{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3YARAZ7LWGO7VLAZVXLOTDP66K","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":"fa0fd69c80fa25bef494c3f4c97047c6b27770bc71be1bc9ba27864e4c386d7d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-21T02:56:33Z","title_canon_sha256":"5f3383771f5ee14ead79db5afa45b8bee079d16123d3e3f523b9fd10a3126fe3"},"schema_version":"1.0","source":{"id":"1206.4764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4764","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4764v1","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4764","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"3YARAZ7LWGO7","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3YARAZ7LWGO7VLAZ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3YARAZ7L","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:7d4d80b9a0559e5801004686225a1f7be42d07b91a8ce31497c2ffeb75d9111f","target":"graph","created_at":"2026-05-18T03:53:03Z","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 a system of a quantum particle interacting with a quantum field and an external potential $V(\\bx)$. The Hamiltonian is defined by a quadratic form $H^V = H^0 + V(\\bx)$, where $H^0$ is a quadratic form which preserves the total momentum. $H^0$ and $H^V$ are assumed to be bounded from below. We give a criterion for the positivity of the binding energy $E_\\mathrm{bin} = E^0-E^V$, where $E^0$ and $E^V$ are the ground state energies of $H^0$ and $H^V$. As examples of the result, the positivity of the binding energy of the semi-relativistic Pauli-Fierz model and Nelson type Hamiltonian i","authors_text":"Christian G\\'erard, Itaru Sasaki","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-21T02:56:33Z","title":"Binding condition for a general class of quantum field Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4764","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":"sha256:7fe5ac40ae2f6c17dafc8e0c2d065f096bdb1a1d42fd1876ee258c6d72fd7bce","target":"record","created_at":"2026-05-18T03:53:03Z","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":"fa0fd69c80fa25bef494c3f4c97047c6b27770bc71be1bc9ba27864e4c386d7d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-06-21T02:56:33Z","title_canon_sha256":"5f3383771f5ee14ead79db5afa45b8bee079d16123d3e3f523b9fd10a3126fe3"},"schema_version":"1.0","source":{"id":"1206.4764","kind":"arxiv","version":1}},"canonical_sha256":"de011067ebb19dfaac19add6e98dfef28dd6e9764e3882ae1999a808e0402450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de011067ebb19dfaac19add6e98dfef28dd6e9764e3882ae1999a808e0402450","first_computed_at":"2026-05-18T03:53:03.795000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:03.795000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V92cualJGvGj8wYQrCUoY/fXLmYwvZ1tIVkeDSIrWJ7+Ln9kuA2F8rr7gu3UdNn/hMCVCl3Sqy5pcz/GiG/PCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:03.795827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fe5ac40ae2f6c17dafc8e0c2d065f096bdb1a1d42fd1876ee258c6d72fd7bce","sha256:7d4d80b9a0559e5801004686225a1f7be42d07b91a8ce31497c2ffeb75d9111f"],"state_sha256":"7a9a0e4fec16dfe49d4aca3c986a399d3ff36de04048411d00008a2ff8a361b5"}