{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5Z2JKNHGVVMY6JL72IL2ZA6H5H","short_pith_number":"pith:5Z2JKNHG","schema_version":"1.0","canonical_sha256":"ee749534e6ad598f257fd217ac83c7e9e92173f2a3dacefe939fd5cf2edabb75","source":{"kind":"arxiv","id":"2607.20711","version":1},"attestation_state":"computed","paper":{"title":"Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Alcala, Mikhail S. Plyushchay","submitted_at":"2026-07-22T20:29:40Z","abstract_excerpt":"We study the one-dimensional linear-potential system as an affine extension of the conformal triangle formed by the free particle, harmonic oscillator (HO) and inverted harmonic oscillator (IHO). Unlike these homogeneous quadratic Hamiltonians in the $sl(2,\\mathbb R)$ sector, the linear-potential Hamiltonian involves the Heisenberg ideal of the Schr\\\"odinger algebra. Its direct relation to the free particle is a regular accelerated-frame transformation, developed here at the levels of the classical action, canonical transformation, wave-function intertwiner and propagator; its HO and IHO reali"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.20711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2026-07-22T20:29:40Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"d7ec5bb19609fe319b71fa7323e0ffdceb58ebdf8b0c0c98ad395181591e3eaa","abstract_canon_sha256":"b1dd1dd76169736cbd0b859422fa371b0a12522ae799a02943ffb2aa2bbca405"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-24T00:23:30.822675Z","signature_b64":"dcIuz+D7T5bESXJ+GX6Y3wvZ0E8pGPeXBj06Pe1hwmkjHTSirerCQkU2/+cMbtNxqnuilX54JPfRhHuzpMVVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee749534e6ad598f257fd217ac83c7e9e92173f2a3dacefe939fd5cf2edabb75","last_reissued_at":"2026-07-24T00:23:30.821843Z","signature_status":"signed_v1","first_computed_at":"2026-07-24T00:23:30.821843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Andrey Alcala, Mikhail S. Plyushchay","submitted_at":"2026-07-22T20:29:40Z","abstract_excerpt":"We study the one-dimensional linear-potential system as an affine extension of the conformal triangle formed by the free particle, harmonic oscillator (HO) and inverted harmonic oscillator (IHO). Unlike these homogeneous quadratic Hamiltonians in the $sl(2,\\mathbb R)$ sector, the linear-potential Hamiltonian involves the Heisenberg ideal of the Schr\\\"odinger algebra. Its direct relation to the free particle is a regular accelerated-frame transformation, developed here at the levels of the classical action, canonical transformation, wave-function intertwiner and propagator; its HO and IHO reali"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20711","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/2607.20711/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.20711","created_at":"2026-07-24T00:23:30.822267+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.20711v1","created_at":"2026-07-24T00:23:30.822267+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.20711","created_at":"2026-07-24T00:23:30.822267+00:00"},{"alias_kind":"pith_short_12","alias_value":"5Z2JKNHGVVMY","created_at":"2026-07-24T00:23:30.822267+00:00"},{"alias_kind":"pith_short_16","alias_value":"5Z2JKNHGVVMY6JL7","created_at":"2026-07-24T00:23:30.822267+00:00"},{"alias_kind":"pith_short_8","alias_value":"5Z2JKNHG","created_at":"2026-07-24T00:23:30.822267+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H","json":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H.json","graph_json":"https://pith.science/api/pith-number/5Z2JKNHGVVMY6JL72IL2ZA6H5H/graph.json","events_json":"https://pith.science/api/pith-number/5Z2JKNHGVVMY6JL72IL2ZA6H5H/events.json","paper":"https://pith.science/paper/5Z2JKNHG"},"agent_actions":{"view_html":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H","download_json":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H.json","view_paper":"https://pith.science/paper/5Z2JKNHG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.20711&json=true","fetch_graph":"https://pith.science/api/pith-number/5Z2JKNHGVVMY6JL72IL2ZA6H5H/graph.json","fetch_events":"https://pith.science/api/pith-number/5Z2JKNHGVVMY6JL72IL2ZA6H5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H/action/storage_attestation","attest_author":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H/action/author_attestation","sign_citation":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H/action/citation_signature","submit_replication":"https://pith.science/pith/5Z2JKNHGVVMY6JL72IL2ZA6H5H/action/replication_record"}},"created_at":"2026-07-24T00:23:30.822267+00:00","updated_at":"2026-07-24T00:23:30.822267+00:00"}