{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GVS24SWOKNHWGKXCN5ZHAETUHU","short_pith_number":"pith:GVS24SWO","canonical_record":{"source":{"id":"1711.00411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T15:59:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"41d0a4ad41344224d9e0d085eabed5967da2c94a194a11b4156f7326bb92d924","abstract_canon_sha256":"ec153ee1b9874dc27ebc54593409658c80e3b0da9999e20c8ccf17ddf8c50b9b"},"schema_version":"1.0"},"canonical_sha256":"3565ae4ace534f632ae26f727012743d394adf37d99df176c16b9056a9ba1116","source":{"kind":"arxiv","id":"1711.00411","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00411","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00411v2","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00411","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"GVS24SWOKNHW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GVS24SWOKNHWGKXC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GVS24SWO","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GVS24SWOKNHWGKXCN5ZHAETUHU","target":"record","payload":{"canonical_record":{"source":{"id":"1711.00411","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T15:59:25Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"41d0a4ad41344224d9e0d085eabed5967da2c94a194a11b4156f7326bb92d924","abstract_canon_sha256":"ec153ee1b9874dc27ebc54593409658c80e3b0da9999e20c8ccf17ddf8c50b9b"},"schema_version":"1.0"},"canonical_sha256":"3565ae4ace534f632ae26f727012743d394adf37d99df176c16b9056a9ba1116","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:35.044257Z","signature_b64":"mEF0yYkkn5mYQ6YMhJeN+ikQpMZhArATvzJUx6RJQS/3hpEmmIjPnKmU3ryI2JYK5UN74KaU8WakFkedIAUsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3565ae4ace534f632ae26f727012743d394adf37d99df176c16b9056a9ba1116","last_reissued_at":"2026-05-18T00:24:35.043540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:35.043540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.00411","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aa0Qmn+bLazH9gRocPoBRxXBps5UENjfS4ZeqIJKAIHDqoq6TlCcg29uLWGq4Ii0uom3JH7pzYFg7KWMhT+ODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:03:38.099802Z"},"content_sha256":"522047e1e0c63fefb9a5f7361e4e533605001cdbcd2b979c23776d7761aaaea0","schema_version":"1.0","event_id":"sha256:522047e1e0c63fefb9a5f7361e4e533605001cdbcd2b979c23776d7761aaaea0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GVS24SWOKNHWGKXCN5ZHAETUHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Values of quadratic forms on quasicrystals and a related problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Oliver Sargent","submitted_at":"2017-11-01T15:59:25Z","abstract_excerpt":"In this paper we study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit closure classification type result in this setting. This result has additional applications. In particular, we use it to study the set of integral values of a system consisting of a quadratic form and several linear forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00411","kind":"arxiv","version":2},"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":"2026-05-18T00:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MeolsPFdoZoeK1OE/fz7vkrqCyVREZuobJxicRaziUSPcjbAk/+zJMzw+UAXG9iW3h83UUVP+aKCMXoal4orCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:03:38.100144Z"},"content_sha256":"8519682d0f9cabe19f40d663f5b448244cdb1dbd8798f859ba4dd26c7aa2d01e","schema_version":"1.0","event_id":"sha256:8519682d0f9cabe19f40d663f5b448244cdb1dbd8798f859ba4dd26c7aa2d01e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/bundle.json","state_url":"https://pith.science/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/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":"2026-06-24T22:03:38Z","links":{"resolver":"https://pith.science/pith/GVS24SWOKNHWGKXCN5ZHAETUHU","bundle":"https://pith.science/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/bundle.json","state":"https://pith.science/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GVS24SWOKNHWGKXCN5ZHAETUHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GVS24SWOKNHWGKXCN5ZHAETUHU","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":"ec153ee1b9874dc27ebc54593409658c80e3b0da9999e20c8ccf17ddf8c50b9b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T15:59:25Z","title_canon_sha256":"41d0a4ad41344224d9e0d085eabed5967da2c94a194a11b4156f7326bb92d924"},"schema_version":"1.0","source":{"id":"1711.00411","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.00411","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1711.00411v2","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.00411","created_at":"2026-05-18T00:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"GVS24SWOKNHW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GVS24SWOKNHWGKXC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GVS24SWO","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:8519682d0f9cabe19f40d663f5b448244cdb1dbd8798f859ba4dd26c7aa2d01e","target":"graph","created_at":"2026-05-18T00:24:35Z","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 study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit closure classification type result in this setting. This result has additional applications. In particular, we use it to study the set of integral values of a system consisting of a quadratic form and several linear forms.","authors_text":"Oliver Sargent","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T15:59:25Z","title":"Values of quadratic forms on quasicrystals and a related problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.00411","kind":"arxiv","version":2},"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":"sha256:522047e1e0c63fefb9a5f7361e4e533605001cdbcd2b979c23776d7761aaaea0","target":"record","created_at":"2026-05-18T00:24:35Z","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":"ec153ee1b9874dc27ebc54593409658c80e3b0da9999e20c8ccf17ddf8c50b9b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-11-01T15:59:25Z","title_canon_sha256":"41d0a4ad41344224d9e0d085eabed5967da2c94a194a11b4156f7326bb92d924"},"schema_version":"1.0","source":{"id":"1711.00411","kind":"arxiv","version":2}},"canonical_sha256":"3565ae4ace534f632ae26f727012743d394adf37d99df176c16b9056a9ba1116","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3565ae4ace534f632ae26f727012743d394adf37d99df176c16b9056a9ba1116","first_computed_at":"2026-05-18T00:24:35.043540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:35.043540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mEF0yYkkn5mYQ6YMhJeN+ikQpMZhArATvzJUx6RJQS/3hpEmmIjPnKmU3ryI2JYK5UN74KaU8WakFkedIAUsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:35.044257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.00411","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:522047e1e0c63fefb9a5f7361e4e533605001cdbcd2b979c23776d7761aaaea0","sha256:8519682d0f9cabe19f40d663f5b448244cdb1dbd8798f859ba4dd26c7aa2d01e"],"state_sha256":"39f0cb1d2ff697daa6df5cfa96d7e4687e38ec89f24be81e4d8e273c778e978c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sPmtrxYzXqevZJPOVltLPSzxErIQEvYqsDNo3BAnniOMG7T8OalFmfYykstct/1BQkHbp0O/CeMLeZg0utEwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:03:38.102131Z","bundle_sha256":"87cdd6168427c2ae1f42f9beb60f5dbda085608c000e672458ab4a4314bb12a6"}}