{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VSTZNCSYZVJ2LOGXML4J4LB6MU","short_pith_number":"pith:VSTZNCSY","canonical_record":{"source":{"id":"1110.4991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-10-22T19:24:01Z","cross_cats_sorted":["nucl-th","physics.atom-ph"],"title_canon_sha256":"27629a6a718dd4eb20eeed99a3c805b997dc3d5eeb448c4e875adbaf6e384dc4","abstract_canon_sha256":"8f8e039ff11846995c3cd0cfda68eaa1e284940c9ae7df69b93be3661c528463"},"schema_version":"1.0"},"canonical_sha256":"aca7968a58cd53a5b8d762f89e2c3e6523c1f3e1e0216ead6b04e1ca1be4344e","source":{"kind":"arxiv","id":"1110.4991","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4991","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4991v1","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4991","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"pith_short_12","alias_value":"VSTZNCSYZVJ2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VSTZNCSYZVJ2LOGX","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VSTZNCSY","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VSTZNCSYZVJ2LOGXML4J4LB6MU","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-10-22T19:24:01Z","cross_cats_sorted":["nucl-th","physics.atom-ph"],"title_canon_sha256":"27629a6a718dd4eb20eeed99a3c805b997dc3d5eeb448c4e875adbaf6e384dc4","abstract_canon_sha256":"8f8e039ff11846995c3cd0cfda68eaa1e284940c9ae7df69b93be3661c528463"},"schema_version":"1.0"},"canonical_sha256":"aca7968a58cd53a5b8d762f89e2c3e6523c1f3e1e0216ead6b04e1ca1be4344e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:06.791253Z","signature_b64":"UJOhzrv3szeR/a24mdJlkk3h05O5jdZyk3vxePIpsCqzM60dP1cPqxPdAUmm91Loiv/IfBqZ3bqEY29xO+j2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aca7968a58cd53a5b8d762f89e2c3e6523c1f3e1e0216ead6b04e1ca1be4344e","last_reissued_at":"2026-05-18T02:00:06.790593Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:06.790593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4991","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":"2026-05-18T02:00:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m68fV08Xoq6igTnLyNSt/UQtq1GRFyq2UWC0RHtTkpdjbd4UndeJ+Bs22fkfK3PXYhwfROe4g/EUuAuZfLlmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:19:30.831179Z"},"content_sha256":"0d86defbfcc54593147e64b8f133e17fb35b93ac82a821b615fea52eac041640","schema_version":"1.0","event_id":"sha256:0d86defbfcc54593147e64b8f133e17fb35b93ac82a821b615fea52eac041640"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VSTZNCSYZVJ2LOGXML4J4LB6MU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-channel analog of the effective-range expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nucl-th","physics.atom-ph"],"primary_cat":"quant-ph","authors_text":"N. Elander, S. A. Rakityansky","submitted_at":"2011-10-22T19:24:01Z","abstract_excerpt":"Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4991","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":"2026-05-18T02:00:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nW31MH4+i22oJq5ncFsYmsj2r29kGfmLpXdY1eRaFzqpQ2jFnwVuwZhGMgFpSD6f4383vppaD3AWJuKyM6kWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T17:19:30.831543Z"},"content_sha256":"e7e1c810e47bff86a8d0047df5500688efd49c6e55d93e04276d0c9d14a7d993","schema_version":"1.0","event_id":"sha256:e7e1c810e47bff86a8d0047df5500688efd49c6e55d93e04276d0c9d14a7d993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/bundle.json","state_url":"https://pith.science/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/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":"2026-07-01T17:19:30Z","links":{"resolver":"https://pith.science/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU","bundle":"https://pith.science/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/bundle.json","state":"https://pith.science/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSTZNCSYZVJ2LOGXML4J4LB6MU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VSTZNCSYZVJ2LOGXML4J4LB6MU","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":"8f8e039ff11846995c3cd0cfda68eaa1e284940c9ae7df69b93be3661c528463","cross_cats_sorted":["nucl-th","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-10-22T19:24:01Z","title_canon_sha256":"27629a6a718dd4eb20eeed99a3c805b997dc3d5eeb448c4e875adbaf6e384dc4"},"schema_version":"1.0","source":{"id":"1110.4991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4991","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4991v1","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4991","created_at":"2026-05-18T02:00:06Z"},{"alias_kind":"pith_short_12","alias_value":"VSTZNCSYZVJ2","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VSTZNCSYZVJ2LOGX","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VSTZNCSY","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e7e1c810e47bff86a8d0047df5500688efd49c6e55d93e04276d0c9d14a7d993","target":"graph","created_at":"2026-05-18T02:00:06Z","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":"Similarly to the standard effective range expansion that is done near the threshold energy, we obtain a generalized power-series expansion of the multi-channel Jost-matrix that can be done near an arbitrary point on the Riemann surface of the energy within the domain of its analyticity. In order to do this, we analytically factorize its momentum dependencies at all the branching points on the Riemann surface. The remaining single-valued matrix functions of the energy are then expanded in the power-series near an arbitrary point in the domain of the complex energy plane where it is analytic. A ","authors_text":"N. Elander, S. A. Rakityansky","cross_cats":["nucl-th","physics.atom-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-10-22T19:24:01Z","title":"Multi-channel analog of the effective-range expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4991","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":"sha256:0d86defbfcc54593147e64b8f133e17fb35b93ac82a821b615fea52eac041640","target":"record","created_at":"2026-05-18T02:00:06Z","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":"8f8e039ff11846995c3cd0cfda68eaa1e284940c9ae7df69b93be3661c528463","cross_cats_sorted":["nucl-th","physics.atom-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-10-22T19:24:01Z","title_canon_sha256":"27629a6a718dd4eb20eeed99a3c805b997dc3d5eeb448c4e875adbaf6e384dc4"},"schema_version":"1.0","source":{"id":"1110.4991","kind":"arxiv","version":1}},"canonical_sha256":"aca7968a58cd53a5b8d762f89e2c3e6523c1f3e1e0216ead6b04e1ca1be4344e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aca7968a58cd53a5b8d762f89e2c3e6523c1f3e1e0216ead6b04e1ca1be4344e","first_computed_at":"2026-05-18T02:00:06.790593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:06.790593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UJOhzrv3szeR/a24mdJlkk3h05O5jdZyk3vxePIpsCqzM60dP1cPqxPdAUmm91Loiv/IfBqZ3bqEY29xO+j2Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:06.791253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d86defbfcc54593147e64b8f133e17fb35b93ac82a821b615fea52eac041640","sha256:e7e1c810e47bff86a8d0047df5500688efd49c6e55d93e04276d0c9d14a7d993"],"state_sha256":"21381895cb8212022ae1e6471871daab415daf318c401273a8a8097fe44f3d44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ppdrKv3+zi+oB0wCp04jZXhy1oLnaU/nltxlyJRohg5LLqs10x2P4A4pSRkF0M6Y+UtT2cvKW8LUGEwWG8VpCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T17:19:30.833741Z","bundle_sha256":"64a9204eba225306346a29ffedbb4c4f351e97dc810d6593c3d27076f73334bd"}}