{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UCWA42APHP5ZSK7SZNNRRYV7GI","short_pith_number":"pith:UCWA42AP","canonical_record":{"source":{"id":"1811.09037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T06:45:37Z","cross_cats_sorted":[],"title_canon_sha256":"07b5cff3ecefa14a974a66416f91ce8c0598a3688ba3da940bfab8a2f7015c60","abstract_canon_sha256":"c29275540bfecb7e71a2b87a437ec0cdc996e32e96a9340bfcd9044fa0b19517"},"schema_version":"1.0"},"canonical_sha256":"a0ac0e680f3bfb992bf2cb5b18e2bf32194ec1a91b6fea2c7a1de563431a08e5","source":{"kind":"arxiv","id":"1811.09037","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09037","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09037v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09037","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"UCWA42APHP5Z","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCWA42APHP5ZSK7S","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCWA42AP","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UCWA42APHP5ZSK7SZNNRRYV7GI","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09037","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T06:45:37Z","cross_cats_sorted":[],"title_canon_sha256":"07b5cff3ecefa14a974a66416f91ce8c0598a3688ba3da940bfab8a2f7015c60","abstract_canon_sha256":"c29275540bfecb7e71a2b87a437ec0cdc996e32e96a9340bfcd9044fa0b19517"},"schema_version":"1.0"},"canonical_sha256":"a0ac0e680f3bfb992bf2cb5b18e2bf32194ec1a91b6fea2c7a1de563431a08e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:07.233040Z","signature_b64":"wlqtRUV1vv0LXWgVZHNq2QYwy7GZ1R2eJkDMibjMIe0jQ7sTxybJymITvPqIK3n6QjY2hqybNKDNAe7lSS+fCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0ac0e680f3bfb992bf2cb5b18e2bf32194ec1a91b6fea2c7a1de563431a08e5","last_reissued_at":"2026-05-18T00:00:07.232460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:07.232460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09037","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":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VpOzgvULzVtvrgSu3OAHdjBNYaO5nZMXQ7BIfs5CbpF1hRs/qPGQyhMx3DGij20y3B+Uzjvw2XLQuQJiwW7TCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:18:54.763679Z"},"content_sha256":"5c451f5d061ccad92c8b58ef74157a901c7bd75c885f53e1f067edbb4db07f58","schema_version":"1.0","event_id":"sha256:5c451f5d061ccad92c8b58ef74157a901c7bd75c885f53e1f067edbb4db07f58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UCWA42APHP5ZSK7SZNNRRYV7GI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large deviations for local mass of branching Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mehmet \\\"Oz","submitted_at":"2018-11-22T06:45:37Z","abstract_excerpt":"We study the local mass of a dyadic branching Brownian motion $Z$ evolving in $\\mathbb{R}^d$. By 'local mass,' we refer to the number of particles of $Z$ that fall inside a ball with fixed radius and time-dependent center, lying in the 'subcritical' zone. Using the strong law of large numbers for the local mass of branching Brownian motion and elementary geometric arguments, we find large deviation results giving the asymptotic behavior of the probability that the local mass is atypically small on an exponential scale. As corollaries, we obtain an asymptotic result for the probability of absen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09037","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":"2026-05-18T00:00:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yvZMZFndklT2NMakI0ohYZWCnXZsMGvDitCsU2feIY9zy14+4jFbU6Pm/skgcuJOzBvagliD5HJIsaEMNxOqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:18:54.764005Z"},"content_sha256":"e6d4b9a792f55f60f714b22758f2f0049451a538d3694ea011a60044b3789546","schema_version":"1.0","event_id":"sha256:e6d4b9a792f55f60f714b22758f2f0049451a538d3694ea011a60044b3789546"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/bundle.json","state_url":"https://pith.science/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/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":"2026-06-30T16:18:54Z","links":{"resolver":"https://pith.science/pith/UCWA42APHP5ZSK7SZNNRRYV7GI","bundle":"https://pith.science/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/bundle.json","state":"https://pith.science/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCWA42APHP5ZSK7SZNNRRYV7GI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UCWA42APHP5ZSK7SZNNRRYV7GI","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":"c29275540bfecb7e71a2b87a437ec0cdc996e32e96a9340bfcd9044fa0b19517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T06:45:37Z","title_canon_sha256":"07b5cff3ecefa14a974a66416f91ce8c0598a3688ba3da940bfab8a2f7015c60"},"schema_version":"1.0","source":{"id":"1811.09037","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09037","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09037v1","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09037","created_at":"2026-05-18T00:00:07Z"},{"alias_kind":"pith_short_12","alias_value":"UCWA42APHP5Z","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UCWA42APHP5ZSK7S","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UCWA42AP","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:e6d4b9a792f55f60f714b22758f2f0049451a538d3694ea011a60044b3789546","target":"graph","created_at":"2026-05-18T00:00:07Z","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 the local mass of a dyadic branching Brownian motion $Z$ evolving in $\\mathbb{R}^d$. By 'local mass,' we refer to the number of particles of $Z$ that fall inside a ball with fixed radius and time-dependent center, lying in the 'subcritical' zone. Using the strong law of large numbers for the local mass of branching Brownian motion and elementary geometric arguments, we find large deviation results giving the asymptotic behavior of the probability that the local mass is atypically small on an exponential scale. As corollaries, we obtain an asymptotic result for the probability of absen","authors_text":"Mehmet \\\"Oz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T06:45:37Z","title":"Large deviations for local mass of branching Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09037","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":"sha256:5c451f5d061ccad92c8b58ef74157a901c7bd75c885f53e1f067edbb4db07f58","target":"record","created_at":"2026-05-18T00:00:07Z","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":"c29275540bfecb7e71a2b87a437ec0cdc996e32e96a9340bfcd9044fa0b19517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-22T06:45:37Z","title_canon_sha256":"07b5cff3ecefa14a974a66416f91ce8c0598a3688ba3da940bfab8a2f7015c60"},"schema_version":"1.0","source":{"id":"1811.09037","kind":"arxiv","version":1}},"canonical_sha256":"a0ac0e680f3bfb992bf2cb5b18e2bf32194ec1a91b6fea2c7a1de563431a08e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ac0e680f3bfb992bf2cb5b18e2bf32194ec1a91b6fea2c7a1de563431a08e5","first_computed_at":"2026-05-18T00:00:07.232460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:07.232460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wlqtRUV1vv0LXWgVZHNq2QYwy7GZ1R2eJkDMibjMIe0jQ7sTxybJymITvPqIK3n6QjY2hqybNKDNAe7lSS+fCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:07.233040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09037","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c451f5d061ccad92c8b58ef74157a901c7bd75c885f53e1f067edbb4db07f58","sha256:e6d4b9a792f55f60f714b22758f2f0049451a538d3694ea011a60044b3789546"],"state_sha256":"5b913bce42cd41875bb454b956464c0724ab4fcc02a4a0fde012ca4c0d5a2516"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kohpAzRE7uePaD7BjP3xdy3GvNOSpnMlbjLZkyPD5xaRbX34g19Gylqvj9El+wl1gVWkAR0YyeeudlGUAt2uDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T16:18:54.765722Z","bundle_sha256":"529845fde389909681fde6e10e039ab4ac7e7ca8cb6a6ddffe91141186a48563"}}