{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RGPYDZI67LP32HIGPTYSMJFMZT","short_pith_number":"pith:RGPYDZI6","canonical_record":{"source":{"id":"1407.0054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T20:50:56Z","cross_cats_sorted":[],"title_canon_sha256":"51f2def5464ffbd3aaffa1d4ba8c21f65134c5b53a9c90fe06e2fc4865be37fd","abstract_canon_sha256":"632e7506abd900bf6f35382b2347be265d5687149527a4c86ed946c915edf02f"},"schema_version":"1.0"},"canonical_sha256":"899f81e51efadfbd1d067cf12624acccee66943137de209bac48f26460194e1c","source":{"kind":"arxiv","id":"1407.0054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0054","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0054v1","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0054","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"RGPYDZI67LP3","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RGPYDZI67LP32HIG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RGPYDZI6","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RGPYDZI67LP32HIGPTYSMJFMZT","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T20:50:56Z","cross_cats_sorted":[],"title_canon_sha256":"51f2def5464ffbd3aaffa1d4ba8c21f65134c5b53a9c90fe06e2fc4865be37fd","abstract_canon_sha256":"632e7506abd900bf6f35382b2347be265d5687149527a4c86ed946c915edf02f"},"schema_version":"1.0"},"canonical_sha256":"899f81e51efadfbd1d067cf12624acccee66943137de209bac48f26460194e1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:35.346008Z","signature_b64":"dFkk0gvS3MKZCbFRFEBZTgcVBJxtGCP7ujTcxCBt9hS9NqcLdWHAjA/fb/m8CKZiEFLI0WIJAn3QRBiuBnGACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"899f81e51efadfbd1d067cf12624acccee66943137de209bac48f26460194e1c","last_reissued_at":"2026-05-18T02:48:35.345390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:35.345390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0054","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":"2026-05-18T02:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2i7cMExAoQFLwzkH38wfGbNlLfKix6o8tfggAq97ezOh6r2UwtmoxPWxd7MOa5xYmEAq3bHu9v2ZAxIf8vqDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:49:13.927805Z"},"content_sha256":"dbd9bb63a18a2e3e56ed1603bcb45ea30aae0380b731bc56e1e62b05c62536bb","schema_version":"1.0","event_id":"sha256:dbd9bb63a18a2e3e56ed1603bcb45ea30aae0380b731bc56e1e62b05c62536bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RGPYDZI67LP32HIGPTYSMJFMZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Squarefull numbers in arithmetic progression II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tsz Ho Chan","submitted_at":"2014-06-30T20:50:56Z","abstract_excerpt":"In this paper, we improve the error term in a previous paper on an asymptotic formula for the number of squarefull numbers in an arithmetic progression."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0054","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":"2026-05-18T02:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mqhwxgoIcFfeHfH7TpQvDix41RQLbFT9m3hpmHT4HRcFRbX7ZwVDXDMYrjZgfdWYOFaQq1qkpmO+svhgE2H0Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:49:13.928141Z"},"content_sha256":"8c72dddcc6feb671f194c5889e4f9ebfab8d96f85dbc021350a384fec99911d2","schema_version":"1.0","event_id":"sha256:8c72dddcc6feb671f194c5889e4f9ebfab8d96f85dbc021350a384fec99911d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGPYDZI67LP32HIGPTYSMJFMZT/bundle.json","state_url":"https://pith.science/pith/RGPYDZI67LP32HIGPTYSMJFMZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGPYDZI67LP32HIGPTYSMJFMZT/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":"2026-06-23T05:49:13Z","links":{"resolver":"https://pith.science/pith/RGPYDZI67LP32HIGPTYSMJFMZT","bundle":"https://pith.science/pith/RGPYDZI67LP32HIGPTYSMJFMZT/bundle.json","state":"https://pith.science/pith/RGPYDZI67LP32HIGPTYSMJFMZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGPYDZI67LP32HIGPTYSMJFMZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RGPYDZI67LP32HIGPTYSMJFMZT","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":"632e7506abd900bf6f35382b2347be265d5687149527a4c86ed946c915edf02f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T20:50:56Z","title_canon_sha256":"51f2def5464ffbd3aaffa1d4ba8c21f65134c5b53a9c90fe06e2fc4865be37fd"},"schema_version":"1.0","source":{"id":"1407.0054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0054","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0054v1","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0054","created_at":"2026-05-18T02:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"RGPYDZI67LP3","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RGPYDZI67LP32HIG","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RGPYDZI6","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:8c72dddcc6feb671f194c5889e4f9ebfab8d96f85dbc021350a384fec99911d2","target":"graph","created_at":"2026-05-18T02:48:35Z","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":"In this paper, we improve the error term in a previous paper on an asymptotic formula for the number of squarefull numbers in an arithmetic progression.","authors_text":"Tsz Ho Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T20:50:56Z","title":"Squarefull numbers in arithmetic progression II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0054","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:dbd9bb63a18a2e3e56ed1603bcb45ea30aae0380b731bc56e1e62b05c62536bb","target":"record","created_at":"2026-05-18T02:48:35Z","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":"632e7506abd900bf6f35382b2347be265d5687149527a4c86ed946c915edf02f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-06-30T20:50:56Z","title_canon_sha256":"51f2def5464ffbd3aaffa1d4ba8c21f65134c5b53a9c90fe06e2fc4865be37fd"},"schema_version":"1.0","source":{"id":"1407.0054","kind":"arxiv","version":1}},"canonical_sha256":"899f81e51efadfbd1d067cf12624acccee66943137de209bac48f26460194e1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"899f81e51efadfbd1d067cf12624acccee66943137de209bac48f26460194e1c","first_computed_at":"2026-05-18T02:48:35.345390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:35.345390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dFkk0gvS3MKZCbFRFEBZTgcVBJxtGCP7ujTcxCBt9hS9NqcLdWHAjA/fb/m8CKZiEFLI0WIJAn3QRBiuBnGACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:35.346008Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbd9bb63a18a2e3e56ed1603bcb45ea30aae0380b731bc56e1e62b05c62536bb","sha256:8c72dddcc6feb671f194c5889e4f9ebfab8d96f85dbc021350a384fec99911d2"],"state_sha256":"d56e8391bc270e56a1bfae690da4045069a891c286378cea4547e90062c5a54d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZesqxANHsVurQHaZlnuvtPwyEVQdcrmipEICVvQPnu4ySKMH0mh1k2j5PDqrzMLn6XdYt0wB510Pu40ICgwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:49:13.930036Z","bundle_sha256":"930936b1d9abf253664d27026e7d5effe270a52c037e355fe6d3630d88d74243"}}