{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4AGT6G3QSWNFMZ5K6XLDJ3CY2C","short_pith_number":"pith:4AGT6G3Q","canonical_record":{"source":{"id":"1605.01532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-05T09:01:19Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"dbc0f22ff78d82d669e41fae816de9f88ec5df5b5642b88781a6fe7e010747d2","abstract_canon_sha256":"01b230eda409acbe3b6040f5a2f52d29fbf09ce6e48e4dd99f71ffc8f6c6108c"},"schema_version":"1.0"},"canonical_sha256":"e00d3f1b70959a5667aaf5d634ec58d0aec00100c5cc46d3a9636daf9be7a1b0","source":{"kind":"arxiv","id":"1605.01532","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01532","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01532v1","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01532","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"4AGT6G3QSWNF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4AGT6G3QSWNFMZ5K","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4AGT6G3Q","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4AGT6G3QSWNFMZ5K6XLDJ3CY2C","target":"record","payload":{"canonical_record":{"source":{"id":"1605.01532","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-05T09:01:19Z","cross_cats_sorted":["nucl-th"],"title_canon_sha256":"dbc0f22ff78d82d669e41fae816de9f88ec5df5b5642b88781a6fe7e010747d2","abstract_canon_sha256":"01b230eda409acbe3b6040f5a2f52d29fbf09ce6e48e4dd99f71ffc8f6c6108c"},"schema_version":"1.0"},"canonical_sha256":"e00d3f1b70959a5667aaf5d634ec58d0aec00100c5cc46d3a9636daf9be7a1b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:16.550015Z","signature_b64":"/8DW2sV4HcSuZtXmvmB+wHIDZZRks6Z5hsP9uO2ESVxA3SXVqvrMCI1c46tSgLpCwyHoHf9iIu6zgtpnk9iACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e00d3f1b70959a5667aaf5d634ec58d0aec00100c5cc46d3a9636daf9be7a1b0","last_reissued_at":"2026-05-18T01:12:16.549686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:16.549686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.01532","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6xduHGnpHQdf/V8hz7vI16FUEmYKnsdd8q5Kk6tMPeMkogEMho/mIj9DViN6Iu55z6uHqtX1Q5RFEhEZyCcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:03:54.279966Z"},"content_sha256":"8da3e0e53744521d165fa6af10d5bad9ccfc0b0990117a72edae131658e33f72","schema_version":"1.0","event_id":"sha256:8da3e0e53744521d165fa6af10d5bad9ccfc0b0990117a72edae131658e33f72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4AGT6G3QSWNFMZ5K6XLDJ3CY2C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lectures on Bound states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th"],"primary_cat":"hep-ph","authors_text":"Paul Hoyer","submitted_at":"2016-05-05T09:01:19Z","abstract_excerpt":"Even a first approximation of bound states requires contributions of all powers in the coupling. This means that the concept of \"lowest order bound state\" needs to be defined. In these lectures I discuss the \"Born\" (no loop, lowest order in $\\hbar$) approximation. Born level states are bound by gauge fields which satisfy the classical field equations.\n  As a check of the method, Positronium states of any momentum are determined as eigenstates of the QED Hamiltonian, quantized at equal time. Analogously, states bound by a strong external field $A^\\mu(\\boldsymbol{x})$ are found as eigenstates of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01532","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eECxg4sQ0ax51OaG8hmf6Ivgw6Q1OtAYka7oDIeUOzhg5GoVAPbze4E/nzli2q7hp1svxZAJida9pPA0Vd6IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:03:54.280365Z"},"content_sha256":"3276b69c4b16c9f92fb336140b89f7cbe053d7edeb31f9269935097296c35c0e","schema_version":"1.0","event_id":"sha256:3276b69c4b16c9f92fb336140b89f7cbe053d7edeb31f9269935097296c35c0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/bundle.json","state_url":"https://pith.science/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T15:03:54Z","links":{"resolver":"https://pith.science/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C","bundle":"https://pith.science/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/bundle.json","state":"https://pith.science/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4AGT6G3QSWNFMZ5K6XLDJ3CY2C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4AGT6G3QSWNFMZ5K6XLDJ3CY2C","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":"01b230eda409acbe3b6040f5a2f52d29fbf09ce6e48e4dd99f71ffc8f6c6108c","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-05T09:01:19Z","title_canon_sha256":"dbc0f22ff78d82d669e41fae816de9f88ec5df5b5642b88781a6fe7e010747d2"},"schema_version":"1.0","source":{"id":"1605.01532","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01532","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01532v1","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01532","created_at":"2026-05-18T01:12:16Z"},{"alias_kind":"pith_short_12","alias_value":"4AGT6G3QSWNF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4AGT6G3QSWNFMZ5K","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4AGT6G3Q","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:3276b69c4b16c9f92fb336140b89f7cbe053d7edeb31f9269935097296c35c0e","target":"graph","created_at":"2026-05-18T01:12:16Z","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":"Even a first approximation of bound states requires contributions of all powers in the coupling. This means that the concept of \"lowest order bound state\" needs to be defined. In these lectures I discuss the \"Born\" (no loop, lowest order in $\\hbar$) approximation. Born level states are bound by gauge fields which satisfy the classical field equations.\n  As a check of the method, Positronium states of any momentum are determined as eigenstates of the QED Hamiltonian, quantized at equal time. Analogously, states bound by a strong external field $A^\\mu(\\boldsymbol{x})$ are found as eigenstates of","authors_text":"Paul Hoyer","cross_cats":["nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-05T09:01:19Z","title":"Lectures on Bound states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01532","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":"sha256:8da3e0e53744521d165fa6af10d5bad9ccfc0b0990117a72edae131658e33f72","target":"record","created_at":"2026-05-18T01:12:16Z","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":"01b230eda409acbe3b6040f5a2f52d29fbf09ce6e48e4dd99f71ffc8f6c6108c","cross_cats_sorted":["nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2016-05-05T09:01:19Z","title_canon_sha256":"dbc0f22ff78d82d669e41fae816de9f88ec5df5b5642b88781a6fe7e010747d2"},"schema_version":"1.0","source":{"id":"1605.01532","kind":"arxiv","version":1}},"canonical_sha256":"e00d3f1b70959a5667aaf5d634ec58d0aec00100c5cc46d3a9636daf9be7a1b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e00d3f1b70959a5667aaf5d634ec58d0aec00100c5cc46d3a9636daf9be7a1b0","first_computed_at":"2026-05-18T01:12:16.549686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:16.549686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/8DW2sV4HcSuZtXmvmB+wHIDZZRks6Z5hsP9uO2ESVxA3SXVqvrMCI1c46tSgLpCwyHoHf9iIu6zgtpnk9iACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:16.550015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01532","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8da3e0e53744521d165fa6af10d5bad9ccfc0b0990117a72edae131658e33f72","sha256:3276b69c4b16c9f92fb336140b89f7cbe053d7edeb31f9269935097296c35c0e"],"state_sha256":"95b6dfb3a87775c08be83b3979beda1b46fc3b75d845569fed5b8b01bb049aef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLJ07Mun8NjKob+JHzmlLmMqtkuQBdUfCviVeohgfl1/LempxfLtk47dIZf0ASCAO5WuIPVVxxfDN0T6ZaNaAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:03:54.282763Z","bundle_sha256":"70b46b35e6684d48764f661b4c52bff0a7c5036ec791343d59c55d287fb2c918"}}