{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WKIBWTLKJ6ZXNDZXCQHRVJU4AV","short_pith_number":"pith:WKIBWTLK","canonical_record":{"source":{"id":"1505.04174","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-15T19:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"882eba6b5b56fcdacfe4f0c149cf6599837bca2b1da099193f36a6e4723981f2","abstract_canon_sha256":"0757d8e253d0b30b0071eb39a0b054f78664972cb972d7c31215cf54ebeaaead"},"schema_version":"1.0"},"canonical_sha256":"b2901b4d6a4fb3768f37140f1aa69c055078dd3ec820105f7eae92744c745a31","source":{"kind":"arxiv","id":"1505.04174","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04174","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04174v2","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04174","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"WKIBWTLKJ6ZX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKIBWTLKJ6ZXNDZX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKIBWTLK","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WKIBWTLKJ6ZXNDZXCQHRVJU4AV","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04174","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-15T19:33:45Z","cross_cats_sorted":[],"title_canon_sha256":"882eba6b5b56fcdacfe4f0c149cf6599837bca2b1da099193f36a6e4723981f2","abstract_canon_sha256":"0757d8e253d0b30b0071eb39a0b054f78664972cb972d7c31215cf54ebeaaead"},"schema_version":"1.0"},"canonical_sha256":"b2901b4d6a4fb3768f37140f1aa69c055078dd3ec820105f7eae92744c745a31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:36.240905Z","signature_b64":"IVA9t4l7VCzJW6jiCseBnd60vzpv/I5NtFUo0Q0fKh4LmSpn9AnDjpA8AnxlDs4YOGGQG9JS1qVdJ27F+y6BAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2901b4d6a4fb3768f37140f1aa69c055078dd3ec820105f7eae92744c745a31","last_reissued_at":"2026-05-18T01:01:36.240418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:36.240418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04174","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3o99MoIVun9327td5GpgbgGalsT8V4jOuOBPxIXgJxmvvgOgQwC6VxFil1sC2RkrMBaffVsUWYjCG7ubL0MZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:56:13.967508Z"},"content_sha256":"4acfde95055f4b765ac4cbf2af5e4347c8cabc7650c0363903d3ae999e083e27","schema_version":"1.0","event_id":"sha256:4acfde95055f4b765ac4cbf2af5e4347c8cabc7650c0363903d3ae999e083e27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WKIBWTLKJ6ZXNDZXCQHRVJU4AV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some examples in the theory of Beurling's generalized prime numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Gregory Debruyne, Jan-Christoph Schlage-Puchta, Jasson Vindas","submitted_at":"2015-05-15T19:33:45Z","abstract_excerpt":"Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04174","kind":"arxiv","version":2},"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":"2026-05-18T01:01:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sn3bsDwAy8rcUY6Yve7s3mw48RseRnYvk6WupNZ3VBYmYlCYS2A/5rlkUr0gwA1ulbqEriv29QC5ma9ChqH5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:56:13.968177Z"},"content_sha256":"69266ee4575faab3f7a6b3a1e7b8de685b7383c82b06a01dffb77bd308a2506b","schema_version":"1.0","event_id":"sha256:69266ee4575faab3f7a6b3a1e7b8de685b7383c82b06a01dffb77bd308a2506b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/bundle.json","state_url":"https://pith.science/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/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":"2026-05-27T11:56:13Z","links":{"resolver":"https://pith.science/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV","bundle":"https://pith.science/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/bundle.json","state":"https://pith.science/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKIBWTLKJ6ZXNDZXCQHRVJU4AV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WKIBWTLKJ6ZXNDZXCQHRVJU4AV","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":"0757d8e253d0b30b0071eb39a0b054f78664972cb972d7c31215cf54ebeaaead","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-15T19:33:45Z","title_canon_sha256":"882eba6b5b56fcdacfe4f0c149cf6599837bca2b1da099193f36a6e4723981f2"},"schema_version":"1.0","source":{"id":"1505.04174","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04174","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04174v2","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04174","created_at":"2026-05-18T01:01:36Z"},{"alias_kind":"pith_short_12","alias_value":"WKIBWTLKJ6ZX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WKIBWTLKJ6ZXNDZX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WKIBWTLK","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:69266ee4575faab3f7a6b3a1e7b8de685b7383c82b06a01dffb77bd308a2506b","target":"graph","created_at":"2026-05-18T01:01:36Z","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":"Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.","authors_text":"Gregory Debruyne, Jan-Christoph Schlage-Puchta, Jasson Vindas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-15T19:33:45Z","title":"Some examples in the theory of Beurling's generalized prime numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04174","kind":"arxiv","version":2},"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":"sha256:4acfde95055f4b765ac4cbf2af5e4347c8cabc7650c0363903d3ae999e083e27","target":"record","created_at":"2026-05-18T01:01:36Z","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":"0757d8e253d0b30b0071eb39a0b054f78664972cb972d7c31215cf54ebeaaead","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-05-15T19:33:45Z","title_canon_sha256":"882eba6b5b56fcdacfe4f0c149cf6599837bca2b1da099193f36a6e4723981f2"},"schema_version":"1.0","source":{"id":"1505.04174","kind":"arxiv","version":2}},"canonical_sha256":"b2901b4d6a4fb3768f37140f1aa69c055078dd3ec820105f7eae92744c745a31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2901b4d6a4fb3768f37140f1aa69c055078dd3ec820105f7eae92744c745a31","first_computed_at":"2026-05-18T01:01:36.240418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:36.240418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVA9t4l7VCzJW6jiCseBnd60vzpv/I5NtFUo0Q0fKh4LmSpn9AnDjpA8AnxlDs4YOGGQG9JS1qVdJ27F+y6BAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:36.240905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04174","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4acfde95055f4b765ac4cbf2af5e4347c8cabc7650c0363903d3ae999e083e27","sha256:69266ee4575faab3f7a6b3a1e7b8de685b7383c82b06a01dffb77bd308a2506b"],"state_sha256":"870faa9e530ff8bd12bc80c7cf719409deca5d39db7a05190d05cb9e6115768b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ZPIMwsy/DiS/93gs367GJjJMvyUzlGi3LI431XCrVFGRgOh4TL1YeqmXDaPPU6HhGm7xCXqn/2xjzkhf/zDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:56:13.971249Z","bundle_sha256":"cbe0bb0a0cdd8dc301c0825be79b02538c3b507a5573795c57e363de8aee348f"}}