{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LPKUARC6OUZEUDR6TNXRLQ63EJ","short_pith_number":"pith:LPKUARC6","canonical_record":{"source":{"id":"1711.05674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-15T17:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"0b2277264f7345286c23c8706acd7eab3bcb66e732d3642f889119e20cfd0e32","abstract_canon_sha256":"725234acee8cf05154f9f6fb7e64d547c1670be02bc808c96cccde1c3441a539"},"schema_version":"1.0"},"canonical_sha256":"5bd540445e75324a0e3e9b6f15c3db225ed29fe03ff7734ce469dddb3422d7d2","source":{"kind":"arxiv","id":"1711.05674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05674","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05674v1","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05674","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"pith_short_12","alias_value":"LPKUARC6OUZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LPKUARC6OUZEUDR6","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LPKUARC6","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LPKUARC6OUZEUDR6TNXRLQ63EJ","target":"record","payload":{"canonical_record":{"source":{"id":"1711.05674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-15T17:07:43Z","cross_cats_sorted":[],"title_canon_sha256":"0b2277264f7345286c23c8706acd7eab3bcb66e732d3642f889119e20cfd0e32","abstract_canon_sha256":"725234acee8cf05154f9f6fb7e64d547c1670be02bc808c96cccde1c3441a539"},"schema_version":"1.0"},"canonical_sha256":"5bd540445e75324a0e3e9b6f15c3db225ed29fe03ff7734ce469dddb3422d7d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:29.240609Z","signature_b64":"x286yJQzzH3cFxrNN8YovoXzmlMPhWYtA6ibcuRRieBa0+c1Kz5HCD4oTwoTq4K0BnrAcLG9Ny+APXAp3P/WCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bd540445e75324a0e3e9b6f15c3db225ed29fe03ff7734ce469dddb3422d7d2","last_reissued_at":"2026-05-18T00:30:29.240168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:29.240168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.05674","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":"2026-05-18T00:30:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m55lfb4C0FJhiSIhqvqpPeKWh3UFM5n9MtGnpizE0+lDv8lgsU8yjMx1pqNZy5wU1oApcmEqEuAUkdSMO9ZVDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:44:00.147075Z"},"content_sha256":"bd65f882cc776a9c836b613f82eb0193383de8e6c1854faa86907e5a0bf8f734","schema_version":"1.0","event_id":"sha256:bd65f882cc776a9c836b613f82eb0193383de8e6c1854faa86907e5a0bf8f734"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LPKUARC6OUZEUDR6TNXRLQ63EJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On laws of large numbers in $L^2$ for supercritical branching Markov processes beyond $\\lambda$-positivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Matthieu Jonckheere, Santiago Saglietti","submitted_at":"2017-11-15T17:07:43Z","abstract_excerpt":"We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\\lambda$-positive systems but also some $\\lambda$-transient ones, such as the branching Brownian motion with drift and absorption at $0$. This is a significant improvement over previous results on this matter, which had only dealt so far with $\\lambda$-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05674","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":"2026-05-18T00:30:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uUc2vBsnfl8imKOk/mGqtR1rYfcoafh5nGJdz637HBfEczXx7jFZ4cn+qyXwVanwuEEgt8jFm7rU61yhb3vBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T03:44:00.147427Z"},"content_sha256":"1411feef64bd21de657ffd6781ca7e38593cf5736ded087605ffde4ee8e0db6e","schema_version":"1.0","event_id":"sha256:1411feef64bd21de657ffd6781ca7e38593cf5736ded087605ffde4ee8e0db6e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/bundle.json","state_url":"https://pith.science/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/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":"2026-06-20T03:44:00Z","links":{"resolver":"https://pith.science/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ","bundle":"https://pith.science/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/bundle.json","state":"https://pith.science/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LPKUARC6OUZEUDR6TNXRLQ63EJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LPKUARC6OUZEUDR6TNXRLQ63EJ","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":"725234acee8cf05154f9f6fb7e64d547c1670be02bc808c96cccde1c3441a539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-15T17:07:43Z","title_canon_sha256":"0b2277264f7345286c23c8706acd7eab3bcb66e732d3642f889119e20cfd0e32"},"schema_version":"1.0","source":{"id":"1711.05674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05674","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05674v1","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05674","created_at":"2026-05-18T00:30:29Z"},{"alias_kind":"pith_short_12","alias_value":"LPKUARC6OUZE","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LPKUARC6OUZEUDR6","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LPKUARC6","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:1411feef64bd21de657ffd6781ca7e38593cf5736ded087605ffde4ee8e0db6e","target":"graph","created_at":"2026-05-18T00:30:29Z","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 give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\\lambda$-positive systems but also some $\\lambda$-transient ones, such as the branching Brownian motion with drift and absorption at $0$. This is a significant improvement over previous results on this matter, which had only dealt so far with $\\lambda$-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is","authors_text":"Matthieu Jonckheere, Santiago Saglietti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-15T17:07:43Z","title":"On laws of large numbers in $L^2$ for supercritical branching Markov processes beyond $\\lambda$-positivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05674","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:bd65f882cc776a9c836b613f82eb0193383de8e6c1854faa86907e5a0bf8f734","target":"record","created_at":"2026-05-18T00:30:29Z","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":"725234acee8cf05154f9f6fb7e64d547c1670be02bc808c96cccde1c3441a539","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-15T17:07:43Z","title_canon_sha256":"0b2277264f7345286c23c8706acd7eab3bcb66e732d3642f889119e20cfd0e32"},"schema_version":"1.0","source":{"id":"1711.05674","kind":"arxiv","version":1}},"canonical_sha256":"5bd540445e75324a0e3e9b6f15c3db225ed29fe03ff7734ce469dddb3422d7d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bd540445e75324a0e3e9b6f15c3db225ed29fe03ff7734ce469dddb3422d7d2","first_computed_at":"2026-05-18T00:30:29.240168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:29.240168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x286yJQzzH3cFxrNN8YovoXzmlMPhWYtA6ibcuRRieBa0+c1Kz5HCD4oTwoTq4K0BnrAcLG9Ny+APXAp3P/WCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:29.240609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd65f882cc776a9c836b613f82eb0193383de8e6c1854faa86907e5a0bf8f734","sha256:1411feef64bd21de657ffd6781ca7e38593cf5736ded087605ffde4ee8e0db6e"],"state_sha256":"f390451e952958fe8405a00301de95e6eb3f732b592f96ff47df9033b19fb289"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iv6TjZWNLoJaiyw71yXF41CVH65qNutwdcTeZjJiogkAR7VC9Q+Ruaqg4T8sjiKW65BOK4UjHxosVq5dqp8yDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T03:44:00.149277Z","bundle_sha256":"c98073eb8c8ccd5b20ce28e17027e2e54b961c36ceac177cff8ef86652e9ce03"}}