{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:A5V24OR7B6TDC35RPBZXZRPMA2","short_pith_number":"pith:A5V24OR7","canonical_record":{"source":{"id":"0903.3856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-23T12:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"bb194ebe668e347ce5d5267ef778878b2ec58bc83304eeda7aaf3062ca5317b1","abstract_canon_sha256":"ec6e6da4090d0f7574818657de6029d873331e8683286e93408157265b9eaaa0"},"schema_version":"1.0"},"canonical_sha256":"076bae3a3f0fa6316fb178737cc5ec06a7fbc4bee29f7a23fe7bc3a1986d6b54","source":{"kind":"arxiv","id":"0903.3856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3856","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3856v1","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3856","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"A5V24OR7B6TD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"A5V24OR7B6TDC35R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"A5V24OR7","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:A5V24OR7B6TDC35RPBZXZRPMA2","target":"record","payload":{"canonical_record":{"source":{"id":"0903.3856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-23T12:58:58Z","cross_cats_sorted":[],"title_canon_sha256":"bb194ebe668e347ce5d5267ef778878b2ec58bc83304eeda7aaf3062ca5317b1","abstract_canon_sha256":"ec6e6da4090d0f7574818657de6029d873331e8683286e93408157265b9eaaa0"},"schema_version":"1.0"},"canonical_sha256":"076bae3a3f0fa6316fb178737cc5ec06a7fbc4bee29f7a23fe7bc3a1986d6b54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:45.108256Z","signature_b64":"as3tB3AZTpwoxKI/igsFWIj2bpHFN2LDJw4zgOEB4aMUA8EP05BMPmvyJJwCJv5tdOGYoW69fJcqJiLhWfh6Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"076bae3a3f0fa6316fb178737cc5ec06a7fbc4bee29f7a23fe7bc3a1986d6b54","last_reissued_at":"2026-05-18T02:37:45.107550Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:45.107550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0903.3856","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":"2026-05-18T02:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYsuLcLjhkkDjFzvTv7fhUm7GWamqbJjyxD4KoMnN/brfSVJoAjDtscvD367m4sEg20lWIjbqQ63jYkV+zb9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:50.662573Z"},"content_sha256":"547f60f95e4e7cc67a7437f8caba414852e2add1241be7dc0bc95c80d4bfe6c1","schema_version":"1.0","event_id":"sha256:547f60f95e4e7cc67a7437f8caba414852e2add1241be7dc0bc95c80d4bfe6c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:A5V24OR7B6TDC35RPBZXZRPMA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic progressions of four squares over quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enrique Gonzalez-Jimenez, Jorn Steuding","submitted_at":"2009-03-23T12:58:58Z","abstract_excerpt":"Let d be a squarefree integer. Does there exist four squares in arithmetic progression over Q(sqrt{d})? We shall give a partial answer to this question, depending on the value of d. In the affirmative case, we construct explicit arithmetic progressions consisting of four squares over Q(sqrt{d})."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3856","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":"2026-05-18T02:37:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mZxX6x4NBGgMnYGm4uVFTRiMPdWKHJ83FQh+PBcymrpr4YsceAWryqQ/qfZAlBfOHt2lOPTaaf1bHM25wvNlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:11:50.663110Z"},"content_sha256":"d511159d24a8d42c1a9aa3de851aec2a75b2b7f6c6097b5139fcd6c89c611215","schema_version":"1.0","event_id":"sha256:d511159d24a8d42c1a9aa3de851aec2a75b2b7f6c6097b5139fcd6c89c611215"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5V24OR7B6TDC35RPBZXZRPMA2/bundle.json","state_url":"https://pith.science/pith/A5V24OR7B6TDC35RPBZXZRPMA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5V24OR7B6TDC35RPBZXZRPMA2/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":"2026-06-09T11:11:50Z","links":{"resolver":"https://pith.science/pith/A5V24OR7B6TDC35RPBZXZRPMA2","bundle":"https://pith.science/pith/A5V24OR7B6TDC35RPBZXZRPMA2/bundle.json","state":"https://pith.science/pith/A5V24OR7B6TDC35RPBZXZRPMA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5V24OR7B6TDC35RPBZXZRPMA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:A5V24OR7B6TDC35RPBZXZRPMA2","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":"ec6e6da4090d0f7574818657de6029d873331e8683286e93408157265b9eaaa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-23T12:58:58Z","title_canon_sha256":"bb194ebe668e347ce5d5267ef778878b2ec58bc83304eeda7aaf3062ca5317b1"},"schema_version":"1.0","source":{"id":"0903.3856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0903.3856","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"arxiv_version","alias_value":"0903.3856v1","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3856","created_at":"2026-05-18T02:37:45Z"},{"alias_kind":"pith_short_12","alias_value":"A5V24OR7B6TD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"A5V24OR7B6TDC35R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"A5V24OR7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d511159d24a8d42c1a9aa3de851aec2a75b2b7f6c6097b5139fcd6c89c611215","target":"graph","created_at":"2026-05-18T02:37:45Z","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":"Let d be a squarefree integer. Does there exist four squares in arithmetic progression over Q(sqrt{d})? We shall give a partial answer to this question, depending on the value of d. In the affirmative case, we construct explicit arithmetic progressions consisting of four squares over Q(sqrt{d}).","authors_text":"Enrique Gonzalez-Jimenez, Jorn Steuding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-23T12:58:58Z","title":"Arithmetic progressions of four squares over quadratic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3856","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":"sha256:547f60f95e4e7cc67a7437f8caba414852e2add1241be7dc0bc95c80d4bfe6c1","target":"record","created_at":"2026-05-18T02:37:45Z","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":"ec6e6da4090d0f7574818657de6029d873331e8683286e93408157265b9eaaa0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-03-23T12:58:58Z","title_canon_sha256":"bb194ebe668e347ce5d5267ef778878b2ec58bc83304eeda7aaf3062ca5317b1"},"schema_version":"1.0","source":{"id":"0903.3856","kind":"arxiv","version":1}},"canonical_sha256":"076bae3a3f0fa6316fb178737cc5ec06a7fbc4bee29f7a23fe7bc3a1986d6b54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"076bae3a3f0fa6316fb178737cc5ec06a7fbc4bee29f7a23fe7bc3a1986d6b54","first_computed_at":"2026-05-18T02:37:45.107550Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:45.107550Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"as3tB3AZTpwoxKI/igsFWIj2bpHFN2LDJw4zgOEB4aMUA8EP05BMPmvyJJwCJv5tdOGYoW69fJcqJiLhWfh6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:45.108256Z","signed_message":"canonical_sha256_bytes"},"source_id":"0903.3856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:547f60f95e4e7cc67a7437f8caba414852e2add1241be7dc0bc95c80d4bfe6c1","sha256:d511159d24a8d42c1a9aa3de851aec2a75b2b7f6c6097b5139fcd6c89c611215"],"state_sha256":"8ddce22c91664c44db064f45b5e26a52a90868daec1d5a386383e793c51bd96c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m2pesqHq6QH/dpTqqScUB3nOZa1xrsmHK6XcsvNsN2EH+h8O9AMogxgvMQpPyly8UusuVaugSxdncVcJ9a9SAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:11:50.665589Z","bundle_sha256":"6629106f09f552d532eddf54d391185c9c2bf39b4423e06dcc9a8745b6a7ab5e"}}