{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:FXSRY4IH23LAEVL6SD476YXHW4","short_pith_number":"pith:FXSRY4IH","schema_version":"1.0","canonical_sha256":"2de51c7107d6d602557e90f9ff62e7b718fdfec28711f6e0f1d4bc3e58f411a2","source":{"kind":"arxiv","id":"math/0505187","version":5},"attestation_state":"computed","paper":{"title":"Mixed sums of squares and triangular numbers (II)","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hao Pan, Song Guo, Zhi-Wei Sun","submitted_at":"2005-05-10T19:16:26Z","abstract_excerpt":"For an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$. Following a recent work of Z. W. Sun, we show that every natural number can be written in any of the following forms with $x,y,z\\in\\Z$: $$x^2+3y^2+t_z, x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$$ This confirms a conjecture of Sun."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0505187","kind":"arxiv","version":5},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2005-05-10T19:16:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5bd0fab1136c0c43c3fb88f7c27ad78ba20145a1d43b66c50465b254c145b110","abstract_canon_sha256":"1092ebc704587ac79daecda789734120396b742e43d844c17124f92215ac35f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:06:27.041959Z","signature_b64":"erqesZVqhSL5l/n8ulbBaqoJoSSl+KE+DkaZAJ29FRZ78x/MwRRioqckWAz6xI13w38vfJkuhVsoSL6olG1dDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2de51c7107d6d602557e90f9ff62e7b718fdfec28711f6e0f1d4bc3e58f411a2","last_reissued_at":"2026-07-04T15:06:27.041510Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:06:27.041510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed sums of squares and triangular numbers (II)","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Hao Pan, Song Guo, Zhi-Wei Sun","submitted_at":"2005-05-10T19:16:26Z","abstract_excerpt":"For an integer $x$ let $t_x$ denote the triangular number $x(x+1)/2$. Following a recent work of Z. W. Sun, we show that every natural number can be written in any of the following forms with $x,y,z\\in\\Z$: $$x^2+3y^2+t_z, x^2+3t_y+t_z, x^2+6t_y+t_z, 3x^2+2t_y+t_z, 4x^2+2t_y+t_z.$$ This confirms a conjecture of Sun."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505187","kind":"arxiv","version":5},"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/math/0505187/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0505187","created_at":"2026-07-04T15:06:27.041589+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0505187v5","created_at":"2026-07-04T15:06:27.041589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505187","created_at":"2026-07-04T15:06:27.041589+00:00"},{"alias_kind":"pith_short_12","alias_value":"FXSRY4IH23LA","created_at":"2026-07-04T15:06:27.041589+00:00"},{"alias_kind":"pith_short_16","alias_value":"FXSRY4IH23LAEVL6","created_at":"2026-07-04T15:06:27.041589+00:00"},{"alias_kind":"pith_short_8","alias_value":"FXSRY4IH","created_at":"2026-07-04T15:06:27.041589+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4","json":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4.json","graph_json":"https://pith.science/api/pith-number/FXSRY4IH23LAEVL6SD476YXHW4/graph.json","events_json":"https://pith.science/api/pith-number/FXSRY4IH23LAEVL6SD476YXHW4/events.json","paper":"https://pith.science/paper/FXSRY4IH"},"agent_actions":{"view_html":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4","download_json":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4.json","view_paper":"https://pith.science/paper/FXSRY4IH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0505187&json=true","fetch_graph":"https://pith.science/api/pith-number/FXSRY4IH23LAEVL6SD476YXHW4/graph.json","fetch_events":"https://pith.science/api/pith-number/FXSRY4IH23LAEVL6SD476YXHW4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4/action/storage_attestation","attest_author":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4/action/author_attestation","sign_citation":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4/action/citation_signature","submit_replication":"https://pith.science/pith/FXSRY4IH23LAEVL6SD476YXHW4/action/replication_record"}},"created_at":"2026-07-04T15:06:27.041589+00:00","updated_at":"2026-07-04T15:06:27.041589+00:00"}