{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QPMVRTH3YG3KZ7S54WQDAE464C","short_pith_number":"pith:QPMVRTH3","canonical_record":{"source":{"id":"1208.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-05T01:51:00Z","cross_cats_sorted":[],"title_canon_sha256":"9c84ba3646659673e62ed1e4fd0adc28fb63314f1d29df6c5e25c221724be58b","abstract_canon_sha256":"f5ebda3cd71614de83ab9e74bddde0d876288383b59b4ac86c2399d5c2bb2528"},"schema_version":"1.0"},"canonical_sha256":"83d958ccfbc1b6acfe5de5a030139ee0ba31206606cec0765dc43900e4db9636","source":{"kind":"arxiv","id":"1208.0974","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0974","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0974v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0974","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"QPMVRTH3YG3K","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPMVRTH3YG3KZ7S5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPMVRTH3","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QPMVRTH3YG3KZ7S54WQDAE464C","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0974","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-05T01:51:00Z","cross_cats_sorted":[],"title_canon_sha256":"9c84ba3646659673e62ed1e4fd0adc28fb63314f1d29df6c5e25c221724be58b","abstract_canon_sha256":"f5ebda3cd71614de83ab9e74bddde0d876288383b59b4ac86c2399d5c2bb2528"},"schema_version":"1.0"},"canonical_sha256":"83d958ccfbc1b6acfe5de5a030139ee0ba31206606cec0765dc43900e4db9636","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:49:20.953610Z","signature_b64":"Y+dPReOb7Rna+bTrACEdAhJx4dTFFr7JeDJS/ifAKZ2p2YygdGo5mYUQbQ5oTujWqftL2DKNcCTc4Yi0sbVBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83d958ccfbc1b6acfe5de5a030139ee0ba31206606cec0765dc43900e4db9636","last_reissued_at":"2026-05-18T03:49:20.952909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:49:20.952909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0974","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2yWH2u1F238LKty4GDHRfrHwXyuULUUqPuWqiNQ2twLZDSnxtx6z9AGvclmnOHG3E/dY21qg4kHhDt7mCaZoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T16:55:17.634678Z"},"content_sha256":"04e9b701d53784ed18bfdf805776fd0ad31050a2acd9f5b2bf07d9f716f6b18a","schema_version":"1.0","event_id":"sha256:04e9b701d53784ed18bfdf805776fd0ad31050a2acd9f5b2bf07d9f716f6b18a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QPMVRTH3YG3KZ7S54WQDAE464C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euclidean Quadratic Forms and ADC Forms I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Pete L. Clark","submitted_at":"2012-08-05T01:51:00Z","abstract_excerpt":"Motivated by classical results of Aubry, Davenport and Cassels, we define the notion of a Euclidean quadratic form over a normed integral domain and an ADC form over an integral domain. The aforementioned classical results generalize to: Euclidean forms are ADC forms. We then initiate the study and classification of these two classes of quadratic forms, especially over discrete valuation rings and Hasse domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0974","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":"2026-05-18T03:49:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwPPFBQSESFjM7lkCbH4VNVXf5ILn+CWwHxAh8nTRimPC1LVtXnpF50A+ixLbSuyUKEhk456i841PazablJ/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T16:55:17.635311Z"},"content_sha256":"0dd35679e5c58a99983333f1928a006440d7e19ea1215720e27623b69d3f9ab9","schema_version":"1.0","event_id":"sha256:0dd35679e5c58a99983333f1928a006440d7e19ea1215720e27623b69d3f9ab9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPMVRTH3YG3KZ7S54WQDAE464C/bundle.json","state_url":"https://pith.science/pith/QPMVRTH3YG3KZ7S54WQDAE464C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPMVRTH3YG3KZ7S54WQDAE464C/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":"2026-05-22T16:55:17Z","links":{"resolver":"https://pith.science/pith/QPMVRTH3YG3KZ7S54WQDAE464C","bundle":"https://pith.science/pith/QPMVRTH3YG3KZ7S54WQDAE464C/bundle.json","state":"https://pith.science/pith/QPMVRTH3YG3KZ7S54WQDAE464C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPMVRTH3YG3KZ7S54WQDAE464C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QPMVRTH3YG3KZ7S54WQDAE464C","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":"f5ebda3cd71614de83ab9e74bddde0d876288383b59b4ac86c2399d5c2bb2528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-05T01:51:00Z","title_canon_sha256":"9c84ba3646659673e62ed1e4fd0adc28fb63314f1d29df6c5e25c221724be58b"},"schema_version":"1.0","source":{"id":"1208.0974","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0974","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0974v1","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0974","created_at":"2026-05-18T03:49:20Z"},{"alias_kind":"pith_short_12","alias_value":"QPMVRTH3YG3K","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPMVRTH3YG3KZ7S5","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPMVRTH3","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:0dd35679e5c58a99983333f1928a006440d7e19ea1215720e27623b69d3f9ab9","target":"graph","created_at":"2026-05-18T03:49:20Z","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":"Motivated by classical results of Aubry, Davenport and Cassels, we define the notion of a Euclidean quadratic form over a normed integral domain and an ADC form over an integral domain. The aforementioned classical results generalize to: Euclidean forms are ADC forms. We then initiate the study and classification of these two classes of quadratic forms, especially over discrete valuation rings and Hasse domains.","authors_text":"Pete L. Clark","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-05T01:51:00Z","title":"Euclidean Quadratic Forms and ADC Forms I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0974","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":"sha256:04e9b701d53784ed18bfdf805776fd0ad31050a2acd9f5b2bf07d9f716f6b18a","target":"record","created_at":"2026-05-18T03:49:20Z","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":"f5ebda3cd71614de83ab9e74bddde0d876288383b59b4ac86c2399d5c2bb2528","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-08-05T01:51:00Z","title_canon_sha256":"9c84ba3646659673e62ed1e4fd0adc28fb63314f1d29df6c5e25c221724be58b"},"schema_version":"1.0","source":{"id":"1208.0974","kind":"arxiv","version":1}},"canonical_sha256":"83d958ccfbc1b6acfe5de5a030139ee0ba31206606cec0765dc43900e4db9636","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83d958ccfbc1b6acfe5de5a030139ee0ba31206606cec0765dc43900e4db9636","first_computed_at":"2026-05-18T03:49:20.952909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:20.952909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y+dPReOb7Rna+bTrACEdAhJx4dTFFr7JeDJS/ifAKZ2p2YygdGo5mYUQbQ5oTujWqftL2DKNcCTc4Yi0sbVBCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:20.953610Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0974","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04e9b701d53784ed18bfdf805776fd0ad31050a2acd9f5b2bf07d9f716f6b18a","sha256:0dd35679e5c58a99983333f1928a006440d7e19ea1215720e27623b69d3f9ab9"],"state_sha256":"fe6133b7e90985c9f51963c10d68d455f1d6dfc389aabfa199d48418023c88b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MO46zKq0GBheOG6f6bG47H+783MAq2CIn7CM+NIFl/mrAu46l5DPtaRPCKDQWBv91oE/iz5exNwbFhjzzkbRCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T16:55:17.639088Z","bundle_sha256":"66172878e79f501992a6cd87f36014e7cd24a7b8057b586adec3ffbebe9f61b2"}}