{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4WCOMHWSENCWYDGSAY5H72ATWK","short_pith_number":"pith:4WCOMHWS","canonical_record":{"source":{"id":"1109.0082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T03:45:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"11069defd4426d2752249f4218cd69848794a293fb1bafa59c54324f4abda0e1","abstract_canon_sha256":"12211df09e756ab0d07908c2f0b1d4535b7f763c20017907f95472d8f2496ec5"},"schema_version":"1.0"},"canonical_sha256":"e584e61ed223456c0cd2063a7fe813b2ac5a1bb50762d369c670a259d3e74b30","source":{"kind":"arxiv","id":"1109.0082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0082","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0082v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0082","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"4WCOMHWSENCW","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WCOMHWSENCWYDGS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WCOMHWS","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4WCOMHWSENCWYDGSAY5H72ATWK","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T03:45:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"11069defd4426d2752249f4218cd69848794a293fb1bafa59c54324f4abda0e1","abstract_canon_sha256":"12211df09e756ab0d07908c2f0b1d4535b7f763c20017907f95472d8f2496ec5"},"schema_version":"1.0"},"canonical_sha256":"e584e61ed223456c0cd2063a7fe813b2ac5a1bb50762d369c670a259d3e74b30","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:17.503687Z","signature_b64":"eoF1L3NmKwMjT7Z7Ms7t+DxyTSvTdZhPAKQjE69GBO+/++IPlRoa8Pz3+itGRo04qu8pIqU5lRHy7QeROH5rDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e584e61ed223456c0cd2063a7fe813b2ac5a1bb50762d369c670a259d3e74b30","last_reissued_at":"2026-05-18T04:14:17.502973Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:17.502973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0082","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MFbQr4b2I134Rf/N8dWw7qvHQuhNty0L/8ZefN4inKY0jynOSBGNfGcoim7KHFSgSW9CAMe8gVMRt1tJoFN+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:51:06.376952Z"},"content_sha256":"d4e8897a677494f4a4dfddd54a4d52a53fbce592d1c703040cf5901f60f33719","schema_version":"1.0","event_id":"sha256:d4e8897a677494f4a4dfddd54a4d52a53fbce592d1c703040cf5901f60f33719"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4WCOMHWSENCWYDGSAY5H72ATWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation Expression for Elements of Algebras (IV) --Matrix elements and related integrals--","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Akira Yoshioka, Hideki Omori, Naoya Miyazaki, Yoshiaki Maeda","submitted_at":"2011-09-01T03:45:28Z","abstract_excerpt":"In this note, we mainly consider the extended Weyl algebra of two generators (u,v), that is, the algebra generated by u,v with the fundamental commutation relation. Weyl algebra is realized on the space of polynomials of u and v by defining various product depending on a symmetric matrix K called the expression parameter. Via such expressions and ordinary calculus one can treat various transcendental elements such as *-exponential functions and elements obtained by integrations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0082","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":"2026-05-18T04:14:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UttavbgnAfmVKHItXmqGimKsbtx3DCZYvvXBfUOyDz47RcD00Rk3U7GylpQAqFA3WKxdExddomv3GzKXOn3XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:51:06.377609Z"},"content_sha256":"0f78c1f765d5b583e0918b9c8e5f735530d0a7acadb2b305a11d895c4ba8b799","schema_version":"1.0","event_id":"sha256:0f78c1f765d5b583e0918b9c8e5f735530d0a7acadb2b305a11d895c4ba8b799"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WCOMHWSENCWYDGSAY5H72ATWK/bundle.json","state_url":"https://pith.science/pith/4WCOMHWSENCWYDGSAY5H72ATWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WCOMHWSENCWYDGSAY5H72ATWK/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":"2026-06-11T07:51:06Z","links":{"resolver":"https://pith.science/pith/4WCOMHWSENCWYDGSAY5H72ATWK","bundle":"https://pith.science/pith/4WCOMHWSENCWYDGSAY5H72ATWK/bundle.json","state":"https://pith.science/pith/4WCOMHWSENCWYDGSAY5H72ATWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WCOMHWSENCWYDGSAY5H72ATWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4WCOMHWSENCWYDGSAY5H72ATWK","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":"12211df09e756ab0d07908c2f0b1d4535b7f763c20017907f95472d8f2496ec5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T03:45:28Z","title_canon_sha256":"11069defd4426d2752249f4218cd69848794a293fb1bafa59c54324f4abda0e1"},"schema_version":"1.0","source":{"id":"1109.0082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0082","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0082v1","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0082","created_at":"2026-05-18T04:14:17Z"},{"alias_kind":"pith_short_12","alias_value":"4WCOMHWSENCW","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4WCOMHWSENCWYDGS","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4WCOMHWS","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:0f78c1f765d5b583e0918b9c8e5f735530d0a7acadb2b305a11d895c4ba8b799","target":"graph","created_at":"2026-05-18T04:14:17Z","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 note, we mainly consider the extended Weyl algebra of two generators (u,v), that is, the algebra generated by u,v with the fundamental commutation relation. Weyl algebra is realized on the space of polynomials of u and v by defining various product depending on a symmetric matrix K called the expression parameter. Via such expressions and ordinary calculus one can treat various transcendental elements such as *-exponential functions and elements obtained by integrations.","authors_text":"Akira Yoshioka, Hideki Omori, Naoya Miyazaki, Yoshiaki Maeda","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T03:45:28Z","title":"Deformation Expression for Elements of Algebras (IV) --Matrix elements and related integrals--"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0082","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:d4e8897a677494f4a4dfddd54a4d52a53fbce592d1c703040cf5901f60f33719","target":"record","created_at":"2026-05-18T04:14:17Z","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":"12211df09e756ab0d07908c2f0b1d4535b7f763c20017907f95472d8f2496ec5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-01T03:45:28Z","title_canon_sha256":"11069defd4426d2752249f4218cd69848794a293fb1bafa59c54324f4abda0e1"},"schema_version":"1.0","source":{"id":"1109.0082","kind":"arxiv","version":1}},"canonical_sha256":"e584e61ed223456c0cd2063a7fe813b2ac5a1bb50762d369c670a259d3e74b30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e584e61ed223456c0cd2063a7fe813b2ac5a1bb50762d369c670a259d3e74b30","first_computed_at":"2026-05-18T04:14:17.502973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:17.502973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eoF1L3NmKwMjT7Z7Ms7t+DxyTSvTdZhPAKQjE69GBO+/++IPlRoa8Pz3+itGRo04qu8pIqU5lRHy7QeROH5rDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:17.503687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4e8897a677494f4a4dfddd54a4d52a53fbce592d1c703040cf5901f60f33719","sha256:0f78c1f765d5b583e0918b9c8e5f735530d0a7acadb2b305a11d895c4ba8b799"],"state_sha256":"a637e2829dbdeeb3426c43822bd613d24d3821dec38234201f04b156dc74e2c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KVmV6C9CpO10f4Z4shYqU/jP44lo15o5hNCK7ynL43ARj/pIOxCng+RLWI6wmIk4Xl6jbmPnC0d/Y2yujnSnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:51:06.381349Z","bundle_sha256":"a477750df6e4a8014acb68e7e7e40be58ad747c832114c0f243837f84915fe05"}}