{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GKMTPIJAQOX35RSLLDISYREMBL","short_pith_number":"pith:GKMTPIJA","canonical_record":{"source":{"id":"1309.0628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-03T09:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"554f2c251136b8e410b45ac360b45e4300145a4ba0f2c823a6187f3a86724001","abstract_canon_sha256":"05a42e9d5ea7ff1411c35716f7fd63e613138fba6a908bbcccc8216887525f95"},"schema_version":"1.0"},"canonical_sha256":"329937a12083afbec64b58d12c448c0aea8e2fe6aa551c9d93ab348847f07c7b","source":{"kind":"arxiv","id":"1309.0628","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0628","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0628v1","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0628","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"GKMTPIJAQOX3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GKMTPIJAQOX35RSL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GKMTPIJA","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GKMTPIJAQOX35RSLLDISYREMBL","target":"record","payload":{"canonical_record":{"source":{"id":"1309.0628","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-03T09:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"554f2c251136b8e410b45ac360b45e4300145a4ba0f2c823a6187f3a86724001","abstract_canon_sha256":"05a42e9d5ea7ff1411c35716f7fd63e613138fba6a908bbcccc8216887525f95"},"schema_version":"1.0"},"canonical_sha256":"329937a12083afbec64b58d12c448c0aea8e2fe6aa551c9d93ab348847f07c7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:18.532843Z","signature_b64":"gG1MCGxRggIBa/btSYH3IJc3cinoBCtH5XVMyeyZC/gnCbPRHgCHyo7QRN+bwZnLL1VDlrYyIxX36hEzzk1ZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"329937a12083afbec64b58d12c448c0aea8e2fe6aa551c9d93ab348847f07c7b","last_reissued_at":"2026-05-18T03:14:18.532222Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:18.532222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.0628","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":"2026-05-18T03:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c380ackjkmYG8tImNz4K19vCQINHkhXoy/XVFkFApAljPUOxpRSj5U+jqgUerUUAVbR3vkLV4NyahI/LKUeYBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:18:30.030943Z"},"content_sha256":"f3251dd2f1f154e9aa762b54cbaf3bbbc60bf6f8d6958171843d1e9e6ad5e6ea","schema_version":"1.0","event_id":"sha256:f3251dd2f1f154e9aa762b54cbaf3bbbc60bf6f8d6958171843d1e9e6ad5e6ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GKMTPIJAQOX35RSLLDISYREMBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Adiabatic Elimination: Systematic Expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"I. L. Egusquiza","submitted_at":"2013-09-03T09:57:29Z","abstract_excerpt":"We restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on adiabatic elimination, connecting with well established quantum mechanical perturbation methods. We prove convergence of the expansions when energy scales are well separated. We state and solve the problem of hermiticity of improved effective hamiltonians."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0628","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":"2026-05-18T03:14:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g3owlAZWMdH0QpIcI6ADbW2IKjpohQ6thmNane3Wc4/aEtqoJgnYrnnzXa/yxd90pqH2I6SDOt2twd4ULGcADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:18:30.031282Z"},"content_sha256":"73a9cd80e1388417545843750bab1805d728352ecf33634aa6996e347cc24e19","schema_version":"1.0","event_id":"sha256:73a9cd80e1388417545843750bab1805d728352ecf33634aa6996e347cc24e19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GKMTPIJAQOX35RSLLDISYREMBL/bundle.json","state_url":"https://pith.science/pith/GKMTPIJAQOX35RSLLDISYREMBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GKMTPIJAQOX35RSLLDISYREMBL/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":"2026-06-12T05:18:30Z","links":{"resolver":"https://pith.science/pith/GKMTPIJAQOX35RSLLDISYREMBL","bundle":"https://pith.science/pith/GKMTPIJAQOX35RSLLDISYREMBL/bundle.json","state":"https://pith.science/pith/GKMTPIJAQOX35RSLLDISYREMBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GKMTPIJAQOX35RSLLDISYREMBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GKMTPIJAQOX35RSLLDISYREMBL","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":"05a42e9d5ea7ff1411c35716f7fd63e613138fba6a908bbcccc8216887525f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-03T09:57:29Z","title_canon_sha256":"554f2c251136b8e410b45ac360b45e4300145a4ba0f2c823a6187f3a86724001"},"schema_version":"1.0","source":{"id":"1309.0628","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.0628","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"arxiv_version","alias_value":"1309.0628v1","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.0628","created_at":"2026-05-18T03:14:18Z"},{"alias_kind":"pith_short_12","alias_value":"GKMTPIJAQOX3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GKMTPIJAQOX35RSL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GKMTPIJA","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:73a9cd80e1388417545843750bab1805d728352ecf33634aa6996e347cc24e19","target":"graph","created_at":"2026-05-18T03:14:18Z","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 restate the adiabatic elimination approximation as the first term in a singular perturbation expansion. We use the invariant manifold formalism for singular perturbations in dynamical systems to identify systematic improvements on adiabatic elimination, connecting with well established quantum mechanical perturbation methods. We prove convergence of the expansions when energy scales are well separated. We state and solve the problem of hermiticity of improved effective hamiltonians.","authors_text":"I. L. Egusquiza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-03T09:57:29Z","title":"Beyond Adiabatic Elimination: Systematic Expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0628","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:f3251dd2f1f154e9aa762b54cbaf3bbbc60bf6f8d6958171843d1e9e6ad5e6ea","target":"record","created_at":"2026-05-18T03:14:18Z","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":"05a42e9d5ea7ff1411c35716f7fd63e613138fba6a908bbcccc8216887525f95","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-09-03T09:57:29Z","title_canon_sha256":"554f2c251136b8e410b45ac360b45e4300145a4ba0f2c823a6187f3a86724001"},"schema_version":"1.0","source":{"id":"1309.0628","kind":"arxiv","version":1}},"canonical_sha256":"329937a12083afbec64b58d12c448c0aea8e2fe6aa551c9d93ab348847f07c7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"329937a12083afbec64b58d12c448c0aea8e2fe6aa551c9d93ab348847f07c7b","first_computed_at":"2026-05-18T03:14:18.532222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:18.532222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gG1MCGxRggIBa/btSYH3IJc3cinoBCtH5XVMyeyZC/gnCbPRHgCHyo7QRN+bwZnLL1VDlrYyIxX36hEzzk1ZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:18.532843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.0628","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3251dd2f1f154e9aa762b54cbaf3bbbc60bf6f8d6958171843d1e9e6ad5e6ea","sha256:73a9cd80e1388417545843750bab1805d728352ecf33634aa6996e347cc24e19"],"state_sha256":"1077e48ba3ff1613c8f9b94d24e7c5880a3e41e80744f9262ec93fb8950b7fbf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HbjXloT3cKCFCRDiZbM5lCrJ5YO6HstrD58DKXhWd9mruU0+w0qNsmqTznwzmoov2Fj8IxkRZEKlHMQQnUA0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:18:30.033567Z","bundle_sha256":"e3cde5545c7b92c57cc693718f87d891a6568e31949112e432ddd0a83da7585b"}}