{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VKSLOF5DPCSY27GIWDJFZOM23L","short_pith_number":"pith:VKSLOF5D","canonical_record":{"source":{"id":"1506.04537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-15T09:57:59Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"d740c7ee767235b5b4e7f5ad04f36c90b8657af42336f4f8080725abd5189cfa","abstract_canon_sha256":"5bfe3abff2eb50ebbec6cd5bfc2151534a0de0a4b3c6d30242ac3622559d3245"},"schema_version":"1.0"},"canonical_sha256":"aaa4b717a378a58d7cc8b0d25cb99adac71f8d5fa2f295baca54a7cd699e9ff1","source":{"kind":"arxiv","id":"1506.04537","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04537","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04537v1","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04537","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"VKSLOF5DPCSY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VKSLOF5DPCSY27GI","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VKSLOF5D","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VKSLOF5DPCSY27GIWDJFZOM23L","target":"record","payload":{"canonical_record":{"source":{"id":"1506.04537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-15T09:57:59Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"d740c7ee767235b5b4e7f5ad04f36c90b8657af42336f4f8080725abd5189cfa","abstract_canon_sha256":"5bfe3abff2eb50ebbec6cd5bfc2151534a0de0a4b3c6d30242ac3622559d3245"},"schema_version":"1.0"},"canonical_sha256":"aaa4b717a378a58d7cc8b0d25cb99adac71f8d5fa2f295baca54a7cd699e9ff1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:30.939374Z","signature_b64":"M9t/PlslmsY47IExQ8+uT7ZU1MZ4m2geYSX9XY0A+S23i/MsiYq5Grm+sKdv9Enm6wC5qBWejwsxBIMZQ1UwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa4b717a378a58d7cc8b0d25cb99adac71f8d5fa2f295baca54a7cd699e9ff1","last_reissued_at":"2026-05-18T01:49:30.938828Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:30.938828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.04537","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":"2026-05-18T01:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wAdj13IHIX9GLBmjWW63CAMi3howzlXWgGd7459S+jNuueklh+DuNOqKZaipTUwh9jZ3nDZnuAW8f4JfZK9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:29:28.957703Z"},"content_sha256":"b1b4416016534186759aa11f8697845fa08c287982bedf2a07022597b53d530e","schema_version":"1.0","event_id":"sha256:b1b4416016534186759aa11f8697845fa08c287982bedf2a07022597b53d530e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VKSLOF5DPCSY27GIWDJFZOM23L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Helffer-Sj{\\\"o}strand formula for Unitary Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Aiman Mbarek (AGM)","submitted_at":"2015-06-15T09:57:59Z","abstract_excerpt":"The objective of this paper to give a formula for unitary operators that corresponds to the Heler-Sj{\\\"o}strand formula for self-adjoint operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04537","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":"2026-05-18T01:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dlpkt6W0HIXIG/+HozdGYOotavDHfepU6ZB5TqmaCen2BLBHBIm1piLMi02hSyO7Xz/Ihcy049FLr1DLGH7GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:29:28.958045Z"},"content_sha256":"970879a88725f38a52d6d6544bdb6af113eb28d0be1a8d2735bcf2d02acdc7ee","schema_version":"1.0","event_id":"sha256:970879a88725f38a52d6d6544bdb6af113eb28d0be1a8d2735bcf2d02acdc7ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKSLOF5DPCSY27GIWDJFZOM23L/bundle.json","state_url":"https://pith.science/pith/VKSLOF5DPCSY27GIWDJFZOM23L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKSLOF5DPCSY27GIWDJFZOM23L/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":"2026-06-24T17:29:28Z","links":{"resolver":"https://pith.science/pith/VKSLOF5DPCSY27GIWDJFZOM23L","bundle":"https://pith.science/pith/VKSLOF5DPCSY27GIWDJFZOM23L/bundle.json","state":"https://pith.science/pith/VKSLOF5DPCSY27GIWDJFZOM23L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKSLOF5DPCSY27GIWDJFZOM23L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VKSLOF5DPCSY27GIWDJFZOM23L","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":"5bfe3abff2eb50ebbec6cd5bfc2151534a0de0a4b3c6d30242ac3622559d3245","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-15T09:57:59Z","title_canon_sha256":"d740c7ee767235b5b4e7f5ad04f36c90b8657af42336f4f8080725abd5189cfa"},"schema_version":"1.0","source":{"id":"1506.04537","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.04537","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1506.04537v1","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04537","created_at":"2026-05-18T01:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"VKSLOF5DPCSY","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"VKSLOF5DPCSY27GI","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"VKSLOF5D","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:970879a88725f38a52d6d6544bdb6af113eb28d0be1a8d2735bcf2d02acdc7ee","target":"graph","created_at":"2026-05-18T01:49:30Z","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":"The objective of this paper to give a formula for unitary operators that corresponds to the Heler-Sj{\\\"o}strand formula for self-adjoint operators.","authors_text":"Aiman Mbarek (AGM)","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-15T09:57:59Z","title":"Helffer-Sj{\\\"o}strand formula for Unitary Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04537","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:b1b4416016534186759aa11f8697845fa08c287982bedf2a07022597b53d530e","target":"record","created_at":"2026-05-18T01:49:30Z","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":"5bfe3abff2eb50ebbec6cd5bfc2151534a0de0a4b3c6d30242ac3622559d3245","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-06-15T09:57:59Z","title_canon_sha256":"d740c7ee767235b5b4e7f5ad04f36c90b8657af42336f4f8080725abd5189cfa"},"schema_version":"1.0","source":{"id":"1506.04537","kind":"arxiv","version":1}},"canonical_sha256":"aaa4b717a378a58d7cc8b0d25cb99adac71f8d5fa2f295baca54a7cd699e9ff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaa4b717a378a58d7cc8b0d25cb99adac71f8d5fa2f295baca54a7cd699e9ff1","first_computed_at":"2026-05-18T01:49:30.938828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:30.938828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M9t/PlslmsY47IExQ8+uT7ZU1MZ4m2geYSX9XY0A+S23i/MsiYq5Grm+sKdv9Enm6wC5qBWejwsxBIMZQ1UwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:30.939374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.04537","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1b4416016534186759aa11f8697845fa08c287982bedf2a07022597b53d530e","sha256:970879a88725f38a52d6d6544bdb6af113eb28d0be1a8d2735bcf2d02acdc7ee"],"state_sha256":"21e93de788867a657af501aa93e2d15c89c99a4ae65a5c5457adae021b8d469e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zuaca4ilJj/Vb66Ne6bQCj08EzbfAg9UJ+R0z65Gk4g1V7qM+dSki9uyzYIrsRSvb9gJn5XCDdoBGiFtKv5RAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:29:28.960030Z","bundle_sha256":"a34ff0e0ea6679b225060200482233a4ce872763ccea20b33819314905fdfc67"}}