{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CLIAT67ZVWWSTWP4AGAVDTL3DG","short_pith_number":"pith:CLIAT67Z","canonical_record":{"source":{"id":"0902.0654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-04T03:10:06Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"a65b34aa3566cf6e038ba5658dd83036e676a1bedfc95c769a0de2a8600e43cc","abstract_canon_sha256":"6b1c28226d39f99399d0cd1b30bb0343d34c2273d6533a9bfc5d45b5dcbdb9ca"},"schema_version":"1.0"},"canonical_sha256":"12d009fbf9adad29d9fc018151cd7b198550a0946b468ea1ad24928ef3786168","source":{"kind":"arxiv","id":"0902.0654","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0654","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0654v1","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0654","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"CLIAT67ZVWWS","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_16","alias_value":"CLIAT67ZVWWSTWP4","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_8","alias_value":"CLIAT67Z","created_at":"2026-07-04T15:37:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CLIAT67ZVWWSTWP4AGAVDTL3DG","target":"record","payload":{"canonical_record":{"source":{"id":"0902.0654","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-04T03:10:06Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"a65b34aa3566cf6e038ba5658dd83036e676a1bedfc95c769a0de2a8600e43cc","abstract_canon_sha256":"6b1c28226d39f99399d0cd1b30bb0343d34c2273d6533a9bfc5d45b5dcbdb9ca"},"schema_version":"1.0"},"canonical_sha256":"12d009fbf9adad29d9fc018151cd7b198550a0946b468ea1ad24928ef3786168","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:37:16.350082Z","signature_b64":"4zCrrfEUC7oigb/NLSlLFLqIRT5DKtAyeyaQ3wpNJfCy75sZjWtBzpKF9we2yg1otrlu0z2IugzCjoSvvUHCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12d009fbf9adad29d9fc018151cd7b198550a0946b468ea1ad24928ef3786168","last_reissued_at":"2026-07-04T15:37:16.349731Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:37:16.349731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0902.0654","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":"2026-07-04T15:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJFA92yZcRucT/m/dSIh4wBnAfS4Y6mcCT/g2FGqqw0E2SpjvIaD0kU+r7hS01fyTnrrT3P8OTRIt1ycRIYOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:13:27.214744Z"},"content_sha256":"09cc4bd277b6330502e34573a91d9d83f55c7eb09eab517eb3a46f93d7d6fff3","schema_version":"1.0","event_id":"sha256:09cc4bd277b6330502e34573a91d9d83f55c7eb09eab517eb3a46f93d7d6fff3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CLIAT67ZVWWSTWP4AGAVDTL3DG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gamow vectors and Borel summability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Min Huang, Ovidiu Costin","submitted_at":"2009-02-04T03:10:06Z","abstract_excerpt":"We analyze the detailed time dependence of the wave function $\\psi(x,t)$ for one dimensional Hamiltonians $H=-\\partial_x^2+V(x)$ where $V$ (for example modeling barriers or wells) and $\\psi(x,0)$ are {\\em compactly supported}. We show that the dispersive part of $\\psi(x,t)$, its asymptotic series in powers of $t^{-1/2}$, is Borel summable. The remainder, the difference between $\\psi$ and the Borel sum, is a convergent expansion of the form $\\sum_{k=0}^{\\infty}g_k \\Gamma_k(x)e^{-\\gamma_k t}$, where $\\Gamma_k$ are the Gamow vectors of $H$, and $\\gamma_k$ are the associated resonances; genericall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0902.0654/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":"2026-07-04T15:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D0ZQh3s3ja80pJvX5J1w6PCshQrdOxsyC+vSWfK+5giH5pAsCTYLi6vMkIHODblyii3d4PHUXIVfkQYgp72VAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T13:13:27.215027Z"},"content_sha256":"f86e74ccabb15d1cbccf7b0c7517af08d8b28a2d55193c067c821a76aefec4f4","schema_version":"1.0","event_id":"sha256:f86e74ccabb15d1cbccf7b0c7517af08d8b28a2d55193c067c821a76aefec4f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/bundle.json","state_url":"https://pith.science/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/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":"2026-08-05T13:13:27Z","links":{"resolver":"https://pith.science/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG","bundle":"https://pith.science/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/bundle.json","state":"https://pith.science/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CLIAT67ZVWWSTWP4AGAVDTL3DG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CLIAT67ZVWWSTWP4AGAVDTL3DG","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":"6b1c28226d39f99399d0cd1b30bb0343d34c2273d6533a9bfc5d45b5dcbdb9ca","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-04T03:10:06Z","title_canon_sha256":"a65b34aa3566cf6e038ba5658dd83036e676a1bedfc95c769a0de2a8600e43cc"},"schema_version":"1.0","source":{"id":"0902.0654","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.0654","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"0902.0654v1","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0654","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"CLIAT67ZVWWS","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_16","alias_value":"CLIAT67ZVWWSTWP4","created_at":"2026-07-04T15:37:16Z"},{"alias_kind":"pith_short_8","alias_value":"CLIAT67Z","created_at":"2026-07-04T15:37:16Z"}],"graph_snapshots":[{"event_id":"sha256:f86e74ccabb15d1cbccf7b0c7517af08d8b28a2d55193c067c821a76aefec4f4","target":"graph","created_at":"2026-07-04T15:37:16Z","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/0902.0654/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the detailed time dependence of the wave function $\\psi(x,t)$ for one dimensional Hamiltonians $H=-\\partial_x^2+V(x)$ where $V$ (for example modeling barriers or wells) and $\\psi(x,0)$ are {\\em compactly supported}. We show that the dispersive part of $\\psi(x,t)$, its asymptotic series in powers of $t^{-1/2}$, is Borel summable. The remainder, the difference between $\\psi$ and the Borel sum, is a convergent expansion of the form $\\sum_{k=0}^{\\infty}g_k \\Gamma_k(x)e^{-\\gamma_k t}$, where $\\Gamma_k$ are the Gamow vectors of $H$, and $\\gamma_k$ are the associated resonances; genericall","authors_text":"Min Huang, Ovidiu Costin","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-04T03:10:06Z","title":"Gamow vectors and Borel summability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0654","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":"sha256:09cc4bd277b6330502e34573a91d9d83f55c7eb09eab517eb3a46f93d7d6fff3","target":"record","created_at":"2026-07-04T15:37:16Z","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":"6b1c28226d39f99399d0cd1b30bb0343d34c2273d6533a9bfc5d45b5dcbdb9ca","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-02-04T03:10:06Z","title_canon_sha256":"a65b34aa3566cf6e038ba5658dd83036e676a1bedfc95c769a0de2a8600e43cc"},"schema_version":"1.0","source":{"id":"0902.0654","kind":"arxiv","version":1}},"canonical_sha256":"12d009fbf9adad29d9fc018151cd7b198550a0946b468ea1ad24928ef3786168","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12d009fbf9adad29d9fc018151cd7b198550a0946b468ea1ad24928ef3786168","first_computed_at":"2026-07-04T15:37:16.349731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:37:16.349731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4zCrrfEUC7oigb/NLSlLFLqIRT5DKtAyeyaQ3wpNJfCy75sZjWtBzpKF9we2yg1otrlu0z2IugzCjoSvvUHCAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:37:16.350082Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.0654","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09cc4bd277b6330502e34573a91d9d83f55c7eb09eab517eb3a46f93d7d6fff3","sha256:f86e74ccabb15d1cbccf7b0c7517af08d8b28a2d55193c067c821a76aefec4f4"],"state_sha256":"2cb203852bf3b4b1d11b6dcab833051d2ddc0f7e9eff79316f5d67b94c56ce3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ok4H6Po+TW9kUi0FhaeOilbySesy2xKGADO/QQtb7eNsUeuDqAE9ZenhjfpXMg5P/+DnpRisSGmYPDP4KfebBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T13:13:27.218279Z","bundle_sha256":"0806de124441ebdfb125fb39fabb77a247fc2d1308895b9f50ca55c10bdbdc21"}}