{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D5CKRBLE37NTKL4MWHHJAYN66G","short_pith_number":"pith:D5CKRBLE","canonical_record":{"source":{"id":"1703.10521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-30T15:19:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4a242b94506a9b99169ec3471a1d14bf1253bfde0ec2c33550dc4629ae72dcc0","abstract_canon_sha256":"12c16ef27cb994243912607df186e534b02d50c63b053b42a700a5651d82d7ae"},"schema_version":"1.0"},"canonical_sha256":"1f44a88564dfdb352f8cb1ce9061bef1814818af1075b41ad69eeaef560f0ec8","source":{"kind":"arxiv","id":"1703.10521","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10521","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10521v2","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10521","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"pith_short_12","alias_value":"D5CKRBLE37NT","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D5CKRBLE37NTKL4M","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D5CKRBLE","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D5CKRBLE37NTKL4MWHHJAYN66G","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-30T15:19:58Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"4a242b94506a9b99169ec3471a1d14bf1253bfde0ec2c33550dc4629ae72dcc0","abstract_canon_sha256":"12c16ef27cb994243912607df186e534b02d50c63b053b42a700a5651d82d7ae"},"schema_version":"1.0"},"canonical_sha256":"1f44a88564dfdb352f8cb1ce9061bef1814818af1075b41ad69eeaef560f0ec8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:51.231130Z","signature_b64":"mhJvnj8aa8QuQB/oSFb2M6QDEPdudaVoDxLNQODW3bR5+OYAwTsxZhJDVtaRoVXuEmXIufPGMYT0vQEqoI/iCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f44a88564dfdb352f8cb1ce9061bef1814818af1075b41ad69eeaef560f0ec8","last_reissued_at":"2026-05-18T00:44:51.230361Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:51.230361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10521","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":"2026-05-18T00:44:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kwuQnthIHWDYgAk9V/ikb8Y1GaiB5kwhhvPFEW1EuRfmMRr1Zc/XhBLjqlT70fkv/RZcrFANtIzUf432Nq5uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:13:42.753466Z"},"content_sha256":"d25c787a9a7b103916197c4f77472a8919dda311de90fe0c1a8621503d78e112","schema_version":"1.0","event_id":"sha256:d25c787a9a7b103916197c4f77472a8919dda311de90fe0c1a8621503d78e112"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D5CKRBLE37NTKL4MWHHJAYN66G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An arithmetic site of Connes-Consani type for imaginary quadratic fields with class number 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Aur\\'elien Sagnier","submitted_at":"2017-03-30T15:19:58Z","abstract_excerpt":"We construct, for imaginary quadratic number fields with class number 1, an arithmetic site of Connes-Consani type. The main difficulty here is that the constructions of Connes and Consani and part of their results strongly rely on the natural order existing on real numbers which is compatible with basic arithmetic operations. Of course nothing of this sort exists in the case of imaginary quadratic number fields with class number 1. We first define what we call arithmetic site for such number fields, we then calculate the points of those arithmetic sites and we express them in terms of the ad\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10521","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":"2026-05-18T00:44:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lG5YmP0L2j+BM59yS8d7Krj9NZ/6g4sL/eAU1yS3Qe2YSbjh7rhX2WYj3nmxW5WufrND9lQ8QF268Y7uOC5EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:13:42.753815Z"},"content_sha256":"a8948b6bfcf704ca046bb80b40d70de5fd007814ec4ffaed83bd1bc39f2137df","schema_version":"1.0","event_id":"sha256:a8948b6bfcf704ca046bb80b40d70de5fd007814ec4ffaed83bd1bc39f2137df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5CKRBLE37NTKL4MWHHJAYN66G/bundle.json","state_url":"https://pith.science/pith/D5CKRBLE37NTKL4MWHHJAYN66G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5CKRBLE37NTKL4MWHHJAYN66G/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":"2026-06-04T17:13:42Z","links":{"resolver":"https://pith.science/pith/D5CKRBLE37NTKL4MWHHJAYN66G","bundle":"https://pith.science/pith/D5CKRBLE37NTKL4MWHHJAYN66G/bundle.json","state":"https://pith.science/pith/D5CKRBLE37NTKL4MWHHJAYN66G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5CKRBLE37NTKL4MWHHJAYN66G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D5CKRBLE37NTKL4MWHHJAYN66G","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":"12c16ef27cb994243912607df186e534b02d50c63b053b42a700a5651d82d7ae","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-30T15:19:58Z","title_canon_sha256":"4a242b94506a9b99169ec3471a1d14bf1253bfde0ec2c33550dc4629ae72dcc0"},"schema_version":"1.0","source":{"id":"1703.10521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10521","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10521v2","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10521","created_at":"2026-05-18T00:44:51Z"},{"alias_kind":"pith_short_12","alias_value":"D5CKRBLE37NT","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D5CKRBLE37NTKL4M","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D5CKRBLE","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:a8948b6bfcf704ca046bb80b40d70de5fd007814ec4ffaed83bd1bc39f2137df","target":"graph","created_at":"2026-05-18T00:44:51Z","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 construct, for imaginary quadratic number fields with class number 1, an arithmetic site of Connes-Consani type. The main difficulty here is that the constructions of Connes and Consani and part of their results strongly rely on the natural order existing on real numbers which is compatible with basic arithmetic operations. Of course nothing of this sort exists in the case of imaginary quadratic number fields with class number 1. We first define what we call arithmetic site for such number fields, we then calculate the points of those arithmetic sites and we express them in terms of the ad\\","authors_text":"Aur\\'elien Sagnier","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-30T15:19:58Z","title":"An arithmetic site of Connes-Consani type for imaginary quadratic fields with class number 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10521","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:d25c787a9a7b103916197c4f77472a8919dda311de90fe0c1a8621503d78e112","target":"record","created_at":"2026-05-18T00:44:51Z","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":"12c16ef27cb994243912607df186e534b02d50c63b053b42a700a5651d82d7ae","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-30T15:19:58Z","title_canon_sha256":"4a242b94506a9b99169ec3471a1d14bf1253bfde0ec2c33550dc4629ae72dcc0"},"schema_version":"1.0","source":{"id":"1703.10521","kind":"arxiv","version":2}},"canonical_sha256":"1f44a88564dfdb352f8cb1ce9061bef1814818af1075b41ad69eeaef560f0ec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f44a88564dfdb352f8cb1ce9061bef1814818af1075b41ad69eeaef560f0ec8","first_computed_at":"2026-05-18T00:44:51.230361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:51.230361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mhJvnj8aa8QuQB/oSFb2M6QDEPdudaVoDxLNQODW3bR5+OYAwTsxZhJDVtaRoVXuEmXIufPGMYT0vQEqoI/iCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:51.231130Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d25c787a9a7b103916197c4f77472a8919dda311de90fe0c1a8621503d78e112","sha256:a8948b6bfcf704ca046bb80b40d70de5fd007814ec4ffaed83bd1bc39f2137df"],"state_sha256":"fb00d07f4df8cf6dbbdefa227bb98a87a60ddf21b3db3c7a80d38a029d156606"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0Ku7SKVwt49LHb8E8wTA6gHEcBOWOMMGzT7KoB48Xvzj6ueDppBMFZyec+cHEhgnbE3pkupzn3tDzwIh/wyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:13:42.755865Z","bundle_sha256":"e3d01899b73dfc82b7a5b22d8a4ce12d40caca430f47f692724301c96c979c05"}}