{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HBSUP365WEUJUAJSIGARCLZEAC","short_pith_number":"pith:HBSUP365","canonical_record":{"source":{"id":"1308.3959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T09:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"d31e86f0b0081c228a9cc4f6ee3b7b41075976023a413e22295f884edf44f5aa","abstract_canon_sha256":"d5f4e4efdf1eab735fe46d12840445b4d64bfa92fe575cbc038d67bf6c543824"},"schema_version":"1.0"},"canonical_sha256":"386547efddb1289a01324181112f240097f93fc9714b351731c7a191178e6c26","source":{"kind":"arxiv","id":"1308.3959","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3959","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3959v1","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3959","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"HBSUP365WEUJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HBSUP365WEUJUAJS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HBSUP365","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HBSUP365WEUJUAJSIGARCLZEAC","target":"record","payload":{"canonical_record":{"source":{"id":"1308.3959","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T09:11:47Z","cross_cats_sorted":[],"title_canon_sha256":"d31e86f0b0081c228a9cc4f6ee3b7b41075976023a413e22295f884edf44f5aa","abstract_canon_sha256":"d5f4e4efdf1eab735fe46d12840445b4d64bfa92fe575cbc038d67bf6c543824"},"schema_version":"1.0"},"canonical_sha256":"386547efddb1289a01324181112f240097f93fc9714b351731c7a191178e6c26","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:35.163801Z","signature_b64":"NlAB5C7v8VJNgKC1XCbzVZM+pf4cLGmY8o6DVSKWZXPH4Rxcwvhqx0c59CJ93zkKPcZgDCG/qCITYLTlsS86BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"386547efddb1289a01324181112f240097f93fc9714b351731c7a191178e6c26","last_reissued_at":"2026-05-18T03:15:35.163101Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:35.163101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.3959","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":"2026-05-18T03:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rz+lojahrn6Uxdqb9VPR22vmFbi4Yyz06F5ADGOnDskz+W851VkrDvvv6xGLF3g/STzL3MYbav5tcKVKWMtdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:29:58.340025Z"},"content_sha256":"e16e8050af6319786ef199bff47607c06f3975338e93cfb2460e6cea9c8cd201","schema_version":"1.0","event_id":"sha256:e16e8050af6319786ef199bff47607c06f3975338e93cfb2460e6cea9c8cd201"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HBSUP365WEUJUAJSIGARCLZEAC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spontaneous breaking of rotational symmetry in the presence of defects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Franz Merkl, Markus Heydenreich, Silke W.W. Rolles","submitted_at":"2013-08-19T09:11:47Z","abstract_excerpt":"We prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3959","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":"2026-05-18T03:15:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVXVhHOGfXimO+IrLnVvRePvAMKfbvSl99K81S5ToIHd+0F9P3m90lGxMGxxgoPDLdeOhH/9AJ+hO55+GctKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T22:29:58.340379Z"},"content_sha256":"bbcd3300d11692ff22b0c342f220029b25d1d453a5f9d5ee5d665f9fbf31cc75","schema_version":"1.0","event_id":"sha256:bbcd3300d11692ff22b0c342f220029b25d1d453a5f9d5ee5d665f9fbf31cc75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBSUP365WEUJUAJSIGARCLZEAC/bundle.json","state_url":"https://pith.science/pith/HBSUP365WEUJUAJSIGARCLZEAC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBSUP365WEUJUAJSIGARCLZEAC/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":"2026-06-25T22:29:58Z","links":{"resolver":"https://pith.science/pith/HBSUP365WEUJUAJSIGARCLZEAC","bundle":"https://pith.science/pith/HBSUP365WEUJUAJSIGARCLZEAC/bundle.json","state":"https://pith.science/pith/HBSUP365WEUJUAJSIGARCLZEAC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBSUP365WEUJUAJSIGARCLZEAC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HBSUP365WEUJUAJSIGARCLZEAC","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":"d5f4e4efdf1eab735fe46d12840445b4d64bfa92fe575cbc038d67bf6c543824","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T09:11:47Z","title_canon_sha256":"d31e86f0b0081c228a9cc4f6ee3b7b41075976023a413e22295f884edf44f5aa"},"schema_version":"1.0","source":{"id":"1308.3959","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3959","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3959v1","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3959","created_at":"2026-05-18T03:15:35Z"},{"alias_kind":"pith_short_12","alias_value":"HBSUP365WEUJ","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HBSUP365WEUJUAJS","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HBSUP365","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:bbcd3300d11692ff22b0c342f220029b25d1d453a5f9d5ee5d665f9fbf31cc75","target":"graph","created_at":"2026-05-18T03:15:35Z","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 prove a strong form of spontaneous breaking of rotational symmetry for a simple model of two-dimensional crystals with random defects in thermal equilibrium at low temperature. The defects consist of isolated missing atoms.","authors_text":"Franz Merkl, Markus Heydenreich, Silke W.W. Rolles","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T09:11:47Z","title":"Spontaneous breaking of rotational symmetry in the presence of defects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3959","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:e16e8050af6319786ef199bff47607c06f3975338e93cfb2460e6cea9c8cd201","target":"record","created_at":"2026-05-18T03:15:35Z","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":"d5f4e4efdf1eab735fe46d12840445b4d64bfa92fe575cbc038d67bf6c543824","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-19T09:11:47Z","title_canon_sha256":"d31e86f0b0081c228a9cc4f6ee3b7b41075976023a413e22295f884edf44f5aa"},"schema_version":"1.0","source":{"id":"1308.3959","kind":"arxiv","version":1}},"canonical_sha256":"386547efddb1289a01324181112f240097f93fc9714b351731c7a191178e6c26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"386547efddb1289a01324181112f240097f93fc9714b351731c7a191178e6c26","first_computed_at":"2026-05-18T03:15:35.163101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:35.163101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NlAB5C7v8VJNgKC1XCbzVZM+pf4cLGmY8o6DVSKWZXPH4Rxcwvhqx0c59CJ93zkKPcZgDCG/qCITYLTlsS86BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:35.163801Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3959","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e16e8050af6319786ef199bff47607c06f3975338e93cfb2460e6cea9c8cd201","sha256:bbcd3300d11692ff22b0c342f220029b25d1d453a5f9d5ee5d665f9fbf31cc75"],"state_sha256":"8bd27ce5f36f1f6708a5b7d9cae8894f44b2260a3b85155993a40a77255c2214"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BsPKFkI5zRfkV61SygZFNHvHwdvUyoNs9c0GAuUxJo293KEcxAAJ3RYcwBWAzrZto3gcIqgPuJWWOF9YFiveCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T22:29:58.342339Z","bundle_sha256":"96765e89397209ed49fc81d483212f9c10f8f26ef51a85699915de6df73bb4dc"}}