{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:7NZFEXZXYI2H6V4AGXPUAYVBBV","short_pith_number":"pith:7NZFEXZX","canonical_record":{"source":{"id":"1612.07901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T08:25:02Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"e24099309fd4214a746955011e3557a9a3baa2a3a6433af137850f9d0a98954f","abstract_canon_sha256":"661d8c376f6bb0c59ef25b750e3e049986c318a0d2720db2d917392bab48ecfb"},"schema_version":"1.0"},"canonical_sha256":"fb72525f37c2347f578035df4062a10d533815f61dca9e1bf210ba678a192de9","source":{"kind":"arxiv","id":"1612.07901","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07901","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07901v2","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07901","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"pith_short_12","alias_value":"7NZFEXZXYI2H","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7NZFEXZXYI2H6V4A","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7NZFEXZX","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:7NZFEXZXYI2H6V4AGXPUAYVBBV","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07901","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T08:25:02Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"e24099309fd4214a746955011e3557a9a3baa2a3a6433af137850f9d0a98954f","abstract_canon_sha256":"661d8c376f6bb0c59ef25b750e3e049986c318a0d2720db2d917392bab48ecfb"},"schema_version":"1.0"},"canonical_sha256":"fb72525f37c2347f578035df4062a10d533815f61dca9e1bf210ba678a192de9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:30.867398Z","signature_b64":"rSajXZbb5OfSn9TLirnWEG6T17Vme7um8xTD0pFu3UkwuqeRhxBxQzSyqaJKt4/sti01wWw1HsFfyX1GbNnuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb72525f37c2347f578035df4062a10d533815f61dca9e1bf210ba678a192de9","last_reissued_at":"2026-05-18T00:10:30.866843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:30.866843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07901","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvvP1KL4TAK64FKVU40d0AEKoyV+HpqmyQcauRIYTESOw6wOOW4ec50drtNQnefTkWAule6Yvk72wDdgzVmMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:48:00.081704Z"},"content_sha256":"a2af5838b52e1c0d01b16df91cadf252cef6f8136843255651dd777576cbd48d","schema_version":"1.0","event_id":"sha256:a2af5838b52e1c0d01b16df91cadf252cef6f8136843255651dd777576cbd48d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:7NZFEXZXYI2H6V4AGXPUAYVBBV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Concentration inequalities for Poisson point processes with application to adaptive intensity estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Martin Kroll","submitted_at":"2016-12-23T08:25:02Z","abstract_excerpt":"We derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained concentration inequalities by application to adaptive intensity estimation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07901","kind":"arxiv","version":2},"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":"2026-05-18T00:10:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1vZuHbMX1W37u9Oh6Rz5dlhfq6iZD1fXs7x9BnA0dpZyQ8Z9OimcQ5rsQYyM3TlWsbOPBQrvlvoxyxJh9i3aBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:48:00.082410Z"},"content_sha256":"6c5c5f94aff269e89fa215ef027098d2ac11c9009df960a169bbd2deb9cf9798","schema_version":"1.0","event_id":"sha256:6c5c5f94aff269e89fa215ef027098d2ac11c9009df960a169bbd2deb9cf9798"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/bundle.json","state_url":"https://pith.science/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/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":"2026-06-06T06:48:00Z","links":{"resolver":"https://pith.science/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV","bundle":"https://pith.science/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/bundle.json","state":"https://pith.science/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NZFEXZXYI2H6V4AGXPUAYVBBV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7NZFEXZXYI2H6V4AGXPUAYVBBV","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":"661d8c376f6bb0c59ef25b750e3e049986c318a0d2720db2d917392bab48ecfb","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T08:25:02Z","title_canon_sha256":"e24099309fd4214a746955011e3557a9a3baa2a3a6433af137850f9d0a98954f"},"schema_version":"1.0","source":{"id":"1612.07901","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07901","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07901v2","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07901","created_at":"2026-05-18T00:10:30Z"},{"alias_kind":"pith_short_12","alias_value":"7NZFEXZXYI2H","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7NZFEXZXYI2H6V4A","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7NZFEXZX","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:6c5c5f94aff269e89fa215ef027098d2ac11c9009df960a169bbd2deb9cf9798","target":"graph","created_at":"2026-05-18T00:10:30Z","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 derive concentration inequalities for maxima of empirical processes associated with Poisson point processes. The proofs are based on a careful application of Ledoux's entropy method. We demonstrate the utility of the obtained concentration inequalities by application to adaptive intensity estimation.","authors_text":"Martin Kroll","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T08:25:02Z","title":"Concentration inequalities for Poisson point processes with application to adaptive intensity estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07901","kind":"arxiv","version":2},"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:a2af5838b52e1c0d01b16df91cadf252cef6f8136843255651dd777576cbd48d","target":"record","created_at":"2026-05-18T00:10:30Z","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":"661d8c376f6bb0c59ef25b750e3e049986c318a0d2720db2d917392bab48ecfb","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-23T08:25:02Z","title_canon_sha256":"e24099309fd4214a746955011e3557a9a3baa2a3a6433af137850f9d0a98954f"},"schema_version":"1.0","source":{"id":"1612.07901","kind":"arxiv","version":2}},"canonical_sha256":"fb72525f37c2347f578035df4062a10d533815f61dca9e1bf210ba678a192de9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb72525f37c2347f578035df4062a10d533815f61dca9e1bf210ba678a192de9","first_computed_at":"2026-05-18T00:10:30.866843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:30.866843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rSajXZbb5OfSn9TLirnWEG6T17Vme7um8xTD0pFu3UkwuqeRhxBxQzSyqaJKt4/sti01wWw1HsFfyX1GbNnuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:30.867398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07901","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2af5838b52e1c0d01b16df91cadf252cef6f8136843255651dd777576cbd48d","sha256:6c5c5f94aff269e89fa215ef027098d2ac11c9009df960a169bbd2deb9cf9798"],"state_sha256":"59db3bc3186905d1c6ada06bcbe33593996c928e24bb3da93792457f2b8f0301"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ySUcKOSqQk1rFwiLJaA3IVgs7MErR9mCcqdGMai/2x6TDzMptsFjcs0Zx3wLnNi8UiKnpqGKI/ASwvFzkf5pDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:48:00.086406Z","bundle_sha256":"3746049644f235425d9ffa304dbaef68c8013cc36f97a2a15dee307260481248"}}