{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:TGEO6T3EPCUJRFKUG5DRUMFFQC","short_pith_number":"pith:TGEO6T3E","canonical_record":{"source":{"id":"quant-ph/9812041","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-12-16T17:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"ec83808077bb3292ad0b0b36148484d60d4c1c447569b2d815f1c9465808e31f","abstract_canon_sha256":"94d60ddaacfbfcb68ddb4ef5c832f7d29086798f391382a7623d029279773685"},"schema_version":"1.0"},"canonical_sha256":"9988ef4f6478a898955437471a30a58092b869042efabac32135c89b99e7831f","source":{"kind":"arxiv","id":"quant-ph/9812041","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9812041","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9812041v2","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9812041","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"TGEO6T3EPCUJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"TGEO6T3EPCUJRFKU","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"TGEO6T3E","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:TGEO6T3EPCUJRFKUG5DRUMFFQC","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9812041","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1998-12-16T17:16:04Z","cross_cats_sorted":[],"title_canon_sha256":"ec83808077bb3292ad0b0b36148484d60d4c1c447569b2d815f1c9465808e31f","abstract_canon_sha256":"94d60ddaacfbfcb68ddb4ef5c832f7d29086798f391382a7623d029279773685"},"schema_version":"1.0"},"canonical_sha256":"9988ef4f6478a898955437471a30a58092b869042efabac32135c89b99e7831f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:12.816076Z","signature_b64":"AUfx7j4IMCAtRCtlfVPHoG7BNUNV3ZvakXiMNQtkp/gui9KT5RkZRieJJm5NPtMXdLPeJFDbUrAgJp4EqdDTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9988ef4f6478a898955437471a30a58092b869042efabac32135c89b99e7831f","last_reissued_at":"2026-05-18T01:09:12.815645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:12.815645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9812041","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":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4BCGwowqQHPp7W3wqx5X93NIcFvnK3sFTvUBCjUXkncw/4sJw03TMnVZNHLHHYr+THGS4Y4iHFhRQ7nogxIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:19:31.895389Z"},"content_sha256":"855b82f858d0a95ebd8578eb597c7e710effd36488f988fa48cc4e37b05dbe81","schema_version":"1.0","event_id":"sha256:855b82f858d0a95ebd8578eb597c7e710effd36488f988fa48cc4e37b05dbe81"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:TGEO6T3EPCUJRFKUG5DRUMFFQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algebraic construction of the coherent states of the Morse potential based on SUSY QM","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bal\\'azs Moln\\'ar, Mih\\'aly G. Benedict","submitted_at":"1998-12-16T17:16:04Z","abstract_excerpt":"By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal set, which we call the pseudo number states, the Morse Hamiltonian is tridiagonal. By using this basis we construct coherent states algebraically for the Morse potential, in a close analogy with the harmonic oscillator. We also show that there exists an unitary displacement operator creating these coherent states from the ground state. We show that our cohere"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9812041","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":""},"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":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4++aLDF6+GgbfSBr9Ygx9cLOBScz48+sUXXMj4ZylHNlLUwcIfAtulcoYjCamVbqRdpbLmpf8tp13yWhDIVMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:19:31.896227Z"},"content_sha256":"bd659d5d38baf65b76430c6a8bc9c17d88fc6d1642e6c2c8f773e8f48be1f453","schema_version":"1.0","event_id":"sha256:bd659d5d38baf65b76430c6a8bc9c17d88fc6d1642e6c2c8f773e8f48be1f453"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/bundle.json","state_url":"https://pith.science/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/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":"2026-05-31T17:19:31Z","links":{"resolver":"https://pith.science/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC","bundle":"https://pith.science/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/bundle.json","state":"https://pith.science/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TGEO6T3EPCUJRFKUG5DRUMFFQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:TGEO6T3EPCUJRFKUG5DRUMFFQC","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":"94d60ddaacfbfcb68ddb4ef5c832f7d29086798f391382a7623d029279773685","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-12-16T17:16:04Z","title_canon_sha256":"ec83808077bb3292ad0b0b36148484d60d4c1c447569b2d815f1c9465808e31f"},"schema_version":"1.0","source":{"id":"quant-ph/9812041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9812041","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9812041v2","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9812041","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"TGEO6T3EPCUJ","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"TGEO6T3EPCUJRFKU","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"TGEO6T3E","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:bd659d5d38baf65b76430c6a8bc9c17d88fc6d1642e6c2c8f773e8f48be1f453","target":"graph","created_at":"2026-05-18T01:09:12Z","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":"By introducing the shape invariant Lie algebra spanned by the SUSY ladder operators plus the unity operator, a new basis is presented for the quantum treatment of the one-dimensional Morse potential. In this discrete, complete orthonormal set, which we call the pseudo number states, the Morse Hamiltonian is tridiagonal. By using this basis we construct coherent states algebraically for the Morse potential, in a close analogy with the harmonic oscillator. We also show that there exists an unitary displacement operator creating these coherent states from the ground state. We show that our cohere","authors_text":"Bal\\'azs Moln\\'ar, Mih\\'aly G. Benedict","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1998-12-16T17:16:04Z","title":"An algebraic construction of the coherent states of the Morse potential based on SUSY QM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9812041","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":"sha256:855b82f858d0a95ebd8578eb597c7e710effd36488f988fa48cc4e37b05dbe81","target":"record","created_at":"2026-05-18T01:09:12Z","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":"94d60ddaacfbfcb68ddb4ef5c832f7d29086798f391382a7623d029279773685","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1998-12-16T17:16:04Z","title_canon_sha256":"ec83808077bb3292ad0b0b36148484d60d4c1c447569b2d815f1c9465808e31f"},"schema_version":"1.0","source":{"id":"quant-ph/9812041","kind":"arxiv","version":2}},"canonical_sha256":"9988ef4f6478a898955437471a30a58092b869042efabac32135c89b99e7831f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9988ef4f6478a898955437471a30a58092b869042efabac32135c89b99e7831f","first_computed_at":"2026-05-18T01:09:12.815645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:12.815645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AUfx7j4IMCAtRCtlfVPHoG7BNUNV3ZvakXiMNQtkp/gui9KT5RkZRieJJm5NPtMXdLPeJFDbUrAgJp4EqdDTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:12.816076Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9812041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:855b82f858d0a95ebd8578eb597c7e710effd36488f988fa48cc4e37b05dbe81","sha256:bd659d5d38baf65b76430c6a8bc9c17d88fc6d1642e6c2c8f773e8f48be1f453"],"state_sha256":"d64f66e39ca3947cf5313935d51ae205ac4d44562430fb375ff260a8d0960307"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+mWdYE9e5KfAVLMFNYv8wwBuPi1EjHjBY8WF6qy9BQXtMU7QlV5S1ilI/LOEWhcEUFWGaI1y4wJ25lnMIC7OCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:19:31.901006Z","bundle_sha256":"ead99dd1f868429c3fd800987f049fa13a45d0390f7d94481ba0a431c138e41b"}}