{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:5RVIPBV2ADV5QWSGRZCT7XQRPD","short_pith_number":"pith:5RVIPBV2","canonical_record":{"source":{"id":"2007.08167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-07-16T08:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"9645a3ceb1c255f4b4cfa9fefd38d4cf80e5965938a80e3aca01ef42f06eb4aa","abstract_canon_sha256":"e135f3f60bf11fa96e52d42e9a3fe90907fceac1a39b07aadc103be514c2069d"},"schema_version":"1.0"},"canonical_sha256":"ec6a8786ba00ebd85a468e453fde1178c5f62382e60f8c2cc93fd4b251213f10","source":{"kind":"arxiv","id":"2007.08167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.08167","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"2007.08167v2","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.08167","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"5RVIPBV2ADV5","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_16","alias_value":"5RVIPBV2ADV5QWSG","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_8","alias_value":"5RVIPBV2","created_at":"2026-07-05T03:10:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:5RVIPBV2ADV5QWSGRZCT7XQRPD","target":"record","payload":{"canonical_record":{"source":{"id":"2007.08167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-07-16T08:02:51Z","cross_cats_sorted":[],"title_canon_sha256":"9645a3ceb1c255f4b4cfa9fefd38d4cf80e5965938a80e3aca01ef42f06eb4aa","abstract_canon_sha256":"e135f3f60bf11fa96e52d42e9a3fe90907fceac1a39b07aadc103be514c2069d"},"schema_version":"1.0"},"canonical_sha256":"ec6a8786ba00ebd85a468e453fde1178c5f62382e60f8c2cc93fd4b251213f10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:10:25.097123Z","signature_b64":"YWweGsJMuYoOUwKD7hnnelxPDGvtbbAVMQHAPBFrrce8qEeLsodswX+zhUYTO99SNQKETvySzAD73oNX7tG8Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec6a8786ba00ebd85a468e453fde1178c5f62382e60f8c2cc93fd4b251213f10","last_reissued_at":"2026-07-05T03:10:25.096731Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:10:25.096731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.08167","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hqBODreU6Om7DDE0fqQD0SFQiLQZZ9vd5+F5dxaI85kB91pjdhilGOtHky0dvgHM7uqgIm1hy+0P5y0SY4PoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:12:54.236388Z"},"content_sha256":"8f8433f25806e7665fb7c0a2b2d311424a6343cee989b775fcfb588a2558c65e","schema_version":"1.0","event_id":"sha256:8f8433f25806e7665fb7c0a2b2d311424a6343cee989b775fcfb588a2558c65e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:5RVIPBV2ADV5QWSGRZCT7XQRPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symplectic Microgeometry IV: Quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Alan Weinstein, Alberto S. Cattaneo, Benoit Dherin","submitted_at":"2020-07-16T08:02:51Z","abstract_excerpt":"We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the cotangent microbundle category, and they admit a total symbol calculus in terms of symplectic micromorphisms enhanced with half-density germs. This new operator category encompasses the semi-classical pseudo-differential calculus and offers a functorial framework for the semi-classical analysis of the Schr\\\"odinger equation. We also comment on applications "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08167","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.08167/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:10:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKoozdtuF3N7S7ygLWnET44XRt70MKc0AgKsgN2VeHK/WIVr+nMWzmsCvgXElmnbTNB1Zb8KRQKGpyaVGAHhDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-08T23:12:54.236771Z"},"content_sha256":"cc360fc167f4c30b5e9b25177b178269bdcd063c19b80a9b6435b67404d2f1ed","schema_version":"1.0","event_id":"sha256:cc360fc167f4c30b5e9b25177b178269bdcd063c19b80a9b6435b67404d2f1ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/bundle.json","state_url":"https://pith.science/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/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":"2026-07-08T23:12:54Z","links":{"resolver":"https://pith.science/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD","bundle":"https://pith.science/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/bundle.json","state":"https://pith.science/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5RVIPBV2ADV5QWSGRZCT7XQRPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5RVIPBV2ADV5QWSGRZCT7XQRPD","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":"e135f3f60bf11fa96e52d42e9a3fe90907fceac1a39b07aadc103be514c2069d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-07-16T08:02:51Z","title_canon_sha256":"9645a3ceb1c255f4b4cfa9fefd38d4cf80e5965938a80e3aca01ef42f06eb4aa"},"schema_version":"1.0","source":{"id":"2007.08167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.08167","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"2007.08167v2","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.08167","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"5RVIPBV2ADV5","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_16","alias_value":"5RVIPBV2ADV5QWSG","created_at":"2026-07-05T03:10:25Z"},{"alias_kind":"pith_short_8","alias_value":"5RVIPBV2","created_at":"2026-07-05T03:10:25Z"}],"graph_snapshots":[{"event_id":"sha256:cc360fc167f4c30b5e9b25177b178269bdcd063c19b80a9b6435b67404d2f1ed","target":"graph","created_at":"2026-07-05T03:10:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2007.08167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the wave front map becomes a functor into the cotangent microbundle category, and they admit a total symbol calculus in terms of symplectic micromorphisms enhanced with half-density germs. This new operator category encompasses the semi-classical pseudo-differential calculus and offers a functorial framework for the semi-classical analysis of the Schr\\\"odinger equation. We also comment on applications ","authors_text":"Alan Weinstein, Alberto S. Cattaneo, Benoit Dherin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-07-16T08:02:51Z","title":"Symplectic Microgeometry IV: Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.08167","kind":"arxiv","version":2},"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":"sha256:8f8433f25806e7665fb7c0a2b2d311424a6343cee989b775fcfb588a2558c65e","target":"record","created_at":"2026-07-05T03:10:25Z","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":"e135f3f60bf11fa96e52d42e9a3fe90907fceac1a39b07aadc103be514c2069d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2020-07-16T08:02:51Z","title_canon_sha256":"9645a3ceb1c255f4b4cfa9fefd38d4cf80e5965938a80e3aca01ef42f06eb4aa"},"schema_version":"1.0","source":{"id":"2007.08167","kind":"arxiv","version":2}},"canonical_sha256":"ec6a8786ba00ebd85a468e453fde1178c5f62382e60f8c2cc93fd4b251213f10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec6a8786ba00ebd85a468e453fde1178c5f62382e60f8c2cc93fd4b251213f10","first_computed_at":"2026-07-05T03:10:25.096731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:10:25.096731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YWweGsJMuYoOUwKD7hnnelxPDGvtbbAVMQHAPBFrrce8qEeLsodswX+zhUYTO99SNQKETvySzAD73oNX7tG8Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T03:10:25.097123Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.08167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f8433f25806e7665fb7c0a2b2d311424a6343cee989b775fcfb588a2558c65e","sha256:cc360fc167f4c30b5e9b25177b178269bdcd063c19b80a9b6435b67404d2f1ed"],"state_sha256":"135176dbf096b95da79d41d84aafa727067e07df880cd30d81a224879634fba4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N6TL8np7P/xjH30bDPZvwZUFj5ihx09t1ppDZRlj9pgXnVL9iODTM7WtUwuiO1oH6vhH6H7uQqMI9ZW8pUqhBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-08T23:12:54.238988Z","bundle_sha256":"8bc00dcc81bbc985d0badf21fa62b5272411d49f7998b7965919e24ef7ae9526"}}