{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:LSY2IVTRUSAZHPYVN6DVJ7F4EK","short_pith_number":"pith:LSY2IVTR","canonical_record":{"source":{"id":"2606.27117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T14:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"bf1dd7faa9171fa06f0a9143cb866919ad0a9d7df2ee02797603751ab474f5af","abstract_canon_sha256":"b9df870da0b9c49dfeeb2b109cd6bf495c8f00f4c51269ec8a5a1817e0c3af82"},"schema_version":"1.0"},"canonical_sha256":"5cb1a45671a48193bf156f8754fcbc228227b5dc7c1969fcef61473ddab6d3b4","source":{"kind":"arxiv","id":"2606.27117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27117","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27117v1","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27117","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"LSY2IVTRUSAZ","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_16","alias_value":"LSY2IVTRUSAZHPYV","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_8","alias_value":"LSY2IVTR","created_at":"2026-06-26T01:16:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:LSY2IVTRUSAZHPYVN6DVJ7F4EK","target":"record","payload":{"canonical_record":{"source":{"id":"2606.27117","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T14:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"bf1dd7faa9171fa06f0a9143cb866919ad0a9d7df2ee02797603751ab474f5af","abstract_canon_sha256":"b9df870da0b9c49dfeeb2b109cd6bf495c8f00f4c51269ec8a5a1817e0c3af82"},"schema_version":"1.0"},"canonical_sha256":"5cb1a45671a48193bf156f8754fcbc228227b5dc7c1969fcef61473ddab6d3b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T01:16:09.999920Z","signature_b64":"M0OgmSwFtad4Gx50lcMdwl3oC7szY36artt1qgZaxNI1uTrUeKs7ujs979X+a8x7P1f+mLEnQypTqt33UoW5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cb1a45671a48193bf156f8754fcbc228227b5dc7c1969fcef61473ddab6d3b4","last_reissued_at":"2026-06-26T01:16:09.999524Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T01:16:09.999524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.27117","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":"2026-06-26T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vHaoMsLsarLKIyPZPeKnFE78SCkLdowRfUWfM7Xo3iaNWb22zPIWZiFVfhevfiyODuZM4awfthmlZQ8hA5BkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:19:45.510309Z"},"content_sha256":"51fd1d3c0eb9b8638e14631640ec673a5db5415a45ff3cf2f203a9e9a25edbc6","schema_version":"1.0","event_id":"sha256:51fd1d3c0eb9b8638e14631640ec673a5db5415a45ff3cf2f203a9e9a25edbc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:LSY2IVTRUSAZHPYVN6DVJ7F4EK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Occupation-Time Fluctuations of an Age-Dependent Branching System Driven by Poisson Immigration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ekaterina T. Kolkovska, Jos\\'e Alfredo L\\'opez-Mimbela, Maroussia Slavtchova-Bojkova","submitted_at":"2026-06-25T14:56:01Z","abstract_excerpt":"We study the occupation-time fluctuations of a critical age-dependent branching particle system with immigration in $\\mathbb{R}^d$. Immigrants arrive according to a homogeneous Poisson random measure in space and time. Each particle moves independently according to a symmetric $\\alpha$-stable process and, at the end of its lifetime, either dies or splits into two offspring with equal probability. The lifetime distribution is allowed to have either finite mean or a heavy tail of index $\\gamma\\in(0,1]$. We investigate the asymptotic behavior of the centered occupation-time process under a suitab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27117","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.27117/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-26T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZEOs3sb57Yspj7yMWw9y1Myc0Q2QZtH7Sf/xCfoq3yXSoCrD88xNwys5XR+6hbpdi+ygBtchufZgOuhP5nUzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:19:45.510684Z"},"content_sha256":"fe94d1728774081e2de5e4a7d4faffa156cabc94f95fdd12f9eca4151a1064a5","schema_version":"1.0","event_id":"sha256:fe94d1728774081e2de5e4a7d4faffa156cabc94f95fdd12f9eca4151a1064a5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/bundle.json","state_url":"https://pith.science/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/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":"2026-06-30T16:19:45Z","links":{"resolver":"https://pith.science/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK","bundle":"https://pith.science/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/bundle.json","state":"https://pith.science/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LSY2IVTRUSAZHPYVN6DVJ7F4EK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LSY2IVTRUSAZHPYVN6DVJ7F4EK","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":"b9df870da0b9c49dfeeb2b109cd6bf495c8f00f4c51269ec8a5a1817e0c3af82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T14:56:01Z","title_canon_sha256":"bf1dd7faa9171fa06f0a9143cb866919ad0a9d7df2ee02797603751ab474f5af"},"schema_version":"1.0","source":{"id":"2606.27117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27117","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27117v1","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27117","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"LSY2IVTRUSAZ","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_16","alias_value":"LSY2IVTRUSAZHPYV","created_at":"2026-06-26T01:16:09Z"},{"alias_kind":"pith_short_8","alias_value":"LSY2IVTR","created_at":"2026-06-26T01:16:09Z"}],"graph_snapshots":[{"event_id":"sha256:fe94d1728774081e2de5e4a7d4faffa156cabc94f95fdd12f9eca4151a1064a5","target":"graph","created_at":"2026-06-26T01:16:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.27117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the occupation-time fluctuations of a critical age-dependent branching particle system with immigration in $\\mathbb{R}^d$. Immigrants arrive according to a homogeneous Poisson random measure in space and time. Each particle moves independently according to a symmetric $\\alpha$-stable process and, at the end of its lifetime, either dies or splits into two offspring with equal probability. The lifetime distribution is allowed to have either finite mean or a heavy tail of index $\\gamma\\in(0,1]$. We investigate the asymptotic behavior of the centered occupation-time process under a suitab","authors_text":"Ekaterina T. Kolkovska, Jos\\'e Alfredo L\\'opez-Mimbela, Maroussia Slavtchova-Bojkova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T14:56:01Z","title":"Occupation-Time Fluctuations of an Age-Dependent Branching System Driven by Poisson Immigration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27117","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":"sha256:51fd1d3c0eb9b8638e14631640ec673a5db5415a45ff3cf2f203a9e9a25edbc6","target":"record","created_at":"2026-06-26T01:16:09Z","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":"b9df870da0b9c49dfeeb2b109cd6bf495c8f00f4c51269ec8a5a1817e0c3af82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-25T14:56:01Z","title_canon_sha256":"bf1dd7faa9171fa06f0a9143cb866919ad0a9d7df2ee02797603751ab474f5af"},"schema_version":"1.0","source":{"id":"2606.27117","kind":"arxiv","version":1}},"canonical_sha256":"5cb1a45671a48193bf156f8754fcbc228227b5dc7c1969fcef61473ddab6d3b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5cb1a45671a48193bf156f8754fcbc228227b5dc7c1969fcef61473ddab6d3b4","first_computed_at":"2026-06-26T01:16:09.999524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:09.999524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M0OgmSwFtad4Gx50lcMdwl3oC7szY36artt1qgZaxNI1uTrUeKs7ujs979X+a8x7P1f+mLEnQypTqt33UoW5AA==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:09.999920Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51fd1d3c0eb9b8638e14631640ec673a5db5415a45ff3cf2f203a9e9a25edbc6","sha256:fe94d1728774081e2de5e4a7d4faffa156cabc94f95fdd12f9eca4151a1064a5"],"state_sha256":"f40b9d6ecdd7d63d258cd363f748265329a680fc88e1e81c0aa6fb00deab4389"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9eWVbm7UR3LiURUDxrNkka+Xs9tZ5YDbll9p7ox6ts95DdrDPZ/i9NDIZCCir3VFoQuXsW/9VjjVVjy4SQKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T16:19:45.512539Z","bundle_sha256":"72167481b7381c0418fc241d44a065de68c409e3515e7b215591fc990e774742"}}