{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WNJCY3RU2JLMUYDUVZPQSW4BUJ","short_pith_number":"pith:WNJCY3RU","canonical_record":{"source":{"id":"1105.1362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-06T19:27:44Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5959e38784cc1f2d066b586c82af69059352d1539926946b405ffa97012dc9f6","abstract_canon_sha256":"bf60c68ac0ece219f1d76d0bdc93ecf4e916aaa0dc1b3eb89a6f76cab85e9851"},"schema_version":"1.0"},"canonical_sha256":"b3522c6e34d256ca6074ae5f095b81a272204606e92252e1ad9606737c677c45","source":{"kind":"arxiv","id":"1105.1362","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1362","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1362v1","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1362","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"WNJCY3RU2JLM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WNJCY3RU2JLMUYDU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WNJCY3RU","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WNJCY3RU2JLMUYDUVZPQSW4BUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1362","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-06T19:27:44Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5959e38784cc1f2d066b586c82af69059352d1539926946b405ffa97012dc9f6","abstract_canon_sha256":"bf60c68ac0ece219f1d76d0bdc93ecf4e916aaa0dc1b3eb89a6f76cab85e9851"},"schema_version":"1.0"},"canonical_sha256":"b3522c6e34d256ca6074ae5f095b81a272204606e92252e1ad9606737c677c45","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:39.629149Z","signature_b64":"Ntah/qhOWHoafU8+dI50e3Gd5DK2KWup0T74lvXqskxxIC1l9oVPdp9DY/eKuCPg9CcAOBxoLo+5/o01kfkHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3522c6e34d256ca6074ae5f095b81a272204606e92252e1ad9606737c677c45","last_reissued_at":"2026-05-18T04:22:39.628722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:39.628722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1362","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":"2026-05-18T04:22:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HZ/rhU+7Zhrm0a5YAiVOeIIDu5eWf3aDAkNnULCuXuFRJvbGWf6i9jL5VVw8LlwCYZToBj2fLHwbYTg7/YLaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:24:30.234678Z"},"content_sha256":"e880c401aa23f2332467eb20f41af887de6292ddd19bdfe09d5c7ac710022ba6","schema_version":"1.0","event_id":"sha256:e880c401aa23f2332467eb20f41af887de6292ddd19bdfe09d5c7ac710022ba6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WNJCY3RU2JLMUYDUVZPQSW4BUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"To the multidimensional tame symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AG","authors_text":"Denis Osipov","submitted_at":"2011-05-06T19:27:44Z","abstract_excerpt":"We give a construction of the two-dimensional tame symbol as the commutator of a group-like monoidal groupoid which is obtained from some group of k-linear operators acting in a two-dimensional local field and corresponds to some third cohomology class of this group. We give also the hypothetical method for the proof of the two-dimensional Parshin reciprocity laws.\n  This text was written in 2003 as preprint 03-13 of the Humboldt University of Berlin and was available at http://edoc.hu-berlin.de/docviews/abstract.php?id=26204 (only evident misprints are corrected now). Later E. Frenkel and X. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1362","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":"2026-05-18T04:22:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ybsarJjT8XMGvzwpsFxEXDV/oyQJFXrkxXWr2IwHRvdlkNzbKzOc/BSzSat9xOJ9wjNHumdzfVxqrvf2BJpaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:24:30.235456Z"},"content_sha256":"604e7c131c0a262549168941e87c49a5700bc61c5795e4a275e6a21daf44f9b4","schema_version":"1.0","event_id":"sha256:604e7c131c0a262549168941e87c49a5700bc61c5795e4a275e6a21daf44f9b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/bundle.json","state_url":"https://pith.science/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/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":"2026-06-09T05:24:30Z","links":{"resolver":"https://pith.science/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ","bundle":"https://pith.science/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/bundle.json","state":"https://pith.science/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNJCY3RU2JLMUYDUVZPQSW4BUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WNJCY3RU2JLMUYDUVZPQSW4BUJ","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":"bf60c68ac0ece219f1d76d0bdc93ecf4e916aaa0dc1b3eb89a6f76cab85e9851","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-06T19:27:44Z","title_canon_sha256":"5959e38784cc1f2d066b586c82af69059352d1539926946b405ffa97012dc9f6"},"schema_version":"1.0","source":{"id":"1105.1362","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1362","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1362v1","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1362","created_at":"2026-05-18T04:22:39Z"},{"alias_kind":"pith_short_12","alias_value":"WNJCY3RU2JLM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WNJCY3RU2JLMUYDU","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WNJCY3RU","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:604e7c131c0a262549168941e87c49a5700bc61c5795e4a275e6a21daf44f9b4","target":"graph","created_at":"2026-05-18T04:22:39Z","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 give a construction of the two-dimensional tame symbol as the commutator of a group-like monoidal groupoid which is obtained from some group of k-linear operators acting in a two-dimensional local field and corresponds to some third cohomology class of this group. We give also the hypothetical method for the proof of the two-dimensional Parshin reciprocity laws.\n  This text was written in 2003 as preprint 03-13 of the Humboldt University of Berlin and was available at http://edoc.hu-berlin.de/docviews/abstract.php?id=26204 (only evident misprints are corrected now). Later E. Frenkel and X. ","authors_text":"Denis Osipov","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-06T19:27:44Z","title":"To the multidimensional tame symbol"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1362","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:e880c401aa23f2332467eb20f41af887de6292ddd19bdfe09d5c7ac710022ba6","target":"record","created_at":"2026-05-18T04:22:39Z","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":"bf60c68ac0ece219f1d76d0bdc93ecf4e916aaa0dc1b3eb89a6f76cab85e9851","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-05-06T19:27:44Z","title_canon_sha256":"5959e38784cc1f2d066b586c82af69059352d1539926946b405ffa97012dc9f6"},"schema_version":"1.0","source":{"id":"1105.1362","kind":"arxiv","version":1}},"canonical_sha256":"b3522c6e34d256ca6074ae5f095b81a272204606e92252e1ad9606737c677c45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3522c6e34d256ca6074ae5f095b81a272204606e92252e1ad9606737c677c45","first_computed_at":"2026-05-18T04:22:39.628722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:39.628722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ntah/qhOWHoafU8+dI50e3Gd5DK2KWup0T74lvXqskxxIC1l9oVPdp9DY/eKuCPg9CcAOBxoLo+5/o01kfkHAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:39.629149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1362","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e880c401aa23f2332467eb20f41af887de6292ddd19bdfe09d5c7ac710022ba6","sha256:604e7c131c0a262549168941e87c49a5700bc61c5795e4a275e6a21daf44f9b4"],"state_sha256":"acbcb598a44edce4e3afa9a06976a406097e49aea807d4ab5b8aa397e69c547f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Szf/Fhdo3JVizB9Bf3p/pcHYymUNb9r99zQJKqBw60VXCDSdshnxG3mcwyBmvJSgIfv5r/mTBHdzIHa3CO+6AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:24:30.240181Z","bundle_sha256":"2a0c3d75f101073f5dc315d23f72102951b25f194249de319b70349d643289b0"}}