{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OL7VGLULYKEBEPB2TVWKE4KWBR","short_pith_number":"pith:OL7VGLUL","canonical_record":{"source":{"id":"1509.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T12:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"28cb96b3c5c116d57181be4348216f2975fdfe63b9b9d69fbb5049d78ebe9379","abstract_canon_sha256":"645f7b13ac95723e9cfb2f78120cf6b0ec7efa6b595c735961d70f46651c4686"},"schema_version":"1.0"},"canonical_sha256":"72ff532e8bc288123c3a9d6ca271560c68d8ca730976b48c1c54660758fbcf32","source":{"kind":"arxiv","id":"1509.06946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06946","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06946v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06946","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"OL7VGLULYKEB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OL7VGLULYKEBEPB2","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OL7VGLUL","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OL7VGLULYKEBEPB2TVWKE4KWBR","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T12:44:42Z","cross_cats_sorted":[],"title_canon_sha256":"28cb96b3c5c116d57181be4348216f2975fdfe63b9b9d69fbb5049d78ebe9379","abstract_canon_sha256":"645f7b13ac95723e9cfb2f78120cf6b0ec7efa6b595c735961d70f46651c4686"},"schema_version":"1.0"},"canonical_sha256":"72ff532e8bc288123c3a9d6ca271560c68d8ca730976b48c1c54660758fbcf32","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.439510Z","signature_b64":"G65a8YwJtIPxtFBg2S/1oy1Gkg+GziImPzAR1UWqk9qKZzeLrTRpA6Ogu9GJvwTT1aOAoZxbjzFTFCnSCzkjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72ff532e8bc288123c3a9d6ca271560c68d8ca730976b48c1c54660758fbcf32","last_reissued_at":"2026-05-18T01:32:17.438845Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.438845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06946","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":"2026-05-18T01:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ovm0EBp+wsYvRIEOrJ8HtqPxDfBEPsE8edPNDlBU+Vz44dk11OMWqIzdeH8OKrUPU2KRLw5Uz+SHSXr6A65xDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:14:16.632770Z"},"content_sha256":"89b4f65b9bf37b0c1d04b50233f8eb315f5bb4235830576d513a252dfaa9c491","schema_version":"1.0","event_id":"sha256:89b4f65b9bf37b0c1d04b50233f8eb315f5bb4235830576d513a252dfaa9c491"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OL7VGLULYKEBEPB2TVWKE4KWBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic shape in a continuum growth model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Maria Deijfen","submitted_at":"2015-09-23T12:44:42Z","abstract_excerpt":"A continuum growth model is introduced. The state at time $t$, $S_t$, is a subset of $\\mathbb{R}^d$ and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs somewhere in $S_t$ after an exponentially distributed time with expected value $|S_t|^{-1}$ and the location of the outburst is uniformly distributed over $S_t$. The main result is that if the distribution of the radii of the outburst balls has bounded support, then $S_t$ grows linearly and $S_t/t$ has a non-random shape as $t\\rightarrow \\infty$. Due to rota"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06946","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":"2026-05-18T01:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GsfIoyyb0t7n76bYlKymhqCNjIdLGVVDBRM7Jemr07Mzquxsecoqna9WtXC7G1Wzgvm7W/vmK4gKPvkiykE7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:14:16.633104Z"},"content_sha256":"393d626fb0201e7b43594527c2d14cff1952efca5a3eab8b30878c9d497117eb","schema_version":"1.0","event_id":"sha256:393d626fb0201e7b43594527c2d14cff1952efca5a3eab8b30878c9d497117eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/bundle.json","state_url":"https://pith.science/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/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":"2026-06-20T06:14:16Z","links":{"resolver":"https://pith.science/pith/OL7VGLULYKEBEPB2TVWKE4KWBR","bundle":"https://pith.science/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/bundle.json","state":"https://pith.science/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OL7VGLULYKEBEPB2TVWKE4KWBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OL7VGLULYKEBEPB2TVWKE4KWBR","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":"645f7b13ac95723e9cfb2f78120cf6b0ec7efa6b595c735961d70f46651c4686","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T12:44:42Z","title_canon_sha256":"28cb96b3c5c116d57181be4348216f2975fdfe63b9b9d69fbb5049d78ebe9379"},"schema_version":"1.0","source":{"id":"1509.06946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06946","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06946v1","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06946","created_at":"2026-05-18T01:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"OL7VGLULYKEB","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OL7VGLULYKEBEPB2","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OL7VGLUL","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:393d626fb0201e7b43594527c2d14cff1952efca5a3eab8b30878c9d497117eb","target":"graph","created_at":"2026-05-18T01:32:17Z","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":"A continuum growth model is introduced. The state at time $t$, $S_t$, is a subset of $\\mathbb{R}^d$ and consists of a connected union of randomly sized Euclidean balls, which emerge from outbursts at their center points. An outburst occurs somewhere in $S_t$ after an exponentially distributed time with expected value $|S_t|^{-1}$ and the location of the outburst is uniformly distributed over $S_t$. The main result is that if the distribution of the radii of the outburst balls has bounded support, then $S_t$ grows linearly and $S_t/t$ has a non-random shape as $t\\rightarrow \\infty$. Due to rota","authors_text":"Maria Deijfen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T12:44:42Z","title":"Asymptotic shape in a continuum growth model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06946","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":"sha256:89b4f65b9bf37b0c1d04b50233f8eb315f5bb4235830576d513a252dfaa9c491","target":"record","created_at":"2026-05-18T01:32:17Z","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":"645f7b13ac95723e9cfb2f78120cf6b0ec7efa6b595c735961d70f46651c4686","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-23T12:44:42Z","title_canon_sha256":"28cb96b3c5c116d57181be4348216f2975fdfe63b9b9d69fbb5049d78ebe9379"},"schema_version":"1.0","source":{"id":"1509.06946","kind":"arxiv","version":1}},"canonical_sha256":"72ff532e8bc288123c3a9d6ca271560c68d8ca730976b48c1c54660758fbcf32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72ff532e8bc288123c3a9d6ca271560c68d8ca730976b48c1c54660758fbcf32","first_computed_at":"2026-05-18T01:32:17.438845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:17.438845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G65a8YwJtIPxtFBg2S/1oy1Gkg+GziImPzAR1UWqk9qKZzeLrTRpA6Ogu9GJvwTT1aOAoZxbjzFTFCnSCzkjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:17.439510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89b4f65b9bf37b0c1d04b50233f8eb315f5bb4235830576d513a252dfaa9c491","sha256:393d626fb0201e7b43594527c2d14cff1952efca5a3eab8b30878c9d497117eb"],"state_sha256":"f9cc24b90de202f018474353d4a87881b973ba7e48ed040e8c14d2b81540c749"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bNi1lPpGyk4IQRToQ1O7UXR+nfgaju0Ys+n9wFG9xcXmjNe9p+X8iMZ9EPno2LmlZ+1C82ty0K0mYhA1AZVWAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:14:16.634969Z","bundle_sha256":"8a48948ff27e63f24995a37bdef572d323db901a8fd1caa22de0eb952113cd81"}}