{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3KRHDNLIPF74RHQBNCKH4YB3GT","short_pith_number":"pith:3KRHDNLI","canonical_record":{"source":{"id":"1211.1349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T18:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"f13a8fee0402fb5612cebc66fbc9547a51fab66ed89db6fe3496316f5b80d120","abstract_canon_sha256":"b7bd7a1dad15e174407f71d71ca75139d7f958008e89e094befda69ef0583bd2"},"schema_version":"1.0"},"canonical_sha256":"daa271b568797fc89e0168947e603b34dbdd7b30b1910788fe3dac52d591226b","source":{"kind":"arxiv","id":"1211.1349","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1349","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1349v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1349","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"3KRHDNLIPF74","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KRHDNLIPF74RHQB","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KRHDNLI","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3KRHDNLIPF74RHQBNCKH4YB3GT","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1349","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T18:50:38Z","cross_cats_sorted":[],"title_canon_sha256":"f13a8fee0402fb5612cebc66fbc9547a51fab66ed89db6fe3496316f5b80d120","abstract_canon_sha256":"b7bd7a1dad15e174407f71d71ca75139d7f958008e89e094befda69ef0583bd2"},"schema_version":"1.0"},"canonical_sha256":"daa271b568797fc89e0168947e603b34dbdd7b30b1910788fe3dac52d591226b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:21.783329Z","signature_b64":"+yLBBg7z7Bm6zijVMY9K07COFYb5bR94MNDEV7ejB58i41TRItY0tTZEXwg/8m/khJcD6eERP7SZj+9fepMoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"daa271b568797fc89e0168947e603b34dbdd7b30b1910788fe3dac52d591226b","last_reissued_at":"2026-05-18T03:41:21.782772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:21.782772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1349","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":"2026-05-18T03:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkAMM7AEl9oJFzQTtpflpbyrTYtqbxL7quh1hIkn0/9M9Lzo46If6mkzQ5bmvcU7X59iFl+MX27izABL5RlFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:43:50.427585Z"},"content_sha256":"1bc720123f22cf51d84d627aa51f9f525065a6272831ffbb5da1b530705fbd1e","schema_version":"1.0","event_id":"sha256:1bc720123f22cf51d84d627aa51f9f525065a6272831ffbb5da1b530705fbd1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3KRHDNLIPF74RHQBNCKH4YB3GT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some results about ergodicity in shape for a crystal growth model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}ois Ezanno","submitted_at":"2012-11-06T18:50:38Z","abstract_excerpt":"We study a crystal growth Markov model proposed by Gates and Westcott (\\cite{Kinetics1}, \\cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model is parametrized by three values $(\\beta_i, i=0,1,2)$ corresponding to depositions on three different types of sites. The main problem is to determine, for the shape of the crystal, when recurrence and when ergodicity do occur. In \\cite{AMS} and \\cite{MarkovModels} sufficient conditions are given both for ergodicity and transience. We establish some improved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1349","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":"2026-05-18T03:41:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L1fVsrflOcAfPob7K3ifFZD75zVhtsMM40H1gV8VV0jh5HeMICKPPUsM4EDwC12GIkkUtLaWbGpGRwNpVHoKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T08:43:50.427925Z"},"content_sha256":"5de85b47e3d793ab6582169537e58cf3519f7444a50afcc7fcec8805f5f85d81","schema_version":"1.0","event_id":"sha256:5de85b47e3d793ab6582169537e58cf3519f7444a50afcc7fcec8805f5f85d81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/bundle.json","state_url":"https://pith.science/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/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":"2026-07-02T08:43:50Z","links":{"resolver":"https://pith.science/pith/3KRHDNLIPF74RHQBNCKH4YB3GT","bundle":"https://pith.science/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/bundle.json","state":"https://pith.science/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3KRHDNLIPF74RHQBNCKH4YB3GT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3KRHDNLIPF74RHQBNCKH4YB3GT","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":"b7bd7a1dad15e174407f71d71ca75139d7f958008e89e094befda69ef0583bd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T18:50:38Z","title_canon_sha256":"f13a8fee0402fb5612cebc66fbc9547a51fab66ed89db6fe3496316f5b80d120"},"schema_version":"1.0","source":{"id":"1211.1349","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1349","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1349v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1349","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"3KRHDNLIPF74","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3KRHDNLIPF74RHQB","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3KRHDNLI","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:5de85b47e3d793ab6582169537e58cf3519f7444a50afcc7fcec8805f5f85d81","target":"graph","created_at":"2026-05-18T03:41:21Z","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 study a crystal growth Markov model proposed by Gates and Westcott (\\cite{Kinetics1}, \\cite{Kinetics2}). This is an aggregation process where particles are packed in a square lattice accordingly to prescribed deposition rates. This model is parametrized by three values $(\\beta_i, i=0,1,2)$ corresponding to depositions on three different types of sites. The main problem is to determine, for the shape of the crystal, when recurrence and when ergodicity do occur. In \\cite{AMS} and \\cite{MarkovModels} sufficient conditions are given both for ergodicity and transience. We establish some improved","authors_text":"Fran\\c{c}ois Ezanno","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T18:50:38Z","title":"Some results about ergodicity in shape for a crystal growth model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1349","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":"sha256:1bc720123f22cf51d84d627aa51f9f525065a6272831ffbb5da1b530705fbd1e","target":"record","created_at":"2026-05-18T03:41:21Z","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":"b7bd7a1dad15e174407f71d71ca75139d7f958008e89e094befda69ef0583bd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-06T18:50:38Z","title_canon_sha256":"f13a8fee0402fb5612cebc66fbc9547a51fab66ed89db6fe3496316f5b80d120"},"schema_version":"1.0","source":{"id":"1211.1349","kind":"arxiv","version":1}},"canonical_sha256":"daa271b568797fc89e0168947e603b34dbdd7b30b1910788fe3dac52d591226b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"daa271b568797fc89e0168947e603b34dbdd7b30b1910788fe3dac52d591226b","first_computed_at":"2026-05-18T03:41:21.782772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:21.782772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+yLBBg7z7Bm6zijVMY9K07COFYb5bR94MNDEV7ejB58i41TRItY0tTZEXwg/8m/khJcD6eERP7SZj+9fepMoAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:21.783329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1349","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bc720123f22cf51d84d627aa51f9f525065a6272831ffbb5da1b530705fbd1e","sha256:5de85b47e3d793ab6582169537e58cf3519f7444a50afcc7fcec8805f5f85d81"],"state_sha256":"300c895c6bd6f878ad5990a000ec1c721656dc4fa46d2d1c44bfb5a6b2643ec5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NN8cJfDMkIbiyqp6u/psteUXNB75hOZbmFwisKfh+jM9xc8/Hw0PMAu9kIEY3Z/TALH1YZnOZGWMvuxDiJOqAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T08:43:50.429715Z","bundle_sha256":"a2a7d8746588648398ddee3f7a8961bfae0e35a162e7c450aa3fc81d69bef14e"}}