{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:NCPVO3HU3G34KISNE4367JC3F6","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":"51ed03fd60373ac9a742bdb450d285732b7a063c18fdf73e1ac61fdfabd492e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-06-09T08:17:52Z","title_canon_sha256":"6436b99e76319550b02a844a75d53f61aaa6449e0dbc12dae380889e0bedbeb5"},"schema_version":"1.0","source":{"id":"math-ph/0606029","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0606029","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0606029v6","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0606029","created_at":"2026-05-18T03:09:23Z"},{"alias_kind":"pith_short_12","alias_value":"NCPVO3HU3G34","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"NCPVO3HU3G34KISN","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"NCPVO3HU","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:d33622c4c779090c40a2e68eab4afbf6f8f8da7d83ab7df22bce4706996569ab","target":"graph","created_at":"2026-05-18T03:09:23Z","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":"A system of a Dirac particle interacting with the radiation field is considered. The Hamiltonian of the system is defined by $H = \\alpha\\cdot(\\hat\\mathbf{p}-q\\mathbf{A}(\\hat\\mathbf{x}))+m\\beta + H_f$ where $q\\in\\mathbb{R}$ is a coupling constant, $\\mathbf{A}(\\hat\\mathbf{x})$ denotes the quantized vector potential and $H_f$ denotes the free photon Hamiltonian. Since the total momentum is conserved, $H$ is decomposed with respect to the total momentum with fiber Hamiltonian $H(\\mathbf{p}), (\\mathbf{p}\\in\\mathbb{R}^3)$. Since the self-adjoint operator $H(\\mathbf{p})$ is bounded from below, one ca","authors_text":"Itaru Sasaki","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-06-09T08:17:52Z","title":"Spectral Analysis of the Dirac Polaron"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0606029","kind":"arxiv","version":6},"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":"sha256:2b18bc8ce618ac73669aec05039c677f83ba83cf0be63bdda9773c5d9178ef08","target":"record","created_at":"2026-05-18T03:09:23Z","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":"51ed03fd60373ac9a742bdb450d285732b7a063c18fdf73e1ac61fdfabd492e0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2006-06-09T08:17:52Z","title_canon_sha256":"6436b99e76319550b02a844a75d53f61aaa6449e0dbc12dae380889e0bedbeb5"},"schema_version":"1.0","source":{"id":"math-ph/0606029","kind":"arxiv","version":6}},"canonical_sha256":"689f576cf4d9b7c5224d2737efa45b2fa6ab864d4a44362735864f326fe6e9f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"689f576cf4d9b7c5224d2737efa45b2fa6ab864d4a44362735864f326fe6e9f6","first_computed_at":"2026-05-18T03:09:23.409775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:23.409775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JkKSW3gzF1bZRp4l6ff9oKX55h6Xh7jpFCT7+Gy6U46mSHSoJFRt9tS4jnbtpo4TSPd3OKyQj91rVhDiF80zBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:23.410634Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0606029","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b18bc8ce618ac73669aec05039c677f83ba83cf0be63bdda9773c5d9178ef08","sha256:d33622c4c779090c40a2e68eab4afbf6f8f8da7d83ab7df22bce4706996569ab"],"state_sha256":"7b058bbfe9ac11612df1e7673382bb8437959a73507a73481bafb04530b81cc0"}