{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:CRBNKEAHSP3MF4BRUGK2I6MBDY","short_pith_number":"pith:CRBNKEAH","canonical_record":{"source":{"id":"2605.19449","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T07:04:04Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"cf5b2a868906e1637a4c5baca07e9b3ed9625c5914bbdd72ba417c248a7f43b3","abstract_canon_sha256":"fc10d4a8ce454fb59d2615cdae780fd14be0a8617a2272d5cac637c0d2f3f9b2"},"schema_version":"1.0"},"canonical_sha256":"1442d5100793f6c2f031a195a479811e1aef35b85ca1cca8e2e385f467dc5fdc","source":{"kind":"arxiv","id":"2605.19449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19449","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19449v1","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19449","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"CRBNKEAHSP3M","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_16","alias_value":"CRBNKEAHSP3MF4BR","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_8","alias_value":"CRBNKEAH","created_at":"2026-05-20T01:05:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:CRBNKEAHSP3MF4BRUGK2I6MBDY","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19449","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T07:04:04Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"cf5b2a868906e1637a4c5baca07e9b3ed9625c5914bbdd72ba417c248a7f43b3","abstract_canon_sha256":"fc10d4a8ce454fb59d2615cdae780fd14be0a8617a2272d5cac637c0d2f3f9b2"},"schema_version":"1.0"},"canonical_sha256":"1442d5100793f6c2f031a195a479811e1aef35b85ca1cca8e2e385f467dc5fdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:46.420280Z","signature_b64":"nPXU4VxosWXEBskqgYcFWrVxvwpBsaT+cNMKWj0uEKmB3pDUQuC95RrVtw1W0UODmfJOZjHGDONfaXTJbtb/AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1442d5100793f6c2f031a195a479811e1aef35b85ca1cca8e2e385f467dc5fdc","last_reissued_at":"2026-05-20T01:05:46.419678Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:46.419678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19449","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":"2026-05-20T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5iyUjQVSV4906whyttbP48dhAz9jjXPKd0bl0EJ0zh+KKAJnfgqcnbZUI1KusQ/PDRg6OOsz2/VoBOL9JtMbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:47:52.338310Z"},"content_sha256":"f7e9cebf32263b957b9eb387b2822b55a145135c9c4bc86789f61d997e39fc12","schema_version":"1.0","event_id":"sha256:f7e9cebf32263b957b9eb387b2822b55a145135c9c4bc86789f61d997e39fc12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:CRBNKEAHSP3MF4BRUGK2I6MBDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the number of finite additive 2-bases","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Konrad Zyhalko, Stefan Weltge","submitted_at":"2026-05-19T07:04:04Z","abstract_excerpt":"The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short proof using elementary probabilistic arguments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19449","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/2605.19449/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":"2026-05-20T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t8BGUBrBLYRO+sF2/fS0rNKG9nKGkcP7bhzqVvKVOxRcXwVmkABeXdHuzjAz3NWoI5dn+3in9iBiVRM2N0zSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:47:52.339000Z"},"content_sha256":"d71ee9799802b25c6cb47fda1bf146b389b03d78034699e7b24438a1e206c50e","schema_version":"1.0","event_id":"sha256:d71ee9799802b25c6cb47fda1bf146b389b03d78034699e7b24438a1e206c50e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/bundle.json","state_url":"https://pith.science/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/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":"2026-05-26T08:47:52Z","links":{"resolver":"https://pith.science/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY","bundle":"https://pith.science/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/bundle.json","state":"https://pith.science/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRBNKEAHSP3MF4BRUGK2I6MBDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CRBNKEAHSP3MF4BRUGK2I6MBDY","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":"fc10d4a8ce454fb59d2615cdae780fd14be0a8617a2272d5cac637c0d2f3f9b2","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T07:04:04Z","title_canon_sha256":"cf5b2a868906e1637a4c5baca07e9b3ed9625c5914bbdd72ba417c248a7f43b3"},"schema_version":"1.0","source":{"id":"2605.19449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19449","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19449v1","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19449","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"CRBNKEAHSP3M","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_16","alias_value":"CRBNKEAHSP3MF4BR","created_at":"2026-05-20T01:05:46Z"},{"alias_kind":"pith_short_8","alias_value":"CRBNKEAH","created_at":"2026-05-20T01:05:46Z"}],"graph_snapshots":[{"event_id":"sha256:d71ee9799802b25c6cb47fda1bf146b389b03d78034699e7b24438a1e206c50e","target":"graph","created_at":"2026-05-20T01:05:46Z","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/2605.19449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The number of finite additive 2-bases is known to grow exponentially. While this fact has been established by Marzuola and Miller (2010) using complex analytic techniques embedded in the study of numerical sets, we provide a direct, short proof using elementary probabilistic arguments.","authors_text":"Konrad Zyhalko, Stefan Weltge","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T07:04:04Z","title":"On the number of finite additive 2-bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19449","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:f7e9cebf32263b957b9eb387b2822b55a145135c9c4bc86789f61d997e39fc12","target":"record","created_at":"2026-05-20T01:05:46Z","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":"fc10d4a8ce454fb59d2615cdae780fd14be0a8617a2272d5cac637c0d2f3f9b2","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-19T07:04:04Z","title_canon_sha256":"cf5b2a868906e1637a4c5baca07e9b3ed9625c5914bbdd72ba417c248a7f43b3"},"schema_version":"1.0","source":{"id":"2605.19449","kind":"arxiv","version":1}},"canonical_sha256":"1442d5100793f6c2f031a195a479811e1aef35b85ca1cca8e2e385f467dc5fdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1442d5100793f6c2f031a195a479811e1aef35b85ca1cca8e2e385f467dc5fdc","first_computed_at":"2026-05-20T01:05:46.419678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:46.419678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nPXU4VxosWXEBskqgYcFWrVxvwpBsaT+cNMKWj0uEKmB3pDUQuC95RrVtw1W0UODmfJOZjHGDONfaXTJbtb/AA==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:46.420280Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7e9cebf32263b957b9eb387b2822b55a145135c9c4bc86789f61d997e39fc12","sha256:d71ee9799802b25c6cb47fda1bf146b389b03d78034699e7b24438a1e206c50e"],"state_sha256":"4ed0c059b30262322b124d2412c48c4c0100b3429765c19531d43af5fa82a9d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrkQU0R7Csb5FavbJ3h+8MCO2wA0NjUECAtVo3h5T8poKv+uT4/98adn0sdCJwiZuWQSPwAb2ZCybI2pXcLpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:47:52.342986Z","bundle_sha256":"09c5f63d952aa038c07e93f13685a38c7a89bedc0fcd2405c44d5bdb08a26fb3"}}