{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YJ5W7XMAB4TDTWDQJMU6NXSJKV","short_pith_number":"pith:YJ5W7XMA","canonical_record":{"source":{"id":"1408.1435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-06T22:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"b317d07d8a3198bf7643391ba674c27024d1e0eb7a1156aca81a057e264eb06c","abstract_canon_sha256":"0025d4207c4d4014f3641a237b19e294052c7ba8e8d6606c63e4805625c39db9"},"schema_version":"1.0"},"canonical_sha256":"c27b6fdd800f2639d8704b29e6de49554ca0bf18f162922106b63bdf03746583","source":{"kind":"arxiv","id":"1408.1435","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1435","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1435v3","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1435","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"YJ5W7XMAB4TD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJ5W7XMAB4TDTWDQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJ5W7XMA","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YJ5W7XMAB4TDTWDQJMU6NXSJKV","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1435","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-06T22:00:54Z","cross_cats_sorted":[],"title_canon_sha256":"b317d07d8a3198bf7643391ba674c27024d1e0eb7a1156aca81a057e264eb06c","abstract_canon_sha256":"0025d4207c4d4014f3641a237b19e294052c7ba8e8d6606c63e4805625c39db9"},"schema_version":"1.0"},"canonical_sha256":"c27b6fdd800f2639d8704b29e6de49554ca0bf18f162922106b63bdf03746583","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:01.027415Z","signature_b64":"sAR0OI9t35YgeVeXBLNvs/E4kntaQVF0eFJem8H7yMf7LotOJC/Kheb6jKcopp3l+s5O4NPDvRtejPQSm1NoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c27b6fdd800f2639d8704b29e6de49554ca0bf18f162922106b63bdf03746583","last_reissued_at":"2026-05-18T02:19:01.026911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:01.026911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1435","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":"2026-05-18T02:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4b4GzwD17P0HRzG1bGjvuu+el19PjcFCwhkWHhreOcTfzuYD6CqHEUwp2CR3X6BUjFYL91auJooAJL4h3QSCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:55:38.929116Z"},"content_sha256":"6909e6abe2469609e1d502fad78e1c5087f7347e2a30c0e1e35d3dfeb3bdf5fd","schema_version":"1.0","event_id":"sha256:6909e6abe2469609e1d502fad78e1c5087f7347e2a30c0e1e35d3dfeb3bdf5fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YJ5W7XMAB4TDTWDQJMU6NXSJKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On integers which are representable as sums of large squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Alessio Moscariello","submitted_at":"2014-08-06T22:00:54Z","abstract_excerpt":"We prove that the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\\{n^2,(n+1)^2,\\ldots \\}$ is asymptotically $O(n^2)$, verifying thus a conjecture of Dutch and Rickett. Furthermore we ask a question on the representation of integers as sum of four large squares."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1435","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":"2026-05-18T02:19:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KG+pBf15fp4DD631WdZzfC3hsRnbEQcoC/wxGYEZAckIKJmBtUMnNz+5nyrHBQi+WDxtjoRhT2b0dEi6ecdlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:55:38.929658Z"},"content_sha256":"8821d8f42d8c5595f320a9ca088067cbacb6055ebe7c7c6a0711785755160b49","schema_version":"1.0","event_id":"sha256:8821d8f42d8c5595f320a9ca088067cbacb6055ebe7c7c6a0711785755160b49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/bundle.json","state_url":"https://pith.science/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/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":"2026-06-01T06:55:38Z","links":{"resolver":"https://pith.science/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV","bundle":"https://pith.science/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/bundle.json","state":"https://pith.science/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJ5W7XMAB4TDTWDQJMU6NXSJKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YJ5W7XMAB4TDTWDQJMU6NXSJKV","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":"0025d4207c4d4014f3641a237b19e294052c7ba8e8d6606c63e4805625c39db9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-06T22:00:54Z","title_canon_sha256":"b317d07d8a3198bf7643391ba674c27024d1e0eb7a1156aca81a057e264eb06c"},"schema_version":"1.0","source":{"id":"1408.1435","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1435","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1435v3","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1435","created_at":"2026-05-18T02:19:01Z"},{"alias_kind":"pith_short_12","alias_value":"YJ5W7XMAB4TD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YJ5W7XMAB4TDTWDQ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YJ5W7XMA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:8821d8f42d8c5595f320a9ca088067cbacb6055ebe7c7c6a0711785755160b49","target":"graph","created_at":"2026-05-18T02:19:01Z","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 the greatest positive integer that is not expressible as a linear combination with integer coefficients of elements of the set $\\{n^2,(n+1)^2,\\ldots \\}$ is asymptotically $O(n^2)$, verifying thus a conjecture of Dutch and Rickett. Furthermore we ask a question on the representation of integers as sum of four large squares.","authors_text":"Alessio Moscariello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-06T22:00:54Z","title":"On integers which are representable as sums of large squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1435","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":"sha256:6909e6abe2469609e1d502fad78e1c5087f7347e2a30c0e1e35d3dfeb3bdf5fd","target":"record","created_at":"2026-05-18T02:19:01Z","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":"0025d4207c4d4014f3641a237b19e294052c7ba8e8d6606c63e4805625c39db9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-06T22:00:54Z","title_canon_sha256":"b317d07d8a3198bf7643391ba674c27024d1e0eb7a1156aca81a057e264eb06c"},"schema_version":"1.0","source":{"id":"1408.1435","kind":"arxiv","version":3}},"canonical_sha256":"c27b6fdd800f2639d8704b29e6de49554ca0bf18f162922106b63bdf03746583","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c27b6fdd800f2639d8704b29e6de49554ca0bf18f162922106b63bdf03746583","first_computed_at":"2026-05-18T02:19:01.026911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:01.026911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sAR0OI9t35YgeVeXBLNvs/E4kntaQVF0eFJem8H7yMf7LotOJC/Kheb6jKcopp3l+s5O4NPDvRtejPQSm1NoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:01.027415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1435","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6909e6abe2469609e1d502fad78e1c5087f7347e2a30c0e1e35d3dfeb3bdf5fd","sha256:8821d8f42d8c5595f320a9ca088067cbacb6055ebe7c7c6a0711785755160b49"],"state_sha256":"137ad5fc9754769a380fadd5b51a73845e12c9c19acefd08d83d1865e5e6c13b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EQysrAo9J730tRoQDk7f0Axxb6IATvn+UCteKNPQ4x3ONAXm+gtGzKuHvLbB4ELVsjLaw4NrVeh1rpI7bHrrCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:55:38.933034Z","bundle_sha256":"ad334a4f44fe2f57e2cdaf6d572b51ff81d0a29d32f3db69f0c35b450edbd862"}}