{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:M6KQ6R5V3CKS4HUVL7ZZAXM7GT","short_pith_number":"pith:M6KQ6R5V","canonical_record":{"source":{"id":"1309.1071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-04T15:24:24Z","cross_cats_sorted":[],"title_canon_sha256":"4cc05d30c6589c2efb9e5324263d68c368a20ee2ce20b1d336090291c7367e10","abstract_canon_sha256":"c76835cd478e13bc452d99f7a93fd3d619dd2603ab06828d9062496989070895"},"schema_version":"1.0"},"canonical_sha256":"67950f47b5d8952e1e955ff3905d9f34ccabcb58cb3376ac2dc2e5ddb72204f0","source":{"kind":"arxiv","id":"1309.1071","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1071","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1071v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1071","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"M6KQ6R5V3CKS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6KQ6R5V3CKS4HUV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6KQ6R5V","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:M6KQ6R5V3CKS4HUVL7ZZAXM7GT","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-04T15:24:24Z","cross_cats_sorted":[],"title_canon_sha256":"4cc05d30c6589c2efb9e5324263d68c368a20ee2ce20b1d336090291c7367e10","abstract_canon_sha256":"c76835cd478e13bc452d99f7a93fd3d619dd2603ab06828d9062496989070895"},"schema_version":"1.0"},"canonical_sha256":"67950f47b5d8952e1e955ff3905d9f34ccabcb58cb3376ac2dc2e5ddb72204f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:09.175266Z","signature_b64":"6kHNbOEWIRJvI00/ziVGZEw9/AvLMPLqxKxZun4he8w+PWnZ8r/VkkSMRzkOOor9mpbpmd/hzgkIIlx6iOhbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67950f47b5d8952e1e955ff3905d9f34ccabcb58cb3376ac2dc2e5ddb72204f0","last_reissued_at":"2026-05-18T03:14:09.174804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:09.174804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1071","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":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6PI0MGuI5dW41icTmkDG8S00mciaMEGFxQGf8P/S+AelExco4QEJdHUyFC2JvHE80Nl+2k4MvJ1Z3aW/eZGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:37:31.805409Z"},"content_sha256":"b5ce185b9153883cacfcc96b087073c340c45adbdc13d0eea7489dc69d5b8f50","schema_version":"1.0","event_id":"sha256:b5ce185b9153883cacfcc96b087073c340c45adbdc13d0eea7489dc69d5b8f50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:M6KQ6R5V3CKS4HUVL7ZZAXM7GT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Ambiguous Class Number Formula Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Franz Lemmermeyer","submitted_at":"2013-09-04T15:24:24Z","abstract_excerpt":"We will give a simple proof of the ambiguous class number formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1071","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":"2026-05-18T03:14:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTOyZe8djTgk3/oMLuWGuHAwv5+46w0YMzN+dIcIDfh11GDUAwWyYnX1PZCUiZ7036klPbRJ5d4jM+JW6aMnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T16:37:31.806045Z"},"content_sha256":"cec221558e194752238b1c1a419fd5cc8acf644d552eaf58db1ace8fc24d9601","schema_version":"1.0","event_id":"sha256:cec221558e194752238b1c1a419fd5cc8acf644d552eaf58db1ace8fc24d9601"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/bundle.json","state_url":"https://pith.science/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/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":"2026-06-11T16:37:31Z","links":{"resolver":"https://pith.science/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT","bundle":"https://pith.science/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/bundle.json","state":"https://pith.science/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6KQ6R5V3CKS4HUVL7ZZAXM7GT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M6KQ6R5V3CKS4HUVL7ZZAXM7GT","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":"c76835cd478e13bc452d99f7a93fd3d619dd2603ab06828d9062496989070895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-04T15:24:24Z","title_canon_sha256":"4cc05d30c6589c2efb9e5324263d68c368a20ee2ce20b1d336090291c7367e10"},"schema_version":"1.0","source":{"id":"1309.1071","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1071","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1071v1","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1071","created_at":"2026-05-18T03:14:09Z"},{"alias_kind":"pith_short_12","alias_value":"M6KQ6R5V3CKS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M6KQ6R5V3CKS4HUV","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M6KQ6R5V","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:cec221558e194752238b1c1a419fd5cc8acf644d552eaf58db1ace8fc24d9601","target":"graph","created_at":"2026-05-18T03:14:09Z","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 will give a simple proof of the ambiguous class number formula.","authors_text":"Franz Lemmermeyer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-04T15:24:24Z","title":"The Ambiguous Class Number Formula Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1071","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:b5ce185b9153883cacfcc96b087073c340c45adbdc13d0eea7489dc69d5b8f50","target":"record","created_at":"2026-05-18T03:14:09Z","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":"c76835cd478e13bc452d99f7a93fd3d619dd2603ab06828d9062496989070895","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-09-04T15:24:24Z","title_canon_sha256":"4cc05d30c6589c2efb9e5324263d68c368a20ee2ce20b1d336090291c7367e10"},"schema_version":"1.0","source":{"id":"1309.1071","kind":"arxiv","version":1}},"canonical_sha256":"67950f47b5d8952e1e955ff3905d9f34ccabcb58cb3376ac2dc2e5ddb72204f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67950f47b5d8952e1e955ff3905d9f34ccabcb58cb3376ac2dc2e5ddb72204f0","first_computed_at":"2026-05-18T03:14:09.174804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:09.174804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6kHNbOEWIRJvI00/ziVGZEw9/AvLMPLqxKxZun4he8w+PWnZ8r/VkkSMRzkOOor9mpbpmd/hzgkIIlx6iOhbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:09.175266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1071","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5ce185b9153883cacfcc96b087073c340c45adbdc13d0eea7489dc69d5b8f50","sha256:cec221558e194752238b1c1a419fd5cc8acf644d552eaf58db1ace8fc24d9601"],"state_sha256":"116734629198386a4b8805ba4d6c851e2d29089287b2d8214cdd7503ffca613b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYL/7BwSjU/feSzgQotmVkTIZSuDtC38WtrqAWWfVWXwyW3iE+luk8aQGycSWjderDFfbiN+vjjq58lGhWhUAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T16:37:31.809444Z","bundle_sha256":"25927ffafe3f64cfa6e56262217a7eaa8034376adcf80d5d0d839c81507db321"}}