{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:53NO2ELHIXJ2KPB32FSOGFWR2W","short_pith_number":"pith:53NO2ELH","canonical_record":{"source":{"id":"1504.02271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T11:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"7f536de6ae0c329b8b1f2a0be12486e08e471219726f591c5d0f39251e718c9e","abstract_canon_sha256":"33c4c37c44596948354bcd93324054cf1b3b8d453abbb57acba8c0f6ef67c002"},"schema_version":"1.0"},"canonical_sha256":"eedaed116745d3a53c3bd164e316d1d5a2d29b3c53aaf3a45c81693f4732297c","source":{"kind":"arxiv","id":"1504.02271","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02271","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02271v3","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02271","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"53NO2ELHIXJ2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"53NO2ELHIXJ2KPB3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"53NO2ELH","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:53NO2ELHIXJ2KPB32FSOGFWR2W","target":"record","payload":{"canonical_record":{"source":{"id":"1504.02271","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T11:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"7f536de6ae0c329b8b1f2a0be12486e08e471219726f591c5d0f39251e718c9e","abstract_canon_sha256":"33c4c37c44596948354bcd93324054cf1b3b8d453abbb57acba8c0f6ef67c002"},"schema_version":"1.0"},"canonical_sha256":"eedaed116745d3a53c3bd164e316d1d5a2d29b3c53aaf3a45c81693f4732297c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:42.705951Z","signature_b64":"5bRR3wvTaZmptz0r74S5q5mplGrgIOwmOQdHAviAw7MvXcUPpMfWZG5FhFwphyXNzPPg8M5YRdC3TCvOlZ4xAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eedaed116745d3a53c3bd164e316d1d5a2d29b3c53aaf3a45c81693f4732297c","last_reissued_at":"2026-05-18T00:44:42.705534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:42.705534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.02271","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":"2026-05-18T00:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46IL5+t0kwClYaeZwXhJgf/GyMQEYektYNxRJz+9LSaUR1/XJczo0xzjXm9v+op1hMaa5uj99Xd2eYZW7tGIBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:13:07.456348Z"},"content_sha256":"899128f5dac591ecf4022e6b23df79c1d6a41f3ad42591386b5ff72109b96fe6","schema_version":"1.0","event_id":"sha256:899128f5dac591ecf4022e6b23df79c1d6a41f3ad42591386b5ff72109b96fe6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:53NO2ELHIXJ2KPB32FSOGFWR2W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","submitted_at":"2015-04-09T11:49:10Z","abstract_excerpt":"We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02271","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":""},"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":"2026-05-18T00:44:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DH5OMXRllcoy5bVQ1Wg2mNUBWQLNyQfmwXdOAIK1Z/tQ1x5zWq+M4Z/dbUcvWK1ZxxQzSRtg/uSIgvXf6OvNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:13:07.456971Z"},"content_sha256":"3aea4fdb16907c44cb380f377e7fb177f960ba4743da0443288855f6bace4d96","schema_version":"1.0","event_id":"sha256:3aea4fdb16907c44cb380f377e7fb177f960ba4743da0443288855f6bace4d96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/bundle.json","state_url":"https://pith.science/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/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":"2026-06-07T17:13:07Z","links":{"resolver":"https://pith.science/pith/53NO2ELHIXJ2KPB32FSOGFWR2W","bundle":"https://pith.science/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/bundle.json","state":"https://pith.science/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/53NO2ELHIXJ2KPB32FSOGFWR2W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:53NO2ELHIXJ2KPB32FSOGFWR2W","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":"33c4c37c44596948354bcd93324054cf1b3b8d453abbb57acba8c0f6ef67c002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T11:49:10Z","title_canon_sha256":"7f536de6ae0c329b8b1f2a0be12486e08e471219726f591c5d0f39251e718c9e"},"schema_version":"1.0","source":{"id":"1504.02271","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.02271","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"arxiv_version","alias_value":"1504.02271v3","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02271","created_at":"2026-05-18T00:44:42Z"},{"alias_kind":"pith_short_12","alias_value":"53NO2ELHIXJ2","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"53NO2ELHIXJ2KPB3","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"53NO2ELH","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:3aea4fdb16907c44cb380f377e7fb177f960ba4743da0443288855f6bace4d96","target":"graph","created_at":"2026-05-18T00:44:42Z","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":"We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional case.","authors_text":"Alessandro Languasco, Alessandro Zaccagnini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T11:49:10Z","title":"Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02271","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":"sha256:899128f5dac591ecf4022e6b23df79c1d6a41f3ad42591386b5ff72109b96fe6","target":"record","created_at":"2026-05-18T00:44:42Z","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":"33c4c37c44596948354bcd93324054cf1b3b8d453abbb57acba8c0f6ef67c002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-09T11:49:10Z","title_canon_sha256":"7f536de6ae0c329b8b1f2a0be12486e08e471219726f591c5d0f39251e718c9e"},"schema_version":"1.0","source":{"id":"1504.02271","kind":"arxiv","version":3}},"canonical_sha256":"eedaed116745d3a53c3bd164e316d1d5a2d29b3c53aaf3a45c81693f4732297c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eedaed116745d3a53c3bd164e316d1d5a2d29b3c53aaf3a45c81693f4732297c","first_computed_at":"2026-05-18T00:44:42.705534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:42.705534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5bRR3wvTaZmptz0r74S5q5mplGrgIOwmOQdHAviAw7MvXcUPpMfWZG5FhFwphyXNzPPg8M5YRdC3TCvOlZ4xAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:42.705951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.02271","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:899128f5dac591ecf4022e6b23df79c1d6a41f3ad42591386b5ff72109b96fe6","sha256:3aea4fdb16907c44cb380f377e7fb177f960ba4743da0443288855f6bace4d96"],"state_sha256":"7482eb0e43fb3fc00821ff9f71223db744af0481a3c75245c3fcaf58eb4c7262"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCPH7nNwyU2Ud9OVIZECJ6wQor+ePNEifKL3gL1RlIKsk9usyLtFMNV0DFWBM4HQbq7MGw8gXsaKH2THow+OAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:13:07.460107Z","bundle_sha256":"963db14e12b25b801ede93b95682ae99717dce2363230f4ad4930b5e82146782"}}