{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BSTGPNIPMCODOUGIA6WYDN3QWK","short_pith_number":"pith:BSTGPNIP","canonical_record":{"source":{"id":"1305.0254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T19:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"e92bbfaeea81d61fc4b32c2903aed799ed7c42c86e7a58943e2d0a368dded650","abstract_canon_sha256":"f701606f3817c1dee2d6189ad943da32e01f1e2ac01ca86aaac40f12e8eb4905"},"schema_version":"1.0"},"canonical_sha256":"0ca667b50f609c3750c807ad81b770b28f93fd0a486b3301a020e06de33cec78","source":{"kind":"arxiv","id":"1305.0254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0254","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0254v1","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0254","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"BSTGPNIPMCOD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSTGPNIPMCODOUGI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSTGPNIP","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BSTGPNIPMCODOUGIA6WYDN3QWK","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T19:40:59Z","cross_cats_sorted":[],"title_canon_sha256":"e92bbfaeea81d61fc4b32c2903aed799ed7c42c86e7a58943e2d0a368dded650","abstract_canon_sha256":"f701606f3817c1dee2d6189ad943da32e01f1e2ac01ca86aaac40f12e8eb4905"},"schema_version":"1.0"},"canonical_sha256":"0ca667b50f609c3750c807ad81b770b28f93fd0a486b3301a020e06de33cec78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:41.512472Z","signature_b64":"kuFsBpEAbd8Gw7LYOJKoC361k+dlS8AeN1A6B3tw3ep3F4Sn1AiOtfCJaXAAi67bK8A5rUfFT5AHW+HCNGUhBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ca667b50f609c3750c807ad81b770b28f93fd0a486b3301a020e06de33cec78","last_reissued_at":"2026-05-18T03:26:41.511773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:41.511773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0254","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":"2026-05-18T03:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jml5/2E5DnTOnQBZomzoxtlJyHLyBS7aMBBsXhI/oaZO3mbhTZdJc1SLUg6/YkKBQ0oEL6K21DL0//qrso3UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:48:56.375167Z"},"content_sha256":"f61f370436dc569e472e030391b6553169ba8a6a605d01b08fcbe15bd93c0b50","schema_version":"1.0","event_id":"sha256:f61f370436dc569e472e030391b6553169ba8a6a605d01b08fcbe15bd93c0b50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BSTGPNIPMCODOUGIA6WYDN3QWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The shape of multidimensional Brunet--Derrida particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lee Zhuo Zhao, Nathanael Berestycki","submitted_at":"2013-05-01T19:40:59Z","abstract_excerpt":"We introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to $N > 1$, through the following selection mechanism: at all times only the $N$ fittest particles survive, while all the other particles are removed. Fitness is measured with respect to some given score function $s:\\R^d \\to \\R$. For some choices of the function $s$, it is proved that the cloud of particles travels at positive speed in some possibly random direction. In the case where $s$ is linear, we show under some assumptions on the ini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0254","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":"2026-05-18T03:26:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gw0a0poHs1eJl0HECzdlTf+VSWqRFj0c5g6uCwvnPaVqVsm4E6eQwIduFDT8vChd8uD+88K3oyJsEnXnJNFBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:48:56.375532Z"},"content_sha256":"a0f9596946c34d30a0c3ea6105ec0f180b137c6a265f2ad5fc439d73819761ce","schema_version":"1.0","event_id":"sha256:a0f9596946c34d30a0c3ea6105ec0f180b137c6a265f2ad5fc439d73819761ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/bundle.json","state_url":"https://pith.science/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/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":"2026-06-02T07:48:56Z","links":{"resolver":"https://pith.science/pith/BSTGPNIPMCODOUGIA6WYDN3QWK","bundle":"https://pith.science/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/bundle.json","state":"https://pith.science/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSTGPNIPMCODOUGIA6WYDN3QWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BSTGPNIPMCODOUGIA6WYDN3QWK","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":"f701606f3817c1dee2d6189ad943da32e01f1e2ac01ca86aaac40f12e8eb4905","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T19:40:59Z","title_canon_sha256":"e92bbfaeea81d61fc4b32c2903aed799ed7c42c86e7a58943e2d0a368dded650"},"schema_version":"1.0","source":{"id":"1305.0254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0254","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0254v1","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0254","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"BSTGPNIPMCOD","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BSTGPNIPMCODOUGI","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BSTGPNIP","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a0f9596946c34d30a0c3ea6105ec0f180b137c6a265f2ad5fc439d73819761ce","target":"graph","created_at":"2026-05-18T03:26:41Z","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 introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to $N > 1$, through the following selection mechanism: at all times only the $N$ fittest particles survive, while all the other particles are removed. Fitness is measured with respect to some given score function $s:\\R^d \\to \\R$. For some choices of the function $s$, it is proved that the cloud of particles travels at positive speed in some possibly random direction. In the case where $s$ is linear, we show under some assumptions on the ini","authors_text":"Lee Zhuo Zhao, Nathanael Berestycki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T19:40:59Z","title":"The shape of multidimensional Brunet--Derrida particle systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0254","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:f61f370436dc569e472e030391b6553169ba8a6a605d01b08fcbe15bd93c0b50","target":"record","created_at":"2026-05-18T03:26:41Z","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":"f701606f3817c1dee2d6189ad943da32e01f1e2ac01ca86aaac40f12e8eb4905","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-01T19:40:59Z","title_canon_sha256":"e92bbfaeea81d61fc4b32c2903aed799ed7c42c86e7a58943e2d0a368dded650"},"schema_version":"1.0","source":{"id":"1305.0254","kind":"arxiv","version":1}},"canonical_sha256":"0ca667b50f609c3750c807ad81b770b28f93fd0a486b3301a020e06de33cec78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ca667b50f609c3750c807ad81b770b28f93fd0a486b3301a020e06de33cec78","first_computed_at":"2026-05-18T03:26:41.511773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:41.511773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kuFsBpEAbd8Gw7LYOJKoC361k+dlS8AeN1A6B3tw3ep3F4Sn1AiOtfCJaXAAi67bK8A5rUfFT5AHW+HCNGUhBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:41.512472Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f61f370436dc569e472e030391b6553169ba8a6a605d01b08fcbe15bd93c0b50","sha256:a0f9596946c34d30a0c3ea6105ec0f180b137c6a265f2ad5fc439d73819761ce"],"state_sha256":"7b39d72093b69b14a63ac1315563f332a1c18ea2f6b71129f067cdad3e559fd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q58kDhsUPQshtZ+6IsMzAfrYCzAR4MWheEfVKrQ0YLIuEM+dnntPTK79Wb7VgmW+OBwsRLNTDTOLpsiru8hODg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:48:56.377446Z","bundle_sha256":"2bbbb465cf85dce0540a5bc9d26ef0f6fd2bd9abee568f64cd482fa996a92bbb"}}