{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:5RQKRFAARZ63MGBSW2OXQIGV3U","short_pith_number":"pith:5RQKRFAA","canonical_record":{"source":{"id":"1104.5235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-27T20:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"7d48f49a76c7f1ffe2b8acec9d3b19622fe2628c2a3b566ee9a4270fe067bfec","abstract_canon_sha256":"59b337bfff5169d54cd31d32abca117197091b3fdcf4562352c146362e2f5f78"},"schema_version":"1.0"},"canonical_sha256":"ec60a894008e7db61832b69d7820d5dd0679849c8777d8bf77d0883efd42bddf","source":{"kind":"arxiv","id":"1104.5235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5235","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5235v1","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5235","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"5RQKRFAARZ63","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5RQKRFAARZ63MGBS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5RQKRFAA","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:5RQKRFAARZ63MGBSW2OXQIGV3U","target":"record","payload":{"canonical_record":{"source":{"id":"1104.5235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-27T20:00:50Z","cross_cats_sorted":[],"title_canon_sha256":"7d48f49a76c7f1ffe2b8acec9d3b19622fe2628c2a3b566ee9a4270fe067bfec","abstract_canon_sha256":"59b337bfff5169d54cd31d32abca117197091b3fdcf4562352c146362e2f5f78"},"schema_version":"1.0"},"canonical_sha256":"ec60a894008e7db61832b69d7820d5dd0679849c8777d8bf77d0883efd42bddf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:21.890247Z","signature_b64":"oBPaKY0tA8yBoafd6wpN3VO1+aibBm6NVzX9bzZCXsSH+3EqdLjASzorXEUiAyYj8lEt2MVgoHzCtbFM0+KlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec60a894008e7db61832b69d7820d5dd0679849c8777d8bf77d0883efd42bddf","last_reissued_at":"2026-05-18T04:23:21.889491Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:21.889491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.5235","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":"2026-05-18T04:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuOeWT1X0JdGWlAGy7jJbeGDx2H5cYYBn0DfE4LPjf+JtpjztgV0so5oQzEEpN4A9cH+vnO5VKds9aurKw0EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:40:40.299839Z"},"content_sha256":"8a08131b856d5820808ee5fe0cb4addbb4f4fbf9f45df95cb41d8e44a3012da6","schema_version":"1.0","event_id":"sha256:8a08131b856d5820808ee5fe0cb4addbb4f4fbf9f45df95cb41d8e44a3012da6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:5RQKRFAARZ63MGBSW2OXQIGV3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on the $\\Sopfr(n)$ function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ruslan Sharipov","submitted_at":"2011-04-27T20:00:50Z","abstract_excerpt":"The $\\Sopfr(n)$ function is defined as the sum of prime factors of $n$ each of which is taken with its multiplicity. This function is studied numerically. The analogy between $\\Sopfr(n)$ and the primes distribution function is drawn and some conjectures for prime numbers formulated in terms of the $\\Sopfr(n)$ function are suggested."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5235","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":""},"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":"2026-05-18T04:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8qvg/GT97jb71s35j6aLqmdJD/Lf6P8tHQbFryqJOW/4FeFB8TRPdd6wN2U6XZh4UM2V8RSr85Bc90eG3cUHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T06:40:40.300540Z"},"content_sha256":"0695dfa047a1de24f9a84c0a1cc786356ca48f5b56d544442588674feb552364","schema_version":"1.0","event_id":"sha256:0695dfa047a1de24f9a84c0a1cc786356ca48f5b56d544442588674feb552364"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/bundle.json","state_url":"https://pith.science/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/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":"2026-06-10T06:40:40Z","links":{"resolver":"https://pith.science/pith/5RQKRFAARZ63MGBSW2OXQIGV3U","bundle":"https://pith.science/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/bundle.json","state":"https://pith.science/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RQKRFAARZ63MGBSW2OXQIGV3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5RQKRFAARZ63MGBSW2OXQIGV3U","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":"59b337bfff5169d54cd31d32abca117197091b3fdcf4562352c146362e2f5f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-27T20:00:50Z","title_canon_sha256":"7d48f49a76c7f1ffe2b8acec9d3b19622fe2628c2a3b566ee9a4270fe067bfec"},"schema_version":"1.0","source":{"id":"1104.5235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.5235","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"1104.5235v1","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.5235","created_at":"2026-05-18T04:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"5RQKRFAARZ63","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5RQKRFAARZ63MGBS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5RQKRFAA","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:0695dfa047a1de24f9a84c0a1cc786356ca48f5b56d544442588674feb552364","target":"graph","created_at":"2026-05-18T04:23:21Z","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":"The $\\Sopfr(n)$ function is defined as the sum of prime factors of $n$ each of which is taken with its multiplicity. This function is studied numerically. The analogy between $\\Sopfr(n)$ and the primes distribution function is drawn and some conjectures for prime numbers formulated in terms of the $\\Sopfr(n)$ function are suggested.","authors_text":"Ruslan Sharipov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-27T20:00:50Z","title":"A note on the $\\Sopfr(n)$ function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.5235","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":"sha256:8a08131b856d5820808ee5fe0cb4addbb4f4fbf9f45df95cb41d8e44a3012da6","target":"record","created_at":"2026-05-18T04:23:21Z","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":"59b337bfff5169d54cd31d32abca117197091b3fdcf4562352c146362e2f5f78","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-04-27T20:00:50Z","title_canon_sha256":"7d48f49a76c7f1ffe2b8acec9d3b19622fe2628c2a3b566ee9a4270fe067bfec"},"schema_version":"1.0","source":{"id":"1104.5235","kind":"arxiv","version":1}},"canonical_sha256":"ec60a894008e7db61832b69d7820d5dd0679849c8777d8bf77d0883efd42bddf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec60a894008e7db61832b69d7820d5dd0679849c8777d8bf77d0883efd42bddf","first_computed_at":"2026-05-18T04:23:21.889491Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:21.889491Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oBPaKY0tA8yBoafd6wpN3VO1+aibBm6NVzX9bzZCXsSH+3EqdLjASzorXEUiAyYj8lEt2MVgoHzCtbFM0+KlDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:21.890247Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.5235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a08131b856d5820808ee5fe0cb4addbb4f4fbf9f45df95cb41d8e44a3012da6","sha256:0695dfa047a1de24f9a84c0a1cc786356ca48f5b56d544442588674feb552364"],"state_sha256":"6b6305210a71d6425365eea31b1e8f8d91541bd23f06a77bc4fd4ec7a77476d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YOE3WNJ5M18f72yOiie6wN1UkD8CHzKnmisux/ru0hGy3vbQy1TrOyrzh5/tgjGWXSFP75kbs227K9cxQeSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T06:40:40.304291Z","bundle_sha256":"2163294704f15cffe86738e741fba7ec89d0d3ca720bccea60181ef879e55544"}}