{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:J3ZZ4ZYO5LLZNGPS4ANPIZEXYK","short_pith_number":"pith:J3ZZ4ZYO","canonical_record":{"source":{"id":"2606.24090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-23T03:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"56d0938d2930da633038de6e488a82549ec338d7dc7a3c04b498a6a270c94090","abstract_canon_sha256":"7494dccf0e947397084494eba1ca21625bf889e057dd48cc4a7b067e7d9344f2"},"schema_version":"1.0"},"canonical_sha256":"4ef39e670eead79699f2e01af46497c28e589829f84cd338521ba00662ba8cd3","source":{"kind":"arxiv","id":"2606.24090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24090","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24090v1","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24090","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"J3ZZ4ZYO5LLZ","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"J3ZZ4ZYO5LLZNGPS","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"J3ZZ4ZYO","created_at":"2026-06-24T01:14:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:J3ZZ4ZYO5LLZNGPS4ANPIZEXYK","target":"record","payload":{"canonical_record":{"source":{"id":"2606.24090","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-23T03:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"56d0938d2930da633038de6e488a82549ec338d7dc7a3c04b498a6a270c94090","abstract_canon_sha256":"7494dccf0e947397084494eba1ca21625bf889e057dd48cc4a7b067e7d9344f2"},"schema_version":"1.0"},"canonical_sha256":"4ef39e670eead79699f2e01af46497c28e589829f84cd338521ba00662ba8cd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:14:40.073834Z","signature_b64":"aWBp9fZFR5va5MHwGC7YPTLozYx3tlJGkXeNZkvijLR5FZVqeFFOd2SaXowTgccmhCj8lWBE7nH63GonGya3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ef39e670eead79699f2e01af46497c28e589829f84cd338521ba00662ba8cd3","last_reissued_at":"2026-06-24T01:14:40.073481Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:14:40.073481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.24090","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":"2026-06-24T01:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c4yBH/iuWVfy6G6izxC4LHx4WepxC4QafUmsHyPi4lkfk3LhQhqKC0/9Y3VjGuVZvxqyN4KZEonbMjdMDHi6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:18:59.818374Z"},"content_sha256":"f2fff6dcbba8b4046f1ac91a6916fd8f973c247f5336fb2997ca4fe4a7d3d84e","schema_version":"1.0","event_id":"sha256:f2fff6dcbba8b4046f1ac91a6916fd8f973c247f5336fb2997ca4fe4a7d3d84e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:J3ZZ4ZYO5LLZNGPS4ANPIZEXYK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparsity-adaptive concentration inequalities for random polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guozheng Dai, Ke Wang","submitted_at":"2026-06-23T03:10:49Z","abstract_excerpt":"We prove concentration inequalities for polynomials of independent, sparse $\\alpha$-sub-exponential random variables. Specifically, we consider $X_i=\\delta_i\\xi_i$, where the Bernoulli selectors $\\delta_i$ are independent with parameters $p_i$, and the variables $\\xi_i$ are independent \\(\\alpha\\)-sub-exponential random variables (not necessarily centered). For any polynomial $f:\\mathbb R^n\\to\\mathbb R $ of degree at most $D$ and any $0<\\alpha \\le 1 $, we establish an $L_r$-moment bound for \\(f(X)-\\mathbb E f(X)\\) in terms of partition norms of sparsity-weighted expected derivative tensors. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24090","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/2606.24090/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":"2026-06-24T01:14:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PEom+H+lhRHPIMt7blcMtj4zHkijMd24HoWGFK0UCRY7fTeVCrBqUkWq3M10rWMtvUrdQVnNMNOFtLUbcTVDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T07:18:59.818755Z"},"content_sha256":"5cc6e7ff7a54f2e7c6317439908f4017df311bf018e343c6156927120a360941","schema_version":"1.0","event_id":"sha256:5cc6e7ff7a54f2e7c6317439908f4017df311bf018e343c6156927120a360941"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/bundle.json","state_url":"https://pith.science/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/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":"2026-06-29T07:18:59Z","links":{"resolver":"https://pith.science/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK","bundle":"https://pith.science/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/bundle.json","state":"https://pith.science/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3ZZ4ZYO5LLZNGPS4ANPIZEXYK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:J3ZZ4ZYO5LLZNGPS4ANPIZEXYK","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":"7494dccf0e947397084494eba1ca21625bf889e057dd48cc4a7b067e7d9344f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-23T03:10:49Z","title_canon_sha256":"56d0938d2930da633038de6e488a82549ec338d7dc7a3c04b498a6a270c94090"},"schema_version":"1.0","source":{"id":"2606.24090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24090","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24090v1","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24090","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_12","alias_value":"J3ZZ4ZYO5LLZ","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_16","alias_value":"J3ZZ4ZYO5LLZNGPS","created_at":"2026-06-24T01:14:40Z"},{"alias_kind":"pith_short_8","alias_value":"J3ZZ4ZYO","created_at":"2026-06-24T01:14:40Z"}],"graph_snapshots":[{"event_id":"sha256:5cc6e7ff7a54f2e7c6317439908f4017df311bf018e343c6156927120a360941","target":"graph","created_at":"2026-06-24T01:14:40Z","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/2606.24090/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove concentration inequalities for polynomials of independent, sparse $\\alpha$-sub-exponential random variables. Specifically, we consider $X_i=\\delta_i\\xi_i$, where the Bernoulli selectors $\\delta_i$ are independent with parameters $p_i$, and the variables $\\xi_i$ are independent \\(\\alpha\\)-sub-exponential random variables (not necessarily centered). For any polynomial $f:\\mathbb R^n\\to\\mathbb R $ of degree at most $D$ and any $0<\\alpha \\le 1 $, we establish an $L_r$-moment bound for \\(f(X)-\\mathbb E f(X)\\) in terms of partition norms of sparsity-weighted expected derivative tensors. The","authors_text":"Guozheng Dai, Ke Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-23T03:10:49Z","title":"Sparsity-adaptive concentration inequalities for random polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24090","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:f2fff6dcbba8b4046f1ac91a6916fd8f973c247f5336fb2997ca4fe4a7d3d84e","target":"record","created_at":"2026-06-24T01:14:40Z","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":"7494dccf0e947397084494eba1ca21625bf889e057dd48cc4a7b067e7d9344f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-23T03:10:49Z","title_canon_sha256":"56d0938d2930da633038de6e488a82549ec338d7dc7a3c04b498a6a270c94090"},"schema_version":"1.0","source":{"id":"2606.24090","kind":"arxiv","version":1}},"canonical_sha256":"4ef39e670eead79699f2e01af46497c28e589829f84cd338521ba00662ba8cd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ef39e670eead79699f2e01af46497c28e589829f84cd338521ba00662ba8cd3","first_computed_at":"2026-06-24T01:14:40.073481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:40.073481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aWBp9fZFR5va5MHwGC7YPTLozYx3tlJGkXeNZkvijLR5FZVqeFFOd2SaXowTgccmhCj8lWBE7nH63GonGya3Bg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:40.073834Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2fff6dcbba8b4046f1ac91a6916fd8f973c247f5336fb2997ca4fe4a7d3d84e","sha256:5cc6e7ff7a54f2e7c6317439908f4017df311bf018e343c6156927120a360941"],"state_sha256":"16e2906203fb428111b23b5a00b5cc9628df2dfb8e732ceab5caf8b3d93c3734"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8w8yrQKG2PXEQGuPZhOx04sioe5WzVf6lGWVy2qArVcBG2oir0IYFxmCm4nSixjJ3H+xwvqOWf3gD/vrxzvBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T07:18:59.820706Z","bundle_sha256":"0f833ff379ba4db6bb801dea680583b7d84a7bed9548b73445751c3e3e953c86"}}