{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZGDKSN45MDPJZCLO5MZDWXC3R6","short_pith_number":"pith:ZGDKSN45","canonical_record":{"source":{"id":"1002.0976","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-04T12:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"e3d255edc9b454fbb68442a5e55a20bf2803ded2b4719b28eb13a02b956ef917","abstract_canon_sha256":"f144c0426a1fea8e0d9d2faf02cac2b0337996eccac62bb1fcf5d1c56363de9c"},"schema_version":"1.0"},"canonical_sha256":"c986a9379d60de9c896eeb323b5c5b8fa26c8d3467ee1e1c74d9c4e6df9b9e76","source":{"kind":"arxiv","id":"1002.0976","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0976","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0976v3","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0976","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZGDKSN45MDPJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZGDKSN45MDPJZCLO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZGDKSN45","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZGDKSN45MDPJZCLO5MZDWXC3R6","target":"record","payload":{"canonical_record":{"source":{"id":"1002.0976","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-04T12:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"e3d255edc9b454fbb68442a5e55a20bf2803ded2b4719b28eb13a02b956ef917","abstract_canon_sha256":"f144c0426a1fea8e0d9d2faf02cac2b0337996eccac62bb1fcf5d1c56363de9c"},"schema_version":"1.0"},"canonical_sha256":"c986a9379d60de9c896eeb323b5c5b8fa26c8d3467ee1e1c74d9c4e6df9b9e76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:38.165144Z","signature_b64":"tt0xnUFkX/eTdc0me07SKfe7Dc5ia8aTfnJpxK9qf0uVcFM68gUgMXEM0YLleWTIVJy7fZfC6eStPoDPjVT1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c986a9379d60de9c896eeb323b5c5b8fa26c8d3467ee1e1c74d9c4e6df9b9e76","last_reissued_at":"2026-05-18T04:34:38.164673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:38.164673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.0976","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mg2LEA3GEZbx6TnbfXNpZLzAHbICVAanbjo40qc5h734NGCaXefRiAYL/SzWLnyNwSzHI1vNT5Pfb8mnTDC4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:02:36.620838Z"},"content_sha256":"51768119b0eb8040eb70d600ee0e2b13c64c51f4f4fee0348a7c679e825b465e","schema_version":"1.0","event_id":"sha256:51768119b0eb8040eb70d600ee0e2b13c64c51f4f4fee0348a7c679e825b465e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZGDKSN45MDPJZCLO5MZDWXC3R6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interlacing of positive real zeros of Bessel functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Barnabas Apagyi, Tamas Palmai","submitted_at":"2010-02-04T12:16:29Z","abstract_excerpt":"We unify the three distinct inequality sequences (Abramowitz ans Stegun (1972) [1,9.5.2]) of positive real zeros of Bessel functions into a single one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0976","kind":"arxiv","version":3},"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":"2026-05-18T04:34:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEblDy+GQasVd1lpKvgtBgJeK5WPL5Vv0ab4E60JMnTtSH/hfkgsP8kreWH3qweNXhICp6L0aR0cb70GBfbkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:02:36.621178Z"},"content_sha256":"eb0fd19ccdafd26c9af187565f0e098cb59df6928f929e08cb51e0fd04c82fe9","schema_version":"1.0","event_id":"sha256:eb0fd19ccdafd26c9af187565f0e098cb59df6928f929e08cb51e0fd04c82fe9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/bundle.json","state_url":"https://pith.science/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/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":"2026-06-01T20:02:36Z","links":{"resolver":"https://pith.science/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6","bundle":"https://pith.science/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/bundle.json","state":"https://pith.science/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGDKSN45MDPJZCLO5MZDWXC3R6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZGDKSN45MDPJZCLO5MZDWXC3R6","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":"f144c0426a1fea8e0d9d2faf02cac2b0337996eccac62bb1fcf5d1c56363de9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-04T12:16:29Z","title_canon_sha256":"e3d255edc9b454fbb68442a5e55a20bf2803ded2b4719b28eb13a02b956ef917"},"schema_version":"1.0","source":{"id":"1002.0976","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.0976","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"arxiv_version","alias_value":"1002.0976v3","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.0976","created_at":"2026-05-18T04:34:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZGDKSN45MDPJ","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"ZGDKSN45MDPJZCLO","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"ZGDKSN45","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:eb0fd19ccdafd26c9af187565f0e098cb59df6928f929e08cb51e0fd04c82fe9","target":"graph","created_at":"2026-05-18T04:34:38Z","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 unify the three distinct inequality sequences (Abramowitz ans Stegun (1972) [1,9.5.2]) of positive real zeros of Bessel functions into a single one.","authors_text":"Barnabas Apagyi, Tamas Palmai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-04T12:16:29Z","title":"Interlacing of positive real zeros of Bessel functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.0976","kind":"arxiv","version":3},"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":"sha256:51768119b0eb8040eb70d600ee0e2b13c64c51f4f4fee0348a7c679e825b465e","target":"record","created_at":"2026-05-18T04:34:38Z","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":"f144c0426a1fea8e0d9d2faf02cac2b0337996eccac62bb1fcf5d1c56363de9c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-02-04T12:16:29Z","title_canon_sha256":"e3d255edc9b454fbb68442a5e55a20bf2803ded2b4719b28eb13a02b956ef917"},"schema_version":"1.0","source":{"id":"1002.0976","kind":"arxiv","version":3}},"canonical_sha256":"c986a9379d60de9c896eeb323b5c5b8fa26c8d3467ee1e1c74d9c4e6df9b9e76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c986a9379d60de9c896eeb323b5c5b8fa26c8d3467ee1e1c74d9c4e6df9b9e76","first_computed_at":"2026-05-18T04:34:38.164673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:38.164673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tt0xnUFkX/eTdc0me07SKfe7Dc5ia8aTfnJpxK9qf0uVcFM68gUgMXEM0YLleWTIVJy7fZfC6eStPoDPjVT1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:38.165144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.0976","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51768119b0eb8040eb70d600ee0e2b13c64c51f4f4fee0348a7c679e825b465e","sha256:eb0fd19ccdafd26c9af187565f0e098cb59df6928f929e08cb51e0fd04c82fe9"],"state_sha256":"d7899fd7fbc1de4292a9b0c72cb3613f72dac7bce70a4a8ef82ec1d3164f6471"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M1sItzrvJsqHpsxCnEHLMZm/ez5GrufllsI1UUZ/cgf72nTMnheJ5DI1WRjJz3reFDi0J7bXfKKdnwo5ZsRhCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:02:36.623245Z","bundle_sha256":"fda3c32a3e2a32427ad2cd9b142aaa105d8c2be132bdaed52935d866016d2fff"}}