{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:XJ6BQGASTUCEFPH4OQH44IDXCW","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":"02493dad1a4b61546c62ba4fd366c16e9a4543f400443b9055a78c1c03c46124","cross_cats_sorted":["math.MP","math.SP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-01-12T11:36:15Z","title_canon_sha256":"8530269706b9a6b36513c46b426ca77b740f328f27b83b3fd6d04d4329ad8d7f"},"schema_version":"1.0","source":{"id":"math-ph/0401022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0401022","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0401022v1","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0401022","created_at":"2026-05-18T01:38:33Z"},{"alias_kind":"pith_short_12","alias_value":"XJ6BQGASTUCE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XJ6BQGASTUCEFPH4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XJ6BQGAS","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:b9b3f3c75e192018345a16be614275f6e2c5552d04ccfb698e7c5b3c038dae4e","target":"graph","created_at":"2026-05-18T01:38:33Z","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 obtain, using the Birman-Schwinger method, upper limits on the total number of bound states and on the number of $\\ell$-wave bound states of the semirelativistic spinless Salpeter equation. We also obtain a simple condition, in the ultrarelativistic case ($m=0$), for the existence of at least one $\\ell$-wave bound states: $C(\\ell,p/(p-1))$ $\\int_0^{\\infty}dr r^{p-1} |V^-(r)|^p\\ge 1$, where $C(\\ell,p/(p-1))$ is a known function of $\\ell$ and $p>1$.","authors_text":"Fabian Brau","cross_cats":["math.MP","math.SP","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-01-12T11:36:15Z","title":"Upper limit on the number of bound states of the spinless Salpeter equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0401022","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:f62a73d7d538b15e6dc4768ac1ff77774f59d7d61758dd0006870a4b8dfc97f9","target":"record","created_at":"2026-05-18T01:38:33Z","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":"02493dad1a4b61546c62ba4fd366c16e9a4543f400443b9055a78c1c03c46124","cross_cats_sorted":["math.MP","math.SP","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"2004-01-12T11:36:15Z","title_canon_sha256":"8530269706b9a6b36513c46b426ca77b740f328f27b83b3fd6d04d4329ad8d7f"},"schema_version":"1.0","source":{"id":"math-ph/0401022","kind":"arxiv","version":1}},"canonical_sha256":"ba7c1818129d0442bcfc740fce20771591b30957dd4349b024584a328128f3f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba7c1818129d0442bcfc740fce20771591b30957dd4349b024584a328128f3f9","first_computed_at":"2026-05-18T01:38:33.587234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:33.587234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uoYYZe/+CELtnPWEw/huMMe+sc/zXGvnIn8zeXmFyhEiPjCA+V6vdS8F2v4ujPxuj0Qck8Zzw/aE4l8xo1TsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:33.587678Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0401022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f62a73d7d538b15e6dc4768ac1ff77774f59d7d61758dd0006870a4b8dfc97f9","sha256:b9b3f3c75e192018345a16be614275f6e2c5552d04ccfb698e7c5b3c038dae4e"],"state_sha256":"366297c02c3aab0e33a504345a3a4ceb37223f7fb47d610dcc7cc29bf69c23c9"}