{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E6T7OXSPSPAJWZU3YM7SHRR2RE","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":"ea94ef3aab09dce2b2ac919a4acc25562018d3d9d0b70abd601a3090442a7fa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-28T14:38:49Z","title_canon_sha256":"ee39a6e74dbf13e48e83ba3e7aa117c584961021af0925f46c98d944c244b8c3"},"schema_version":"1.0","source":{"id":"1606.08736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08736","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08736v1","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08736","created_at":"2026-05-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"E6T7OXSPSPAJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"E6T7OXSPSPAJWZU3","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"E6T7OXSP","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:2836892a18487f04208944eff4fd48914d8de062b8487e94402ff8a50efa489b","target":"graph","created_at":"2026-05-18T01:11:47Z","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":"We consider the following perturbed Hamiltonian $\\mathcal{H}= -\\partial_x^2 + V(x)$ on the real line. The potential $V(x)$ is a real - valued function of short range type. We study the equivalence of classical homogeneous Sobolev type spaces $\\dot{H}^s_p$, $p \\in (1,\\infty)$ and the corresponding perturbed homogeneous Sobolev spaces associated with the perturbed Hamiltonian. It is shown that the assumption zero is not a resonance guarantees that the perturbed and unperturbed homogeneous Sobolev norms of order $s = \\gamma - 1 \\in [0,1/p)$ are equivalent. As a corollary, the corresponding wave o","authors_text":"Anna Rita Giammetta, Vladimir Georgiev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-28T14:38:49Z","title":"Hardy inequality and fractional Leibnitz rule for perturbed Hamiltonians on the line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08736","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:b055d1fe4ec70d112bb333810918920d0808e46b907114db2752adc5fd4a939f","target":"record","created_at":"2026-05-18T01:11:47Z","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":"ea94ef3aab09dce2b2ac919a4acc25562018d3d9d0b70abd601a3090442a7fa5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-06-28T14:38:49Z","title_canon_sha256":"ee39a6e74dbf13e48e83ba3e7aa117c584961021af0925f46c98d944c244b8c3"},"schema_version":"1.0","source":{"id":"1606.08736","kind":"arxiv","version":1}},"canonical_sha256":"27a7f75e4f93c09b669bc33f23c63a8937ed5e6247ca1bc8b06841a0225a229e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27a7f75e4f93c09b669bc33f23c63a8937ed5e6247ca1bc8b06841a0225a229e","first_computed_at":"2026-05-18T01:11:47.177677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:47.177677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y/Vc2MovVyjMtINT0gS8G4MKHJpKyM5wiJyXblDIz8bgsb/aAoXohWSDL3md0Vv60x1iaUfXoJ6SgqPQC5v8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:47.178021Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b055d1fe4ec70d112bb333810918920d0808e46b907114db2752adc5fd4a939f","sha256:2836892a18487f04208944eff4fd48914d8de062b8487e94402ff8a50efa489b"],"state_sha256":"2be3622754f14e3364d86b875e00316cef27c03585701c4fae575379347bac0f"}