{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UHLPUY7AHV5AUD5OGHNHOGAUT6","short_pith_number":"pith:UHLPUY7A","canonical_record":{"source":{"id":"1102.0217","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T17:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"bda46b3ec0414b6ad97ce99e230478ed00b438a0c59f3120885438150ab4a071","abstract_canon_sha256":"0ca8786db7a8fc0c0c5bb50e6ef988c2a039c509e99a9ff20a79f2384ad52f4f"},"schema_version":"1.0"},"canonical_sha256":"a1d6fa63e03d7a0a0fae31da7718149f99980dc8cd907841eb5b17ecf1d19d5e","source":{"kind":"arxiv","id":"1102.0217","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0217","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0217v4","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0217","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"UHLPUY7AHV5A","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UHLPUY7AHV5AUD5O","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UHLPUY7A","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UHLPUY7AHV5AUD5OGHNHOGAUT6","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0217","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T17:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"bda46b3ec0414b6ad97ce99e230478ed00b438a0c59f3120885438150ab4a071","abstract_canon_sha256":"0ca8786db7a8fc0c0c5bb50e6ef988c2a039c509e99a9ff20a79f2384ad52f4f"},"schema_version":"1.0"},"canonical_sha256":"a1d6fa63e03d7a0a0fae31da7718149f99980dc8cd907841eb5b17ecf1d19d5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:53.913891Z","signature_b64":"dJsSBL+aDXJ4qgE3e8PEVvgQfVi+tpN4OGqDeheN6BJaNnq7ch+7qR2hiZhN5CAtgCamt1NJVcIAsuZeC/RiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1d6fa63e03d7a0a0fae31da7718149f99980dc8cd907841eb5b17ecf1d19d5e","last_reissued_at":"2026-05-18T02:54:53.913334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:53.913334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0217","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ErG+g31lASIxEZkr/yOUkMOtvOxP/PjOzP6wfZk7ZZf8KA/3aGS03sDYpva9LVADTH9Rf3cPHWNf78+PIgQOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:41:46.796847Z"},"content_sha256":"80f59e494f581407df07e52f56a2924e432cfe2314a7782666eacb86dae000bb","schema_version":"1.0","event_id":"sha256:80f59e494f581407df07e52f56a2924e432cfe2314a7782666eacb86dae000bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UHLPUY7AHV5AUD5OGHNHOGAUT6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Seneta--Heyde scaling for the branching random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"elie aidekon, Zhan Shi","submitted_at":"2011-02-01T17:02:48Z","abstract_excerpt":"We consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609--631] in a one-dimensional super-critical branching random walk, and study the additive martingale $(W_n)$. We prove that, upon the system's survival, $n^{1/2}W_n$ converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou [Adv. in Appl. Probab. 36 (2004) 544--581], of the derivative martingale."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0217","kind":"arxiv","version":4},"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":"2026-05-18T02:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6hLG0B6qo51oEeYsRHnuhXLxwz9Y28iy8z43f1fjiuW86Zg1oGTGhICZ6wqjvXw/iJ1o0yuvCP6qWkcMZREnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:41:46.797212Z"},"content_sha256":"6394cc752c988f223c838375ca0c00a9536b61551abea2cbce5022e1bdc3c73c","schema_version":"1.0","event_id":"sha256:6394cc752c988f223c838375ca0c00a9536b61551abea2cbce5022e1bdc3c73c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/bundle.json","state_url":"https://pith.science/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/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":"2026-06-11T21:41:46Z","links":{"resolver":"https://pith.science/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6","bundle":"https://pith.science/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/bundle.json","state":"https://pith.science/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UHLPUY7AHV5AUD5OGHNHOGAUT6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UHLPUY7AHV5AUD5OGHNHOGAUT6","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":"0ca8786db7a8fc0c0c5bb50e6ef988c2a039c509e99a9ff20a79f2384ad52f4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T17:02:48Z","title_canon_sha256":"bda46b3ec0414b6ad97ce99e230478ed00b438a0c59f3120885438150ab4a071"},"schema_version":"1.0","source":{"id":"1102.0217","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0217","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0217v4","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0217","created_at":"2026-05-18T02:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"UHLPUY7AHV5A","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UHLPUY7AHV5AUD5O","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UHLPUY7A","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6394cc752c988f223c838375ca0c00a9536b61551abea2cbce5022e1bdc3c73c","target":"graph","created_at":"2026-05-18T02:54:53Z","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 consider the boundary case (in the sense of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609--631] in a one-dimensional super-critical branching random walk, and study the additive martingale $(W_n)$. We prove that, upon the system's survival, $n^{1/2}W_n$ converges in probability, but not almost surely, to a positive limit. The limit is identified as a constant multiple of the almost sure limit, discovered by Biggins and Kyprianou [Adv. in Appl. Probab. 36 (2004) 544--581], of the derivative martingale.","authors_text":"elie aidekon, Zhan Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T17:02:48Z","title":"The Seneta--Heyde scaling for the branching random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0217","kind":"arxiv","version":4},"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":"sha256:80f59e494f581407df07e52f56a2924e432cfe2314a7782666eacb86dae000bb","target":"record","created_at":"2026-05-18T02:54:53Z","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":"0ca8786db7a8fc0c0c5bb50e6ef988c2a039c509e99a9ff20a79f2384ad52f4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T17:02:48Z","title_canon_sha256":"bda46b3ec0414b6ad97ce99e230478ed00b438a0c59f3120885438150ab4a071"},"schema_version":"1.0","source":{"id":"1102.0217","kind":"arxiv","version":4}},"canonical_sha256":"a1d6fa63e03d7a0a0fae31da7718149f99980dc8cd907841eb5b17ecf1d19d5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1d6fa63e03d7a0a0fae31da7718149f99980dc8cd907841eb5b17ecf1d19d5e","first_computed_at":"2026-05-18T02:54:53.913334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:53.913334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dJsSBL+aDXJ4qgE3e8PEVvgQfVi+tpN4OGqDeheN6BJaNnq7ch+7qR2hiZhN5CAtgCamt1NJVcIAsuZeC/RiCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:53.913891Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0217","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80f59e494f581407df07e52f56a2924e432cfe2314a7782666eacb86dae000bb","sha256:6394cc752c988f223c838375ca0c00a9536b61551abea2cbce5022e1bdc3c73c"],"state_sha256":"ef16e285d270c915f53a0c7509cc6281f786d95789dc145ec6b7cb0d7e3f3754"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RSF/zBONN4tI6rrGysTh9gnB0lm3hrdR3UcMP6Q1GMgSQcGLgzhINbs7ScrAxCsvoqX9t3Tld7kwI4pluuFYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:41:46.799556Z","bundle_sha256":"4cd3402013015e5dac377897e87aa2eabe7945c167a4e855613365c18f101eec"}}