{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ACJFUYDXWGIHIR4XPQOMFEYFT3","short_pith_number":"pith:ACJFUYDX","canonical_record":{"source":{"id":"2502.13039","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-18T16:50:42Z","cross_cats_sorted":[],"title_canon_sha256":"c64ee556108aae6cdf289a58ab393edf1bf5b076820a5ddcc34115e23454e050","abstract_canon_sha256":"7bc3199a9f530990b1663b00846901f0b7a749e04ecfd7c1199aa279db608670"},"schema_version":"1.0"},"canonical_sha256":"00925a6077b1907447977c1cc293059ef759f1f440da2418d69a98ab962b9e7c","source":{"kind":"arxiv","id":"2502.13039","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13039","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13039v3","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13039","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"ACJFUYDXWGIH","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"ACJFUYDXWGIHIR4X","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"ACJFUYDX","created_at":"2026-07-05T10:17:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ACJFUYDXWGIHIR4XPQOMFEYFT3","target":"record","payload":{"canonical_record":{"source":{"id":"2502.13039","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-18T16:50:42Z","cross_cats_sorted":[],"title_canon_sha256":"c64ee556108aae6cdf289a58ab393edf1bf5b076820a5ddcc34115e23454e050","abstract_canon_sha256":"7bc3199a9f530990b1663b00846901f0b7a749e04ecfd7c1199aa279db608670"},"schema_version":"1.0"},"canonical_sha256":"00925a6077b1907447977c1cc293059ef759f1f440da2418d69a98ab962b9e7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:54.662432Z","signature_b64":"wFgv3ibSkpqy3UsIMLbc+Fy3b3wPy86VZIFFPGP4ziKylEdpX9LT8SIFJObCH9IRlc/A9ntv9GpBRvPEgzQpCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00925a6077b1907447977c1cc293059ef759f1f440da2418d69a98ab962b9e7c","last_reissued_at":"2026-07-05T10:17:54.661993Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:54.661993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.13039","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":"2026-07-05T10:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xBAO0yxqOBKdO7v+/UpGJEcGM3k/fzKKSEQdWtfWJQlpEuntX5V/aMcaEKVEGDyFrEcaMRmvF7MBkwXRk73PBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:30.142039Z"},"content_sha256":"79945bb96282c31b936d275eaa6a2adaec4931370296629a4e808b3482c8238b","schema_version":"1.0","event_id":"sha256:79945bb96282c31b936d275eaa6a2adaec4931370296629a4e808b3482c8238b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ACJFUYDXWGIHIR4XPQOMFEYFT3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"${\\mathbf Q}$-independence and the construction of $B_h$-sets of integers and lattice points","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Melvyn B. Nathanson","submitted_at":"2025-02-18T16:50:42Z","abstract_excerpt":"This paper gives a simple ${\\mathbf Q}$-vector space construction of finite $B_h$-sets of integers and lattice points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13039","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.13039/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":"2026-07-05T10:17:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NF7e2QRpIkuIFEhXc/q3ZkrEvgM7UmNb0k6eqNgenrC/4toTakVAXRTzNyKYEsDUpnuLGbYvzxJPA3J/1eivDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:01:30.142527Z"},"content_sha256":"d739a124a5527083d80dec054d4fd35c7e826326de59629e518d9872f3eeca40","schema_version":"1.0","event_id":"sha256:d739a124a5527083d80dec054d4fd35c7e826326de59629e518d9872f3eeca40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/bundle.json","state_url":"https://pith.science/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/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":"2026-08-09T04:01:30Z","links":{"resolver":"https://pith.science/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3","bundle":"https://pith.science/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/bundle.json","state":"https://pith.science/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACJFUYDXWGIHIR4XPQOMFEYFT3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ACJFUYDXWGIHIR4XPQOMFEYFT3","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":"7bc3199a9f530990b1663b00846901f0b7a749e04ecfd7c1199aa279db608670","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-18T16:50:42Z","title_canon_sha256":"c64ee556108aae6cdf289a58ab393edf1bf5b076820a5ddcc34115e23454e050"},"schema_version":"1.0","source":{"id":"2502.13039","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.13039","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"2502.13039v3","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.13039","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"ACJFUYDXWGIH","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_16","alias_value":"ACJFUYDXWGIHIR4X","created_at":"2026-07-05T10:17:54Z"},{"alias_kind":"pith_short_8","alias_value":"ACJFUYDX","created_at":"2026-07-05T10:17:54Z"}],"graph_snapshots":[{"event_id":"sha256:d739a124a5527083d80dec054d4fd35c7e826326de59629e518d9872f3eeca40","target":"graph","created_at":"2026-07-05T10:17:54Z","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/2502.13039/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper gives a simple ${\\mathbf Q}$-vector space construction of finite $B_h$-sets of integers and lattice points.","authors_text":"Melvyn B. Nathanson","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-18T16:50:42Z","title":"${\\mathbf Q}$-independence and the construction of $B_h$-sets of integers and lattice points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.13039","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":"sha256:79945bb96282c31b936d275eaa6a2adaec4931370296629a4e808b3482c8238b","target":"record","created_at":"2026-07-05T10:17:54Z","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":"7bc3199a9f530990b1663b00846901f0b7a749e04ecfd7c1199aa279db608670","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-18T16:50:42Z","title_canon_sha256":"c64ee556108aae6cdf289a58ab393edf1bf5b076820a5ddcc34115e23454e050"},"schema_version":"1.0","source":{"id":"2502.13039","kind":"arxiv","version":3}},"canonical_sha256":"00925a6077b1907447977c1cc293059ef759f1f440da2418d69a98ab962b9e7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00925a6077b1907447977c1cc293059ef759f1f440da2418d69a98ab962b9e7c","first_computed_at":"2026-07-05T10:17:54.661993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:17:54.661993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wFgv3ibSkpqy3UsIMLbc+Fy3b3wPy86VZIFFPGP4ziKylEdpX9LT8SIFJObCH9IRlc/A9ntv9GpBRvPEgzQpCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:17:54.662432Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.13039","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79945bb96282c31b936d275eaa6a2adaec4931370296629a4e808b3482c8238b","sha256:d739a124a5527083d80dec054d4fd35c7e826326de59629e518d9872f3eeca40"],"state_sha256":"a12dc226f4b1c53e27f7f00017673c92bc0b2e3a8b5d115ba77a2521055902e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qs6DzTe5IxBXGO6PSFxmuF0ZIQQmzIr9+H8Y3MJOXyhHiPBNTFxN7i2ffY0VVXuEudyt9s7CjwnBgeiWNfSiDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:01:30.147776Z","bundle_sha256":"773defc487424879a25274830c604e9175665347111544319c943ec9f9dcccf5"}}