{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:DOKG6ZMLYUPBTGMSOP5OBSHJJC","short_pith_number":"pith:DOKG6ZML","canonical_record":{"source":{"id":"math/0407117","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2004-07-08T05:55:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1d04571b7cd1b7fbbcf6f6bafac8d8c8276beaae0fa1da2a60048ca0fc0e53ba","abstract_canon_sha256":"d70cd38e84f34fd4f2353dba6f784562ea44d5baa8d6555266e0343309dd62e5"},"schema_version":"1.0"},"canonical_sha256":"1b946f658bc51e19999273fae0c8e9489cc23a3e9b05e4fcb864110d490921a9","source":{"kind":"arxiv","id":"math/0407117","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407117","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407117v1","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407117","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"DOKG6ZMLYUPB","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"DOKG6ZMLYUPBTGMS","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"DOKG6ZML","created_at":"2026-07-04T14:38:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:DOKG6ZMLYUPBTGMSOP5OBSHJJC","target":"record","payload":{"canonical_record":{"source":{"id":"math/0407117","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2004-07-08T05:55:42Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1d04571b7cd1b7fbbcf6f6bafac8d8c8276beaae0fa1da2a60048ca0fc0e53ba","abstract_canon_sha256":"d70cd38e84f34fd4f2353dba6f784562ea44d5baa8d6555266e0343309dd62e5"},"schema_version":"1.0"},"canonical_sha256":"1b946f658bc51e19999273fae0c8e9489cc23a3e9b05e4fcb864110d490921a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:38:53.982473Z","signature_b64":"6VZgpRyvo1BLEnmzDsCnoZQmsZpibFErCbqcBQntSa5cOMy1ly1gmif3yge9iLhoP9I1cF/v69ziLokmoFypDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b946f658bc51e19999273fae0c8e9489cc23a3e9b05e4fcb864110d490921a9","last_reissued_at":"2026-07-04T14:38:53.982058Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:38:53.982058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0407117","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":"2026-07-04T14:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0jTjrWGV5PvGmJT8JDRfWI8HTvRnf3J06HpfONkDn7kWzWXvuc6Q+iCwQKOWBV21GxdhwNkcfx0Bor+tqh5fDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:33:53.840400Z"},"content_sha256":"98d39a50957467ff8e6c9c1829cd1bfbb8d0641abd0751452ce7a4240fd44bc9","schema_version":"1.0","event_id":"sha256:98d39a50957467ff8e6c9c1829cd1bfbb8d0641abd0751452ce7a4240fd44bc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:DOKG6ZMLYUPBTGMSOP5OBSHJJC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Complete Annotated Bibliography of Work Related to Sidon Sequences","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Kevin O'Bryant","submitted_at":"2004-07-08T05:55:42Z","abstract_excerpt":"A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\\le j) are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and hyperlinked bibliography of related work."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407117","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/math/0407117/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":"2026-07-04T14:38:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vl8X29YeFfY4QVULV92d41ZqpLK10kiu5lARBXMdmXrG4Ob+R3E5WMTqyHgSONDbUbjI+b4w5tokIEojg62RAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T14:33:53.840935Z"},"content_sha256":"62cedfaa55a7485bee3fc0ea1faf0e7253a028ed25eb4c2a610d577d502abeb2","schema_version":"1.0","event_id":"sha256:62cedfaa55a7485bee3fc0ea1faf0e7253a028ed25eb4c2a610d577d502abeb2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/bundle.json","state_url":"https://pith.science/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/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":"2026-08-19T14:33:53Z","links":{"resolver":"https://pith.science/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC","bundle":"https://pith.science/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/bundle.json","state":"https://pith.science/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DOKG6ZMLYUPBTGMSOP5OBSHJJC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:DOKG6ZMLYUPBTGMSOP5OBSHJJC","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":"d70cd38e84f34fd4f2353dba6f784562ea44d5baa8d6555266e0343309dd62e5","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2004-07-08T05:55:42Z","title_canon_sha256":"1d04571b7cd1b7fbbcf6f6bafac8d8c8276beaae0fa1da2a60048ca0fc0e53ba"},"schema_version":"1.0","source":{"id":"math/0407117","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0407117","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0407117v1","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0407117","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_12","alias_value":"DOKG6ZMLYUPB","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_16","alias_value":"DOKG6ZMLYUPBTGMS","created_at":"2026-07-04T14:38:53Z"},{"alias_kind":"pith_short_8","alias_value":"DOKG6ZML","created_at":"2026-07-04T14:38:53Z"}],"graph_snapshots":[{"event_id":"sha256:62cedfaa55a7485bee3fc0ea1faf0e7253a028ed25eb4c2a610d577d502abeb2","target":"graph","created_at":"2026-07-04T14:38:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0407117/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\\le j) are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and hyperlinked bibliography of related work.","authors_text":"Kevin O'Bryant","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2004-07-08T05:55:42Z","title":"A Complete Annotated Bibliography of Work Related to Sidon Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407117","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":"sha256:98d39a50957467ff8e6c9c1829cd1bfbb8d0641abd0751452ce7a4240fd44bc9","target":"record","created_at":"2026-07-04T14:38:53Z","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":"d70cd38e84f34fd4f2353dba6f784562ea44d5baa8d6555266e0343309dd62e5","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.NT","submitted_at":"2004-07-08T05:55:42Z","title_canon_sha256":"1d04571b7cd1b7fbbcf6f6bafac8d8c8276beaae0fa1da2a60048ca0fc0e53ba"},"schema_version":"1.0","source":{"id":"math/0407117","kind":"arxiv","version":1}},"canonical_sha256":"1b946f658bc51e19999273fae0c8e9489cc23a3e9b05e4fcb864110d490921a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b946f658bc51e19999273fae0c8e9489cc23a3e9b05e4fcb864110d490921a9","first_computed_at":"2026-07-04T14:38:53.982058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:38:53.982058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6VZgpRyvo1BLEnmzDsCnoZQmsZpibFErCbqcBQntSa5cOMy1ly1gmif3yge9iLhoP9I1cF/v69ziLokmoFypDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:38:53.982473Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0407117","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98d39a50957467ff8e6c9c1829cd1bfbb8d0641abd0751452ce7a4240fd44bc9","sha256:62cedfaa55a7485bee3fc0ea1faf0e7253a028ed25eb4c2a610d577d502abeb2"],"state_sha256":"d31598b24bfd6e70985acde5b16828bb2e13313951dcf191968e068956a17fc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yAHLlV0VkxrmrH4AStcBAaKMIwW1wRSSaFypVw/8MFeE2W3hLY70zEqG9RpWDqbVnanDHYY7cDVgTu6yKL2vDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T14:33:53.844963Z","bundle_sha256":"cd2cec089b0ffe9096acec6d55bffcac81d014f7b27e15521e4cdd73412c7fda"}}