{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:RNNJ4B7XKNIXUX4EXQCNLQRFLK","short_pith_number":"pith:RNNJ4B7X","canonical_record":{"source":{"id":"math/0612611","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-12-20T17:46:03Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"64ebe1122410fdf95a6cebcadd15e19cbc61bf492acba8211747a10811bdb419","abstract_canon_sha256":"4c3483a2c32221a60dd42aebec3bf3122b3a9cae31c082a65f08844d6b635886"},"schema_version":"1.0"},"canonical_sha256":"8b5a9e07f753517a5f84bc04d5c2255aa5d296974577c6982989ba408ea0e4a4","source":{"kind":"arxiv","id":"math/0612611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612611","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612611v1","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612611","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"pith_short_12","alias_value":"RNNJ4B7XKNIX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RNNJ4B7XKNIXUX4E","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RNNJ4B7X","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:RNNJ4B7XKNIXUX4EXQCNLQRFLK","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612611","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2006-12-20T17:46:03Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"64ebe1122410fdf95a6cebcadd15e19cbc61bf492acba8211747a10811bdb419","abstract_canon_sha256":"4c3483a2c32221a60dd42aebec3bf3122b3a9cae31c082a65f08844d6b635886"},"schema_version":"1.0"},"canonical_sha256":"8b5a9e07f753517a5f84bc04d5c2255aa5d296974577c6982989ba408ea0e4a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:50.703109Z","signature_b64":"tbzDG8lVCsrFruK8QT/h5bCVzR5qLfB6lAp8qjoNNcjzUbimrv9QP3xQfjqjxCCMQic5NXEzKwzJJw76XfZRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b5a9e07f753517a5f84bc04d5c2255aa5d296974577c6982989ba408ea0e4a4","last_reissued_at":"2026-05-18T04:31:50.702597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:50.702597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612611","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":"2026-05-18T04:31:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NbPcRMkOWr15xUss9Pia973a1exYrF63V0vy32NP3/PvtZX6salUAIDkngqAiyz5+UeTMI/8N5NlCteHfLXNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:58:25.392890Z"},"content_sha256":"efe1594b82e942a048896f09a1423987e2775b91b4f01d45b19d40d537e4198a","schema_version":"1.0","event_id":"sha256:efe1594b82e942a048896f09a1423987e2775b91b4f01d45b19d40d537e4198a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:RNNJ4B7XKNIXUX4EXQCNLQRFLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A $p$-adic analogue of the Borel regulator and the Bloch-Kato exponential map","license":"","headline":"","cross_cats":["math.KT"],"primary_cat":"math.NT","authors_text":"Annette Huber, Guido Kings","submitted_at":"2006-12-20T17:46:03Z","abstract_excerpt":"In this paper we define a $p$-adic analogue of the Borel regulator for the $K$-theory of $p$-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this $p$-adic regulator to the Bloch-Kato exponential and the Soul\\'e regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612611","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":"2026-05-18T04:31:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4IpYbzyL7uG5u5XsYJ0WZnMZuQ/mTitqK+99octuv7wgfceaIyfjkdyRQc0eQLQKTewUwvQXQSrySc1z3lYJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T04:58:25.393530Z"},"content_sha256":"6a17a26968d90b7bc7d8a1d7a8bb409135fa01059eed9f1a95db2f7bb581c3fd","schema_version":"1.0","event_id":"sha256:6a17a26968d90b7bc7d8a1d7a8bb409135fa01059eed9f1a95db2f7bb581c3fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/bundle.json","state_url":"https://pith.science/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/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":"2026-06-11T04:58:25Z","links":{"resolver":"https://pith.science/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK","bundle":"https://pith.science/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/bundle.json","state":"https://pith.science/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RNNJ4B7XKNIXUX4EXQCNLQRFLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RNNJ4B7XKNIXUX4EXQCNLQRFLK","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":"4c3483a2c32221a60dd42aebec3bf3122b3a9cae31c082a65f08844d6b635886","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.NT","submitted_at":"2006-12-20T17:46:03Z","title_canon_sha256":"64ebe1122410fdf95a6cebcadd15e19cbc61bf492acba8211747a10811bdb419"},"schema_version":"1.0","source":{"id":"math/0612611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612611","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612611v1","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612611","created_at":"2026-05-18T04:31:50Z"},{"alias_kind":"pith_short_12","alias_value":"RNNJ4B7XKNIX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RNNJ4B7XKNIXUX4E","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RNNJ4B7X","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:6a17a26968d90b7bc7d8a1d7a8bb409135fa01059eed9f1a95db2f7bb581c3fd","target":"graph","created_at":"2026-05-18T04:31:50Z","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 define a $p$-adic analogue of the Borel regulator for the $K$-theory of $p$-adic fields. The van Est isomorphism in the construction of the classical Borel regulator is replaced by the Lazard isomorphism. The main result relates this $p$-adic regulator to the Bloch-Kato exponential and the Soul\\'e regulator. On the way we give a new description of the Lazard isomorphism for certain formal groups.","authors_text":"Annette Huber, Guido Kings","cross_cats":["math.KT"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2006-12-20T17:46:03Z","title":"A $p$-adic analogue of the Borel regulator and the Bloch-Kato exponential map"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612611","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:efe1594b82e942a048896f09a1423987e2775b91b4f01d45b19d40d537e4198a","target":"record","created_at":"2026-05-18T04:31:50Z","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":"4c3483a2c32221a60dd42aebec3bf3122b3a9cae31c082a65f08844d6b635886","cross_cats_sorted":["math.KT"],"license":"","primary_cat":"math.NT","submitted_at":"2006-12-20T17:46:03Z","title_canon_sha256":"64ebe1122410fdf95a6cebcadd15e19cbc61bf492acba8211747a10811bdb419"},"schema_version":"1.0","source":{"id":"math/0612611","kind":"arxiv","version":1}},"canonical_sha256":"8b5a9e07f753517a5f84bc04d5c2255aa5d296974577c6982989ba408ea0e4a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b5a9e07f753517a5f84bc04d5c2255aa5d296974577c6982989ba408ea0e4a4","first_computed_at":"2026-05-18T04:31:50.702597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:50.702597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tbzDG8lVCsrFruK8QT/h5bCVzR5qLfB6lAp8qjoNNcjzUbimrv9QP3xQfjqjxCCMQic5NXEzKwzJJw76XfZRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:50.703109Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efe1594b82e942a048896f09a1423987e2775b91b4f01d45b19d40d537e4198a","sha256:6a17a26968d90b7bc7d8a1d7a8bb409135fa01059eed9f1a95db2f7bb581c3fd"],"state_sha256":"add46a4b7291bbcce0a543c7dc654a47ed9261d3cbd952d873c2edf96f801ca7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nnXkJuAw1qJQCN2m5I1B5o6vbNCb+lr9Pb9/aKcuC6tuKlg5vtXtY8zFkLNP6Cy4e7bpoNSAocmu4dWOct2hDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T04:58:25.397560Z","bundle_sha256":"2fbf532dd19ff106e2a1be3023e1adf6ccddf65e8060e24c33f509ef784e9a43"}}