{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:EGUKRH6I527IOIG7OB3MVOHULY","short_pith_number":"pith:EGUKRH6I","canonical_record":{"source":{"id":"2205.12226","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-05-24T17:34:54Z","cross_cats_sorted":[],"title_canon_sha256":"84e1286e3528e857f26b49e0b94c5cc7058cfc6776454a30e85ec2283a3bcd78","abstract_canon_sha256":"a0ccc3b0c784600f728071669f52ccc64e8b851cc929b4415eaa8a5e6dddd45f"},"schema_version":"1.0"},"canonical_sha256":"21a8a89fc8eebe8720df7076cab8f45e333152d572abaacb92f84417ff711da4","source":{"kind":"arxiv","id":"2205.12226","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.12226","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"2205.12226v4","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12226","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"EGUKRH6I527I","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_16","alias_value":"EGUKRH6I527IOIG7","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_8","alias_value":"EGUKRH6I","created_at":"2026-07-05T05:29:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:EGUKRH6I527IOIG7OB3MVOHULY","target":"record","payload":{"canonical_record":{"source":{"id":"2205.12226","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-05-24T17:34:54Z","cross_cats_sorted":[],"title_canon_sha256":"84e1286e3528e857f26b49e0b94c5cc7058cfc6776454a30e85ec2283a3bcd78","abstract_canon_sha256":"a0ccc3b0c784600f728071669f52ccc64e8b851cc929b4415eaa8a5e6dddd45f"},"schema_version":"1.0"},"canonical_sha256":"21a8a89fc8eebe8720df7076cab8f45e333152d572abaacb92f84417ff711da4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:29:53.042740Z","signature_b64":"MOmG0m73uV+obUR3iD5rCaHt9kL/KILlNjiQFoDacXg7LHV7U6UcddCJl9+ghSr9c84HqL+U4bmh82vQdOQzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21a8a89fc8eebe8720df7076cab8f45e333152d572abaacb92f84417ff711da4","last_reissued_at":"2026-07-05T05:29:53.042379Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:29:53.042379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.12226","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZK/G9go0JghVhxThuMsvqYIr565tWpkFWbqYtAjNLI6I1zSqdN2GqOTGsltK5sFfjl7CCp5YsamLQhMj1L6qAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:40:52.982484Z"},"content_sha256":"ccfc25534ff9070079ebf6f4a396e5ccd219b73f9775d91f0b4c6d80721c252e","schema_version":"1.0","event_id":"sha256:ccfc25534ff9070079ebf6f4a396e5ccd219b73f9775d91f0b4c6d80721c252e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:EGUKRH6I527IOIG7OB3MVOHULY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A system of certain linear Diophantine equations on analogs of squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kota Saito, Yuya Kanado","submitted_at":"2022-05-24T17:34:54Z","abstract_excerpt":"This study investigates the existence of tuples $(k, \\ell, m)$ of integers such that all of $k$, $\\ell$, $m$, $k+\\ell$, $\\ell+m$, $m+k$, $k+\\ell+m$ belong to $S(\\alpha)$, where $S(\\alpha)$ is the set of all integers of the form $\\lfloor \\alpha n^2 \\rfloor$ for $n\\geq \\alpha^{-1/2}$ and $\\lfloor x\\rfloor$ denotes the integer part of $x$. We show that $T(\\alpha)$, the set of all such tuples, is infinite for all $\\alpha\\in (0,1)\\cap \\mathbb{Q}$ and for almost all $\\alpha\\in (0,1)$ in the sense of the Lebesgue measure. Furthermore, we show that if there exists $\\alpha>0$ such that $T(\\alpha)$ is f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12226","kind":"arxiv","version":4},"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/2205.12226/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:29:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x7P5EdPpMC9BBJJfanX7EmMSO4T+ECOVmuyAjEEMYBesQPw2Gx4T0zdIk5WF+OQS8nNk1l2AxxnHHCpg79M7Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T06:40:52.983013Z"},"content_sha256":"c0533d4c6e0dd6445f1a22a7ded89227ecbe6f5fd13e0363b0e90c7565ce4b4f","schema_version":"1.0","event_id":"sha256:c0533d4c6e0dd6445f1a22a7ded89227ecbe6f5fd13e0363b0e90c7565ce4b4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EGUKRH6I527IOIG7OB3MVOHULY/bundle.json","state_url":"https://pith.science/pith/EGUKRH6I527IOIG7OB3MVOHULY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EGUKRH6I527IOIG7OB3MVOHULY/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":"2026-08-16T06:40:52Z","links":{"resolver":"https://pith.science/pith/EGUKRH6I527IOIG7OB3MVOHULY","bundle":"https://pith.science/pith/EGUKRH6I527IOIG7OB3MVOHULY/bundle.json","state":"https://pith.science/pith/EGUKRH6I527IOIG7OB3MVOHULY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EGUKRH6I527IOIG7OB3MVOHULY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EGUKRH6I527IOIG7OB3MVOHULY","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":"a0ccc3b0c784600f728071669f52ccc64e8b851cc929b4415eaa8a5e6dddd45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-05-24T17:34:54Z","title_canon_sha256":"84e1286e3528e857f26b49e0b94c5cc7058cfc6776454a30e85ec2283a3bcd78"},"schema_version":"1.0","source":{"id":"2205.12226","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.12226","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"arxiv_version","alias_value":"2205.12226v4","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.12226","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_12","alias_value":"EGUKRH6I527I","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_16","alias_value":"EGUKRH6I527IOIG7","created_at":"2026-07-05T05:29:53Z"},{"alias_kind":"pith_short_8","alias_value":"EGUKRH6I","created_at":"2026-07-05T05:29:53Z"}],"graph_snapshots":[{"event_id":"sha256:c0533d4c6e0dd6445f1a22a7ded89227ecbe6f5fd13e0363b0e90c7565ce4b4f","target":"graph","created_at":"2026-07-05T05:29:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2205.12226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This study investigates the existence of tuples $(k, \\ell, m)$ of integers such that all of $k$, $\\ell$, $m$, $k+\\ell$, $\\ell+m$, $m+k$, $k+\\ell+m$ belong to $S(\\alpha)$, where $S(\\alpha)$ is the set of all integers of the form $\\lfloor \\alpha n^2 \\rfloor$ for $n\\geq \\alpha^{-1/2}$ and $\\lfloor x\\rfloor$ denotes the integer part of $x$. We show that $T(\\alpha)$, the set of all such tuples, is infinite for all $\\alpha\\in (0,1)\\cap \\mathbb{Q}$ and for almost all $\\alpha\\in (0,1)$ in the sense of the Lebesgue measure. Furthermore, we show that if there exists $\\alpha>0$ such that $T(\\alpha)$ is f","authors_text":"Kota Saito, Yuya Kanado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-05-24T17:34:54Z","title":"A system of certain linear Diophantine equations on analogs of squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.12226","kind":"arxiv","version":4},"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:ccfc25534ff9070079ebf6f4a396e5ccd219b73f9775d91f0b4c6d80721c252e","target":"record","created_at":"2026-07-05T05:29:53Z","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":"a0ccc3b0c784600f728071669f52ccc64e8b851cc929b4415eaa8a5e6dddd45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2022-05-24T17:34:54Z","title_canon_sha256":"84e1286e3528e857f26b49e0b94c5cc7058cfc6776454a30e85ec2283a3bcd78"},"schema_version":"1.0","source":{"id":"2205.12226","kind":"arxiv","version":4}},"canonical_sha256":"21a8a89fc8eebe8720df7076cab8f45e333152d572abaacb92f84417ff711da4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a8a89fc8eebe8720df7076cab8f45e333152d572abaacb92f84417ff711da4","first_computed_at":"2026-07-05T05:29:53.042379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:29:53.042379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MOmG0m73uV+obUR3iD5rCaHt9kL/KILlNjiQFoDacXg7LHV7U6UcddCJl9+ghSr9c84HqL+U4bmh82vQdOQzDg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:29:53.042740Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.12226","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccfc25534ff9070079ebf6f4a396e5ccd219b73f9775d91f0b4c6d80721c252e","sha256:c0533d4c6e0dd6445f1a22a7ded89227ecbe6f5fd13e0363b0e90c7565ce4b4f"],"state_sha256":"e1c119cd3148d2e52c07454c1d0f4afea84d2a3332ac71e9e342a7be58d9b54d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"takZMm5yximYIHQvwxCbkIjyhc2A2p2wTmzd/nyxYjP4Lgr1y55+d9zGBHdmPPUVjc3q0auIQ+M3Hbhzj5LbDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T06:40:52.988168Z","bundle_sha256":"e12be90afed73bcf2c0e8008bc1681facd21fc0d4cf410384b8a4bcfaf1b32ee"}}