{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HPOCUWQYWYKFXX4H3FRSOMVISI","short_pith_number":"pith:HPOCUWQY","canonical_record":{"source":{"id":"1309.5068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-19T18:28:12Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"13af4c46c6d3afe172f46277658384765688071240838ad74e9e8ddb00c766a3","abstract_canon_sha256":"5424b2a498022707c4336f53f11d900347897edb157d61326279a922b93cdb44"},"schema_version":"1.0"},"canonical_sha256":"3bdc2a5a18b6145bdf87d9632732a892311011af307806a3709f69382a9abe83","source":{"kind":"arxiv","id":"1309.5068","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5068","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5068v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5068","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"HPOCUWQYWYKF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HPOCUWQYWYKFXX4H","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HPOCUWQY","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HPOCUWQYWYKFXX4H3FRSOMVISI","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-19T18:28:12Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"13af4c46c6d3afe172f46277658384765688071240838ad74e9e8ddb00c766a3","abstract_canon_sha256":"5424b2a498022707c4336f53f11d900347897edb157d61326279a922b93cdb44"},"schema_version":"1.0"},"canonical_sha256":"3bdc2a5a18b6145bdf87d9632732a892311011af307806a3709f69382a9abe83","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:44.907990Z","signature_b64":"xWx/K0NLnqPx6fbTUPbnCEznjzLxBtMkurDyoXMKfn48ChDElT+sC5w30kCpt+ug16xIT+Jwfj14EJX77dqADw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bdc2a5a18b6145bdf87d9632732a892311011af307806a3709f69382a9abe83","last_reissued_at":"2026-05-18T02:57:44.907403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:44.907403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5068","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"daQAlOit0n30zZteER2DxbrcEz5vpSyP1AVO7gIBdQe8swHT7Qp/UeNWBbAlSlWMp3eN3t6aBpmznmv/RDVPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:32:21.751476Z"},"content_sha256":"631c27d9bf58d7d1d3e261aaa4cb8c0e539b186f99275c4cd54c6e74648c4c85","schema_version":"1.0","event_id":"sha256:631c27d9bf58d7d1d3e261aaa4cb8c0e539b186f99275c4cd54c6e74648c4c85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HPOCUWQYWYKFXX4H3FRSOMVISI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Metaplectic sheets and caustic traversals in the Weyl representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Alfredo M. Ozorio de Almeida, Gert-Ludwig Ingold","submitted_at":"2013-09-19T18:28:12Z","abstract_excerpt":"The quantum Hamiltonian generates in time a family of evolution operators. Continuity of this family holds within any choice of representation and, in particular, for the Weyl propagator, even though its simplest semiclassical approximation may develop caustic singularities. The phase jumps of the Weyl propagator across caustics have not been previously determined.\n  The semiclassical appproximation relies on individual classical trajectories together with their neighbouring tangent map. Based on the latter, one defines a continuous family of unitary tangent propagators, with an exact Weyl rep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5068","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":"2026-05-18T02:57:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opqyNV1AUvthRZLVNI7haeCmkXGJ82POZSjumFJvZPEaeb2xzdMhPSfzORQDp9qJsd3vhO3kH+bbDqBR46ADBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:32:21.752180Z"},"content_sha256":"718eb329785d3900303394fa070986e2b7000db33a4ceed55d014430bd27a06c","schema_version":"1.0","event_id":"sha256:718eb329785d3900303394fa070986e2b7000db33a4ceed55d014430bd27a06c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/bundle.json","state_url":"https://pith.science/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/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":"2026-05-28T18:32:21Z","links":{"resolver":"https://pith.science/pith/HPOCUWQYWYKFXX4H3FRSOMVISI","bundle":"https://pith.science/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/bundle.json","state":"https://pith.science/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HPOCUWQYWYKFXX4H3FRSOMVISI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HPOCUWQYWYKFXX4H3FRSOMVISI","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":"5424b2a498022707c4336f53f11d900347897edb157d61326279a922b93cdb44","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-19T18:28:12Z","title_canon_sha256":"13af4c46c6d3afe172f46277658384765688071240838ad74e9e8ddb00c766a3"},"schema_version":"1.0","source":{"id":"1309.5068","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5068","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5068v1","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5068","created_at":"2026-05-18T02:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"HPOCUWQYWYKF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HPOCUWQYWYKFXX4H","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HPOCUWQY","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:718eb329785d3900303394fa070986e2b7000db33a4ceed55d014430bd27a06c","target":"graph","created_at":"2026-05-18T02:57:44Z","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 quantum Hamiltonian generates in time a family of evolution operators. Continuity of this family holds within any choice of representation and, in particular, for the Weyl propagator, even though its simplest semiclassical approximation may develop caustic singularities. The phase jumps of the Weyl propagator across caustics have not been previously determined.\n  The semiclassical appproximation relies on individual classical trajectories together with their neighbouring tangent map. Based on the latter, one defines a continuous family of unitary tangent propagators, with an exact Weyl rep","authors_text":"Alfredo M. Ozorio de Almeida, Gert-Ludwig Ingold","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-19T18:28:12Z","title":"Metaplectic sheets and caustic traversals in the Weyl representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5068","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":"sha256:631c27d9bf58d7d1d3e261aaa4cb8c0e539b186f99275c4cd54c6e74648c4c85","target":"record","created_at":"2026-05-18T02:57:44Z","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":"5424b2a498022707c4336f53f11d900347897edb157d61326279a922b93cdb44","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-19T18:28:12Z","title_canon_sha256":"13af4c46c6d3afe172f46277658384765688071240838ad74e9e8ddb00c766a3"},"schema_version":"1.0","source":{"id":"1309.5068","kind":"arxiv","version":1}},"canonical_sha256":"3bdc2a5a18b6145bdf87d9632732a892311011af307806a3709f69382a9abe83","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bdc2a5a18b6145bdf87d9632732a892311011af307806a3709f69382a9abe83","first_computed_at":"2026-05-18T02:57:44.907403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:44.907403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWx/K0NLnqPx6fbTUPbnCEznjzLxBtMkurDyoXMKfn48ChDElT+sC5w30kCpt+ug16xIT+Jwfj14EJX77dqADw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:44.907990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5068","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:631c27d9bf58d7d1d3e261aaa4cb8c0e539b186f99275c4cd54c6e74648c4c85","sha256:718eb329785d3900303394fa070986e2b7000db33a4ceed55d014430bd27a06c"],"state_sha256":"a12aef56ddde02cda661e2196c5ce611178e1611fe686e90b8dd059784927f44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BdetFZ+63esTuhjg4B2dbdqCN4DVW3eJVfXANB9HSlPdu+grWAyfO/mOLtz6pkZ1/C9WyPkP9ZCUV6FK0fYAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:32:21.755936Z","bundle_sha256":"a19e183f94b3cb808a8c672f7eff6f8b90b34c551273ab052f03b8b5aed0d066"}}