{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MO5DQVXGV7SXBC4A5HB6Z6CONL","short_pith_number":"pith:MO5DQVXG","canonical_record":{"source":{"id":"1512.00031","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-30T21:07:39Z","cross_cats_sorted":[],"title_canon_sha256":"7ab39ae8213253060b651e82e42e5274f45cf363e865c5b485c3d87a1c2849a1","abstract_canon_sha256":"42f77cbb8eb7bb10ca3bfba5625026f456c52a75359a9fb268e902ee5b3388aa"},"schema_version":"1.0"},"canonical_sha256":"63ba3856e6afe5708b80e9c3ecf84e6ade2881549cd282f3f88cafdaab2c8ba9","source":{"kind":"arxiv","id":"1512.00031","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00031","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00031v5","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00031","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"MO5DQVXGV7SX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MO5DQVXGV7SXBC4A","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MO5DQVXG","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MO5DQVXGV7SXBC4A5HB6Z6CONL","target":"record","payload":{"canonical_record":{"source":{"id":"1512.00031","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-30T21:07:39Z","cross_cats_sorted":[],"title_canon_sha256":"7ab39ae8213253060b651e82e42e5274f45cf363e865c5b485c3d87a1c2849a1","abstract_canon_sha256":"42f77cbb8eb7bb10ca3bfba5625026f456c52a75359a9fb268e902ee5b3388aa"},"schema_version":"1.0"},"canonical_sha256":"63ba3856e6afe5708b80e9c3ecf84e6ade2881549cd282f3f88cafdaab2c8ba9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:55.458097Z","signature_b64":"C1EGQ8kgFyfIbAUcD70ku1UeAB3CC+ZngeZTD6DlW2kZT5UE+99uW5LZAaKXqkuThi14SM19xivVW5ExNbQ4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63ba3856e6afe5708b80e9c3ecf84e6ade2881549cd282f3f88cafdaab2c8ba9","last_reissued_at":"2026-05-18T00:17:55.457424Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:55.457424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.00031","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a6nXLN3bMb5WAcprozfWd4Qbp6eJlN5FA4gEADNlYWY/3Kmk2XNmwRSjBIaFQ0NiXks7sRi7n4SsV3ohFR7mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:29:17.615195Z"},"content_sha256":"ee17f2f68fca9810f0425e619c7d3b5e61e0bc57a716cd7cd05970b9745e7d53","schema_version":"1.0","event_id":"sha256:ee17f2f68fca9810f0425e619c7d3b5e61e0bc57a716cd7cd05970b9745e7d53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MO5DQVXGV7SXBC4A5HB6Z6CONL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An invariance principle for branching diffusions in bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ellen Powell","submitted_at":"2015-11-30T21:07:39Z","abstract_excerpt":"We study branching diffusions in a bounded domain $D$ of $\\mathbb{R}^d$ in which particles are killed upon hitting the boundary $\\partial D$. It is known that any such process undergoes a phase transition when the branching rate $\\beta$ exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under appropriate rescaling. The result holds under only a mild assumption "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00031","kind":"arxiv","version":5},"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":"2026-05-18T00:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nG5nW2Yhx/UTf90ux8tuiX2D8rmRpduIPa6ZBTkkLMncJbcahLn4Clf2/85VY210EBpLCKU97webkvSq2sAADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:29:17.615654Z"},"content_sha256":"c480cef1d82cd6799352c1be84ecee75cfad5fdd1cef3f3efe3ce932d6df99ed","schema_version":"1.0","event_id":"sha256:c480cef1d82cd6799352c1be84ecee75cfad5fdd1cef3f3efe3ce932d6df99ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/bundle.json","state_url":"https://pith.science/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/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":"2026-08-04T00:29:17Z","links":{"resolver":"https://pith.science/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL","bundle":"https://pith.science/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/bundle.json","state":"https://pith.science/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MO5DQVXGV7SXBC4A5HB6Z6CONL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MO5DQVXGV7SXBC4A5HB6Z6CONL","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":"42f77cbb8eb7bb10ca3bfba5625026f456c52a75359a9fb268e902ee5b3388aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-30T21:07:39Z","title_canon_sha256":"7ab39ae8213253060b651e82e42e5274f45cf363e865c5b485c3d87a1c2849a1"},"schema_version":"1.0","source":{"id":"1512.00031","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00031","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00031v5","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00031","created_at":"2026-05-18T00:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"MO5DQVXGV7SX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MO5DQVXGV7SXBC4A","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MO5DQVXG","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:c480cef1d82cd6799352c1be84ecee75cfad5fdd1cef3f3efe3ce932d6df99ed","target":"graph","created_at":"2026-05-18T00:17:55Z","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 branching diffusions in a bounded domain $D$ of $\\mathbb{R}^d$ in which particles are killed upon hitting the boundary $\\partial D$. It is known that any such process undergoes a phase transition when the branching rate $\\beta$ exceeds a critical value: a multiple of the first eigenvalue of the generator of the diffusion. We investigate the system at criticality and show that the associated genealogical tree, when the process is conditioned to survive for a long time, converges to Aldous' Continuum Random Tree under appropriate rescaling. The result holds under only a mild assumption ","authors_text":"Ellen Powell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-30T21:07:39Z","title":"An invariance principle for branching diffusions in bounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00031","kind":"arxiv","version":5},"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:ee17f2f68fca9810f0425e619c7d3b5e61e0bc57a716cd7cd05970b9745e7d53","target":"record","created_at":"2026-05-18T00:17:55Z","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":"42f77cbb8eb7bb10ca3bfba5625026f456c52a75359a9fb268e902ee5b3388aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-30T21:07:39Z","title_canon_sha256":"7ab39ae8213253060b651e82e42e5274f45cf363e865c5b485c3d87a1c2849a1"},"schema_version":"1.0","source":{"id":"1512.00031","kind":"arxiv","version":5}},"canonical_sha256":"63ba3856e6afe5708b80e9c3ecf84e6ade2881549cd282f3f88cafdaab2c8ba9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63ba3856e6afe5708b80e9c3ecf84e6ade2881549cd282f3f88cafdaab2c8ba9","first_computed_at":"2026-05-18T00:17:55.457424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:55.457424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C1EGQ8kgFyfIbAUcD70ku1UeAB3CC+ZngeZTD6DlW2kZT5UE+99uW5LZAaKXqkuThi14SM19xivVW5ExNbQ4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:55.458097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00031","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee17f2f68fca9810f0425e619c7d3b5e61e0bc57a716cd7cd05970b9745e7d53","sha256:c480cef1d82cd6799352c1be84ecee75cfad5fdd1cef3f3efe3ce932d6df99ed"],"state_sha256":"04fa8211d3e94d59bf1f5cab3a066a6f6a0a7fd32a4e9767fb1d3f0d80ba414c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KtkBodm8zfg1HIpFmuAhMLNHTz9Vbbxg41eyJhqD8/GhyTK/K3XUZgY0v5nk2dI+alj3QXHmrWe5URLKpxSLCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T00:29:17.620862Z","bundle_sha256":"0887959b48ee1dec66c7fd9400c44332094a6a88dc8588151dead8f9fdb97208"}}