{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UDJQSHIRAYTDMNMJZITJABR43Z","short_pith_number":"pith:UDJQSHIR","canonical_record":{"source":{"id":"1011.1751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-08T10:10:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bcf92c15f8b0b4bc3f991d5a9b3c4cbe9e288069458fdfa6513d0c4ec7f7ebde","abstract_canon_sha256":"38b6ce075c423e681f852c61c3529160c6b8a93b1d54a9ce0ca042704b84c933"},"schema_version":"1.0"},"canonical_sha256":"a0d3091d110626363589ca2690063cde6251e2abea074a8bf2bba9d43e167ab6","source":{"kind":"arxiv","id":"1011.1751","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1751","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1751v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1751","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"UDJQSHIRAYTD","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UDJQSHIRAYTDMNMJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UDJQSHIR","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UDJQSHIRAYTDMNMJZITJABR43Z","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1751","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-08T10:10:01Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"bcf92c15f8b0b4bc3f991d5a9b3c4cbe9e288069458fdfa6513d0c4ec7f7ebde","abstract_canon_sha256":"38b6ce075c423e681f852c61c3529160c6b8a93b1d54a9ce0ca042704b84c933"},"schema_version":"1.0"},"canonical_sha256":"a0d3091d110626363589ca2690063cde6251e2abea074a8bf2bba9d43e167ab6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:56.270222Z","signature_b64":"m7+iJ+aN3kN+IuiWC3uQLgJf9ER1Z9i5WBde+w2N4wZGvOB8zCLLCnh8kMXH3MSMwUTFvuysCWl7ipdKtiW+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0d3091d110626363589ca2690063cde6251e2abea074a8bf2bba9d43e167ab6","last_reissued_at":"2026-05-18T03:55:56.269547Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:56.269547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1751","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":"2026-05-18T03:55:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DLgsfjOVXlLYFSzzwtjMZLvhpnb4qyxCc3xNzIrUgKcWUmjKr4xsFk6eDamJ6wO21MYsQG2gQrWQbNqxqV/gCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:20.945500Z"},"content_sha256":"3c6e94836f079ac5a3154ae4b891e6641dc4602505c6d27cdc0a9cf70d8cbf7f","schema_version":"1.0","event_id":"sha256:3c6e94836f079ac5a3154ae4b891e6641dc4602505c6d27cdc0a9cf70d8cbf7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UDJQSHIRAYTDMNMJZITJABR43Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Rayleigh-Schr\\\"odinger perturbation series of quasi-degenerate systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Christian Brouder (IMPMC), Fr\\'ed\\'eric Patras (JAD), Gabor Zsolt Toth, G\\'erard H. E. Duchamp (LIPN)","submitted_at":"2010-11-08T10:10:01Z","abstract_excerpt":"We present the first representation of the general term of the Rayleigh-Schr\\\"odinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. The relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1751","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":"2026-05-18T03:55:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hecQrd/BXKZStYmlknM7Cwsy9CCJ9Gt6kLlaoqfuVKt5wx0gqBK77pHf2S2O+lq1ADM8nB32Tdd1MX/rFRfBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T05:22:20.946104Z"},"content_sha256":"1617d1d778efdd51bc17b3d05d13a548bac13b3fa253fee03043fc75814ff7df","schema_version":"1.0","event_id":"sha256:1617d1d778efdd51bc17b3d05d13a548bac13b3fa253fee03043fc75814ff7df"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UDJQSHIRAYTDMNMJZITJABR43Z/bundle.json","state_url":"https://pith.science/pith/UDJQSHIRAYTDMNMJZITJABR43Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UDJQSHIRAYTDMNMJZITJABR43Z/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":"2026-06-01T05:22:20Z","links":{"resolver":"https://pith.science/pith/UDJQSHIRAYTDMNMJZITJABR43Z","bundle":"https://pith.science/pith/UDJQSHIRAYTDMNMJZITJABR43Z/bundle.json","state":"https://pith.science/pith/UDJQSHIRAYTDMNMJZITJABR43Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UDJQSHIRAYTDMNMJZITJABR43Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UDJQSHIRAYTDMNMJZITJABR43Z","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":"38b6ce075c423e681f852c61c3529160c6b8a93b1d54a9ce0ca042704b84c933","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-08T10:10:01Z","title_canon_sha256":"bcf92c15f8b0b4bc3f991d5a9b3c4cbe9e288069458fdfa6513d0c4ec7f7ebde"},"schema_version":"1.0","source":{"id":"1011.1751","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1751","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1751v1","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1751","created_at":"2026-05-18T03:55:56Z"},{"alias_kind":"pith_short_12","alias_value":"UDJQSHIRAYTD","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UDJQSHIRAYTDMNMJ","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UDJQSHIR","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:1617d1d778efdd51bc17b3d05d13a548bac13b3fa253fee03043fc75814ff7df","target":"graph","created_at":"2026-05-18T03:55:56Z","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 present the first representation of the general term of the Rayleigh-Schr\\\"odinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the analytical expression of the corresponding term. The combinatorial and graphical techniques used in the proof of the series expansion allow us to derive various resummation formulas of the series. The relation with several combinatorial objects used for special cases (degenerate or non-degenerate systems) is established.","authors_text":"Christian Brouder (IMPMC), Fr\\'ed\\'eric Patras (JAD), Gabor Zsolt Toth, G\\'erard H. E. Duchamp (LIPN)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-08T10:10:01Z","title":"The Rayleigh-Schr\\\"odinger perturbation series of quasi-degenerate systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1751","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":"sha256:3c6e94836f079ac5a3154ae4b891e6641dc4602505c6d27cdc0a9cf70d8cbf7f","target":"record","created_at":"2026-05-18T03:55:56Z","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":"38b6ce075c423e681f852c61c3529160c6b8a93b1d54a9ce0ca042704b84c933","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-08T10:10:01Z","title_canon_sha256":"bcf92c15f8b0b4bc3f991d5a9b3c4cbe9e288069458fdfa6513d0c4ec7f7ebde"},"schema_version":"1.0","source":{"id":"1011.1751","kind":"arxiv","version":1}},"canonical_sha256":"a0d3091d110626363589ca2690063cde6251e2abea074a8bf2bba9d43e167ab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0d3091d110626363589ca2690063cde6251e2abea074a8bf2bba9d43e167ab6","first_computed_at":"2026-05-18T03:55:56.269547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:56.269547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m7+iJ+aN3kN+IuiWC3uQLgJf9ER1Z9i5WBde+w2N4wZGvOB8zCLLCnh8kMXH3MSMwUTFvuysCWl7ipdKtiW+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:56.270222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1751","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c6e94836f079ac5a3154ae4b891e6641dc4602505c6d27cdc0a9cf70d8cbf7f","sha256:1617d1d778efdd51bc17b3d05d13a548bac13b3fa253fee03043fc75814ff7df"],"state_sha256":"a49bd4443887ee80f1acda938ef1823971358c667e747bffb33337140e41246b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PwFHT8u1VkwErozvhjXOLuyt0BNtyaxQ5tJadSWzMc67cKbr4PSVgHBZ222ZWCNBHK04uMoo5UKLTasxUCupCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T05:22:20.948892Z","bundle_sha256":"b70fe28163d9ab51211d3da8c8eb8dfa9ada52de4bf38d7f0c4d69a824463a27"}}