{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:W64INKDN2JBQNMFXBWAJDIOGQD","short_pith_number":"pith:W64INKDN","canonical_record":{"source":{"id":"2201.03140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-01-10T02:34:57Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"ab842ee4f74924a0de379ba83fe87df1f68e170b5c43853edb89c23e8f06f624","abstract_canon_sha256":"bff71278ae72171b61a05a13fb5e9a0827ca02c3dfe395cc93a399b4f66db8c9"},"schema_version":"1.0"},"canonical_sha256":"b7b886a86dd24306b0b70d8091a1c680d2b5291c35dd91e916a4cbb01f35eed0","source":{"kind":"arxiv","id":"2201.03140","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.03140","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"2201.03140v3","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.03140","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"W64INKDN2JBQ","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"W64INKDN2JBQNMFX","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"W64INKDN","created_at":"2026-07-05T07:11:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:W64INKDN2JBQNMFXBWAJDIOGQD","target":"record","payload":{"canonical_record":{"source":{"id":"2201.03140","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-01-10T02:34:57Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"ab842ee4f74924a0de379ba83fe87df1f68e170b5c43853edb89c23e8f06f624","abstract_canon_sha256":"bff71278ae72171b61a05a13fb5e9a0827ca02c3dfe395cc93a399b4f66db8c9"},"schema_version":"1.0"},"canonical_sha256":"b7b886a86dd24306b0b70d8091a1c680d2b5291c35dd91e916a4cbb01f35eed0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:11:11.804821Z","signature_b64":"K0MZ0q3wyxEwNvsM0BMaEgAzEXucmCpbD2Ark0e62UjVKWTCuO5QtTu8KtUqh9BLyml7/h1HDRIuyqq7Eno3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7b886a86dd24306b0b70d8091a1c680d2b5291c35dd91e916a4cbb01f35eed0","last_reissued_at":"2026-07-05T07:11:11.804306Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:11:11.804306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.03140","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IDQY7vdZi+CYNDsGdVUsHZz2aLRpD3bd9OW2BMOWVvzfjHkYAbPnTuXq11LvQb51nqt7ONuN3boRPlL0kqJsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:23:40.630814Z"},"content_sha256":"4fe314e529bbedcac3696611d7b397de2c31bb072b38d8b399cd405d250f0e57","schema_version":"1.0","event_id":"sha256:4fe314e529bbedcac3696611d7b397de2c31bb072b38d8b399cd405d250f0e57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:W64INKDN2JBQNMFXBWAJDIOGQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation of singularities and Fredholm analysis for the time-dependent Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Jesse Gell-Redman, Sean Gomes","submitted_at":"2022-01-10T02:34:57Z","abstract_excerpt":"We study the time-dependent Schr\\\"odinger operator $P = D_t + \\Delta_g + V$ acting on functions defined on $\\mathbb{R}^{n+1}$, where, using coordinates $z \\in \\mathbb{R}^n$ and $t \\in \\mathbb{R}$, $D_t$ denotes $-i \\partial_t$, $\\Delta_g$ is the positive Laplacian with respect to a time dependent family of non-trapping metrics $g_{ij}(z, t) dz^i dz^j$ on $\\mathbb{R}^n$ which is equal to the Euclidean metric outside of a compact set in spacetime, and $V = V(z, t)$ is a potential function which is also compactly supported in spacetime. In this paper we introduce a new approach to studying $P$, b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03140","kind":"arxiv","version":3},"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/2201.03140/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":"2026-07-05T07:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeriqSlPk86IsjqhZ44F6MiMmBoVnwI4oALEtOkm7VO+bmu2vphJZtQRJc2x17+MQRBL+orEpWKvyU1myT5cAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T23:23:40.631191Z"},"content_sha256":"96836d23d35f2de670f809d81d0cd22528f2fd6d382e1dc3010b6b7c37a3c9ba","schema_version":"1.0","event_id":"sha256:96836d23d35f2de670f809d81d0cd22528f2fd6d382e1dc3010b6b7c37a3c9ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W64INKDN2JBQNMFXBWAJDIOGQD/bundle.json","state_url":"https://pith.science/pith/W64INKDN2JBQNMFXBWAJDIOGQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W64INKDN2JBQNMFXBWAJDIOGQD/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":"2026-07-06T23:23:40Z","links":{"resolver":"https://pith.science/pith/W64INKDN2JBQNMFXBWAJDIOGQD","bundle":"https://pith.science/pith/W64INKDN2JBQNMFXBWAJDIOGQD/bundle.json","state":"https://pith.science/pith/W64INKDN2JBQNMFXBWAJDIOGQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W64INKDN2JBQNMFXBWAJDIOGQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:W64INKDN2JBQNMFXBWAJDIOGQD","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":"bff71278ae72171b61a05a13fb5e9a0827ca02c3dfe395cc93a399b4f66db8c9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-01-10T02:34:57Z","title_canon_sha256":"ab842ee4f74924a0de379ba83fe87df1f68e170b5c43853edb89c23e8f06f624"},"schema_version":"1.0","source":{"id":"2201.03140","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.03140","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"2201.03140v3","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.03140","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"W64INKDN2JBQ","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_16","alias_value":"W64INKDN2JBQNMFX","created_at":"2026-07-05T07:11:11Z"},{"alias_kind":"pith_short_8","alias_value":"W64INKDN","created_at":"2026-07-05T07:11:11Z"}],"graph_snapshots":[{"event_id":"sha256:96836d23d35f2de670f809d81d0cd22528f2fd6d382e1dc3010b6b7c37a3c9ba","target":"graph","created_at":"2026-07-05T07:11:11Z","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/2201.03140/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the time-dependent Schr\\\"odinger operator $P = D_t + \\Delta_g + V$ acting on functions defined on $\\mathbb{R}^{n+1}$, where, using coordinates $z \\in \\mathbb{R}^n$ and $t \\in \\mathbb{R}$, $D_t$ denotes $-i \\partial_t$, $\\Delta_g$ is the positive Laplacian with respect to a time dependent family of non-trapping metrics $g_{ij}(z, t) dz^i dz^j$ on $\\mathbb{R}^n$ which is equal to the Euclidean metric outside of a compact set in spacetime, and $V = V(z, t)$ is a potential function which is also compactly supported in spacetime. In this paper we introduce a new approach to studying $P$, b","authors_text":"Andrew Hassell, Jesse Gell-Redman, Sean Gomes","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-01-10T02:34:57Z","title":"Propagation of singularities and Fredholm analysis for the time-dependent Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.03140","kind":"arxiv","version":3},"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":"sha256:4fe314e529bbedcac3696611d7b397de2c31bb072b38d8b399cd405d250f0e57","target":"record","created_at":"2026-07-05T07:11:11Z","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":"bff71278ae72171b61a05a13fb5e9a0827ca02c3dfe395cc93a399b4f66db8c9","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-01-10T02:34:57Z","title_canon_sha256":"ab842ee4f74924a0de379ba83fe87df1f68e170b5c43853edb89c23e8f06f624"},"schema_version":"1.0","source":{"id":"2201.03140","kind":"arxiv","version":3}},"canonical_sha256":"b7b886a86dd24306b0b70d8091a1c680d2b5291c35dd91e916a4cbb01f35eed0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7b886a86dd24306b0b70d8091a1c680d2b5291c35dd91e916a4cbb01f35eed0","first_computed_at":"2026-07-05T07:11:11.804306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:11:11.804306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0MZ0q3wyxEwNvsM0BMaEgAzEXucmCpbD2Ark0e62UjVKWTCuO5QtTu8KtUqh9BLyml7/h1HDRIuyqq7Eno3Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T07:11:11.804821Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.03140","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fe314e529bbedcac3696611d7b397de2c31bb072b38d8b399cd405d250f0e57","sha256:96836d23d35f2de670f809d81d0cd22528f2fd6d382e1dc3010b6b7c37a3c9ba"],"state_sha256":"cef32ad2137eac4f5065307c0b4f588753d412426f1a46dba53aaaa56ce48c8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRmwWY3LsZLMr5S2SF4KXtCbPJ1/jJxmIP6tjiF2sNhpkCIIh1ePk1ohIgOUVQ3Wi56HYH3a8XIrqqg8Qc9zDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T23:23:40.633278Z","bundle_sha256":"75415974ba9a26f7636f0094ba728d28102041197b257cfb44db7c7e6962c268"}}