b39e1d2ec609e56d9f","schema_version":"1.0","event_id":"sha256:957b7fcd5c606da756c068115cc3d6203c53c1d7fe0177b39e1d2ec609e56d9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TN52D5BPHTICDA27MBJ7OWOEIU/bundle.json","state_url":"https://pith.science/pith/TN52D5BPHTICDA27MBJ7OWOEIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TN52D5BPHTICDA27MBJ7OWOEIU/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":"2026-05-30T08:43:42Z","links":{"resolver":"https://pith.science/pith/TN52D5BPHTICDA27MBJ7OWOEIU","bundle":"https://pith.science/pith/TN52D5BPHTICDA27MBJ7OWOEIU/bundle.json","state":"https://pith.science/pith/TN52D5BPHTICDA27MBJ7OWOEIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TN52D5BPHTICDA27MBJ7OWOEIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TN52D5BPHTICDA27MBJ7OWOEIU","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":"393b72937de01bf1366a7b00e2da1a813f63f09957b4c16d77159136b851ee02","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-25T10:59:42Z","title_canon_sha256":"889942b42ce0cc731c35120cfcec5598dd1dde0047b507b14d0acfd86a1f5f22"},"schema_version":"1.0","source":{"id":"1509.07672","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07672","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07672v1","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07672","created_at":"2026-05-18T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"TN52D5BPHTIC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TN52D5BPHTICDA27","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TN52D5BP","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:957b7fcd5c606da756c068115cc3d6203c53c1d7fe0177b39e1d2ec609e56d9f","target":"graph","created_at":"2026-05-18T01:04:04Z","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":"Condensation phenomena in particle systems typically occur as one of two distinct types: either as a spontaneous symmetry breaking in a homogeneous system, in which particle interactions enforce condensation in a randomly located site, or as an explicit symmetry breaking in a system with background disorder, in which particles condensate in the site of extremal disorder. In this paper we confirm a recent conjecture by Godr\\`eche and Luck by showing, for a zero range process with weak site disorder, that there exists a phase where condensation occurs with an intermediate type of symmetry-breaki","authors_text":"C\\'ecile Mailler, Daniel Ueltschi, Peter M\\\"orters","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-25T10:59:42Z","title":"Condensation and symmetry-breaking in the zero-range process with weak site disorder"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07672","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:c4a7ec82f1d86622cd694691adcec5f42dddca293cc2e4fec2fc7029ae3af9c3","target":"record","created_at":"2026-05-18T01:04:04Z","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":"393b72937de01bf1366a7b00e2da1a813f63f09957b4c16d77159136b851ee02","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-25T10:59:42Z","title_canon_sha256":"889942b42ce0cc731c35120cfcec5598dd1dde0047b507b14d0acfd86a1f5f22"},"schema_version":"1.0","source":{"id":"1509.07672","kind":"arxiv","version":1}},"canonical_sha256":"9b7ba1f42f3cd021835f6053f759c44500ec5a2f353bca5bbcd54aa417c74cf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b7ba1f42f3cd021835f6053f759c44500ec5a2f353bca5bbcd54aa417c74cf2","first_computed_at":"2026-05-18T01:04:04.193428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:04.193428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7ggvgf1XkUJ+2dlruRlBBkDODR1iK5wgNeeSSWcSQa02g3obQvPCdE8dTgPNYeH2UsCyD5cU5Oms3DwRGHeBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:04.193958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07672","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4a7ec82f1d86622cd694691adcec5f42dddca293cc2e4fec2fc7029ae3af9c3","sha256:957b7fcd5c606da756c068115cc3d6203c53c1d7fe0177b39e1d2ec609e56d9f"],"state_sha256":"4a54d3f63f155640cac9868ad1450384ec67f13164082930189d8ee04afe55e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uOf5hcd91pEVFeLNA+irhQZOTb5r4imjQXKWTVgTgz/LKhA1MEoyF0DKFweZrT1I1TyGyrYbfUIcnf/qXlYsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:43:42.017599Z","bundle_sha256":"9440cd41c409e5c3994f4217b98d2716811e4ba931e9e8f15f19ba3cfd1e2071"}}