{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:4HLMD2S6VA3UOMW566UBKW6G6K","short_pith_number":"pith:4HLMD2S6","schema_version":"1.0","canonical_sha256":"e1d6c1ea5ea8374732ddf7a8155bc6f285cde18830184bc25fcf1acd6d7e9143","source":{"kind":"arxiv","id":"1609.01724","version":3},"attestation_state":"computed","paper":{"title":"Quantum confinement on non-complete Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Dario Prandi, Luca Rizzi, Marcello Seri","submitted_at":"2016-09-06T20:00:03Z","abstract_excerpt":"We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold $M$ equipped with a smooth measure $\\omega$, possibly degenerate or singular near the metric boundary of $M$, and in presence of a real-valued potential $V\\in L^2_{\\mathrm{loc}}(M)$. The main merit of this paper is the identification of an intrinsic quantity, the effective potential $V_{\\mathrm{eff}}$, which allows to formulate simple criteria for quantum confinement. Let $\\delta$ be the distance from the possibly non-compact metric boundary of $M$. A simplified "},"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":"1609.01724","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-06T20:00:03Z","cross_cats_sorted":["math-ph","math.AP","math.MP","math.SP"],"title_canon_sha256":"948dab0521cd1cf3470eea57e7ef4044afca0cb8448ed6e3068c631ac107ee2f","abstract_canon_sha256":"e087aa8e9892bf69eb4b49494da04fce604e2c7945241933cae7b14461c19758"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:39.808265Z","signature_b64":"IVOpHWqzIUYntHdtXQBjNbElTZicxLTqskYpuTouCEo5RtI/atI77VjUrZRwg+ryrFfr0wlzplmRi+cPaiP0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1d6c1ea5ea8374732ddf7a8155bc6f285cde18830184bc25fcf1acd6d7e9143","last_reissued_at":"2026-05-17T23:59:39.807565Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:39.807565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum confinement on non-complete Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP","math.SP"],"primary_cat":"math.DG","authors_text":"Dario Prandi, Luca Rizzi, Marcello Seri","submitted_at":"2016-09-06T20:00:03Z","abstract_excerpt":"We consider the quantum completeness problem, i.e. the problem of confining quantum particles, on a non-complete Riemannian manifold $M$ equipped with a smooth measure $\\omega$, possibly degenerate or singular near the metric boundary of $M$, and in presence of a real-valued potential $V\\in L^2_{\\mathrm{loc}}(M)$. The main merit of this paper is the identification of an intrinsic quantity, the effective potential $V_{\\mathrm{eff}}$, which allows to formulate simple criteria for quantum confinement. Let $\\delta$ be the distance from the possibly non-compact metric boundary of $M$. A simplified "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01724","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1609.01724","created_at":"2026-05-17T23:59:39.807694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.01724v3","created_at":"2026-05-17T23:59:39.807694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01724","created_at":"2026-05-17T23:59:39.807694+00:00"},{"alias_kind":"pith_short_12","alias_value":"4HLMD2S6VA3U","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_16","alias_value":"4HLMD2S6VA3UOMW5","created_at":"2026-05-18T12:29:58.707656+00:00"},{"alias_kind":"pith_short_8","alias_value":"4HLMD2S6","created_at":"2026-05-18T12:29:58.707656+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/4HLMD2S6VA3UOMW566UBKW6G6K","json":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K.json","graph_json":"https://pith.science/api/pith-number/4HLMD2S6VA3UOMW566UBKW6G6K/graph.json","events_json":"https://pith.science/api/pith-number/4HLMD2S6VA3UOMW566UBKW6G6K/events.json","paper":"https://pith.science/paper/4HLMD2S6"},"agent_actions":{"view_html":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K","download_json":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K.json","view_paper":"https://pith.science/paper/4HLMD2S6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.01724&json=true","fetch_graph":"https://pith.science/api/pith-number/4HLMD2S6VA3UOMW566UBKW6G6K/graph.json","fetch_events":"https://pith.science/api/pith-number/4HLMD2S6VA3UOMW566UBKW6G6K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K/action/storage_attestation","attest_author":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K/action/author_attestation","sign_citation":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K/action/citation_signature","submit_replication":"https://pith.science/pith/4HLMD2S6VA3UOMW566UBKW6G6K/action/replication_record"}},"created_at":"2026-05-17T23:59:39.807694+00:00","updated_at":"2026-05-17T23:59:39.807694+00:00"}