{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4CGM7D3YQIQCNAXL3KS7NX3S3T","short_pith_number":"pith:4CGM7D3Y","canonical_record":{"source":{"id":"1004.3906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:51:17Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"60e95be4dae79335f43b494541da9bb74f88d2fdce81d7c61de84212130d27ab","abstract_canon_sha256":"f5881e44e9dba43a4273dfecb0f397d09aebe60c5a45fa1c63ea10c5d405fce6"},"schema_version":"1.0"},"canonical_sha256":"e08ccf8f7882202682ebdaa5f6df72dcd9c1ac34b41342da506e578705260018","source":{"kind":"arxiv","id":"1004.3906","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3906","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3906v1","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3906","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"4CGM7D3YQIQC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4CGM7D3YQIQCNAXL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4CGM7D3Y","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4CGM7D3YQIQCNAXL3KS7NX3S3T","target":"record","payload":{"canonical_record":{"source":{"id":"1004.3906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:51:17Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"60e95be4dae79335f43b494541da9bb74f88d2fdce81d7c61de84212130d27ab","abstract_canon_sha256":"f5881e44e9dba43a4273dfecb0f397d09aebe60c5a45fa1c63ea10c5d405fce6"},"schema_version":"1.0"},"canonical_sha256":"e08ccf8f7882202682ebdaa5f6df72dcd9c1ac34b41342da506e578705260018","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:07:55.128141Z","signature_b64":"JoqqSpoLnBxFrF1Jp+HnhvY403gYh4pPI8q4+who6OR1pzf2jYvv/PS12vzowBieOVn9Oxl5bXhukDLo4dFRAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e08ccf8f7882202682ebdaa5f6df72dcd9c1ac34b41342da506e578705260018","last_reissued_at":"2026-05-18T02:07:55.127150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:07:55.127150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.3906","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":"2026-05-18T02:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pWtLydRTSyRfFS0nl6Cy5M0GHRQ0Nvrssr89kYDlkI1KFNSjVavG8Z5R5Hmg33DI+l79PXsdUR5K4HBN/IkVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:05:14.791372Z"},"content_sha256":"3db5362a8d538d9fd92010dd3534d842ec4ea87549830cdff3f9b5f88211b491","schema_version":"1.0","event_id":"sha256:3db5362a8d538d9fd92010dd3534d842ec4ea87549830cdff3f9b5f88211b491"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4CGM7D3YQIQCNAXL3KS7NX3S3T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extending the class of solvable potentials: III. The hyperbolic single wave","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. D. Alhaidari, H. Bahlouli","submitted_at":"2010-04-22T12:51:17Z","abstract_excerpt":"A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\\\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal matrix representation of the wave operator. However, the eigen-energies associated with this potential cannot be obtained using traditional procedures. Hence, a new approach (the \"potential parameter\" approach) has been adopted for this eigenvalue problem. For a fixed energy, the problem is solvable for a set of values of the potential parameters (the \"parame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3906","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":"2026-05-18T02:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SdD/oKIe2m1DUGB/5PSGll5c0kjUyHW4KbhoyI37SMnBBFAdXwQaCIyXAbY7WG6ySKkH2VjGKOkUXQLMKmQyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:05:14.791971Z"},"content_sha256":"9b22bc4a674d2b4303f3bdaf68e89f725ea58a06c7cbc92340d88ec9c9c6a0da","schema_version":"1.0","event_id":"sha256:9b22bc4a674d2b4303f3bdaf68e89f725ea58a06c7cbc92340d88ec9c9c6a0da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/bundle.json","state_url":"https://pith.science/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/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":"2026-06-25T13:05:14Z","links":{"resolver":"https://pith.science/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T","bundle":"https://pith.science/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/bundle.json","state":"https://pith.science/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CGM7D3YQIQCNAXL3KS7NX3S3T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4CGM7D3YQIQCNAXL3KS7NX3S3T","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":"f5881e44e9dba43a4273dfecb0f397d09aebe60c5a45fa1c63ea10c5d405fce6","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:51:17Z","title_canon_sha256":"60e95be4dae79335f43b494541da9bb74f88d2fdce81d7c61de84212130d27ab"},"schema_version":"1.0","source":{"id":"1004.3906","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.3906","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1004.3906v1","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3906","created_at":"2026-05-18T02:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"4CGM7D3YQIQC","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4CGM7D3YQIQCNAXL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4CGM7D3Y","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:9b22bc4a674d2b4303f3bdaf68e89f725ea58a06c7cbc92340d88ec9c9c6a0da","target":"graph","created_at":"2026-05-18T02:07:55Z","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":"A new solvable hyperbolic single wave potential is found by expanding the regular solution of the 1D Schr\\\"odinger equation in terms of square integrable basis. The main characteristic of the basis is in supporting an infinite tridiagonal matrix representation of the wave operator. However, the eigen-energies associated with this potential cannot be obtained using traditional procedures. Hence, a new approach (the \"potential parameter\" approach) has been adopted for this eigenvalue problem. For a fixed energy, the problem is solvable for a set of values of the potential parameters (the \"parame","authors_text":"A. D. Alhaidari, H. Bahlouli","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:51:17Z","title":"Extending the class of solvable potentials: III. The hyperbolic single wave"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3906","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":"sha256:3db5362a8d538d9fd92010dd3534d842ec4ea87549830cdff3f9b5f88211b491","target":"record","created_at":"2026-05-18T02:07:55Z","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":"f5881e44e9dba43a4273dfecb0f397d09aebe60c5a45fa1c63ea10c5d405fce6","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-04-22T12:51:17Z","title_canon_sha256":"60e95be4dae79335f43b494541da9bb74f88d2fdce81d7c61de84212130d27ab"},"schema_version":"1.0","source":{"id":"1004.3906","kind":"arxiv","version":1}},"canonical_sha256":"e08ccf8f7882202682ebdaa5f6df72dcd9c1ac34b41342da506e578705260018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e08ccf8f7882202682ebdaa5f6df72dcd9c1ac34b41342da506e578705260018","first_computed_at":"2026-05-18T02:07:55.127150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:07:55.127150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JoqqSpoLnBxFrF1Jp+HnhvY403gYh4pPI8q4+who6OR1pzf2jYvv/PS12vzowBieOVn9Oxl5bXhukDLo4dFRAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:07:55.128141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.3906","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db5362a8d538d9fd92010dd3534d842ec4ea87549830cdff3f9b5f88211b491","sha256:9b22bc4a674d2b4303f3bdaf68e89f725ea58a06c7cbc92340d88ec9c9c6a0da"],"state_sha256":"3afec2dcc7dc1a4210c796b1a5fd77d81c05130032153e6e4cec357acabecd60"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxBjl5MXNHrqvSYP+8AxT0P2xww1j9Advj/dX7h6+BhnktBcS4l7LW/MfXbUGi25Jty+E9b+fTj1KHL4+C4GDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:05:14.795068Z","bundle_sha256":"49e0f13264103d45646b5051031f222d6db7bd25df7eede3a56feb4ae37eb51b"}}