{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:EREMMNUUIXCPEJWXWF5AP2QUHQ","short_pith_number":"pith:EREMMNUU","canonical_record":{"source":{"id":"math/0605584","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-05-22T12:02:21Z","cross_cats_sorted":["math.FA","math.SP"],"title_canon_sha256":"9e3c8c671267c90f91732ced1e845f8f32faf34f3c1d3c2a1aed69a043b9b8db","abstract_canon_sha256":"22731e6c705760083f370792b486b57872b289f583d14dc869d298fd306634ef"},"schema_version":"1.0"},"canonical_sha256":"2448c6369445c4f226d7b17a07ea143c27802391637e17e5f7b3d8368be9422f","source":{"kind":"arxiv","id":"math/0605584","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605584","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605584v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605584","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"EREMMNUUIXCP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EREMMNUUIXCPEJWX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EREMMNUU","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:EREMMNUUIXCPEJWXWF5AP2QUHQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0605584","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-05-22T12:02:21Z","cross_cats_sorted":["math.FA","math.SP"],"title_canon_sha256":"9e3c8c671267c90f91732ced1e845f8f32faf34f3c1d3c2a1aed69a043b9b8db","abstract_canon_sha256":"22731e6c705760083f370792b486b57872b289f583d14dc869d298fd306634ef"},"schema_version":"1.0"},"canonical_sha256":"2448c6369445c4f226d7b17a07ea143c27802391637e17e5f7b3d8368be9422f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:45.587848Z","signature_b64":"6nz7rgVxcNcuWE/GhDZCAce0BB1Jzp5g3W8mCqLm0bxPaSb81WCi1iMrr7g6bSN3WxQ8kfzUViHeY4suDLZ6CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2448c6369445c4f226d7b17a07ea143c27802391637e17e5f7b3d8368be9422f","last_reissued_at":"2026-05-18T02:57:45.587427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:45.587427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0605584","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIhr9WWzF1vZCYsj9zKOSbBlqoEozcVLRB7eGQ+ouX9j5W9t0FqmaxkMT0mIBoshymfx2Ilrbp65Kk71d+MtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:39:39.852850Z"},"content_sha256":"0cdbd03af180f41e704c4ea150b49b15025a1a9fd83af102a04f24e88bb53c27","schema_version":"1.0","event_id":"sha256:0cdbd03af180f41e704c4ea150b49b15025a1a9fd83af102a04f24e88bb53c27"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:EREMMNUUIXCPEJWXWF5AP2QUHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analogue of the operator curl for nonabelian gauge groups and scattering theory","license":"","headline":"","cross_cats":["math.FA","math.SP"],"primary_cat":"math.AP","authors_text":"A. Sevostyanov","submitted_at":"2006-05-22T12:02:21Z","abstract_excerpt":"We introduce a new perturbation for the operator curl related to connections with nonabelian gauge groups. We also prove that the perturbed operator is unitary equivalent to the operator curl if the corresponding connection is close enough to the trivial one with respect to a certain topology on the space of connections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605584","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":"2026-05-18T02:57:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8pVyBnVCKlDZ1/Ty2/U26cysfQZlsMgjTYM5ROX1U3aB7vP3TsR4PVz0e0GcAdsfGOqALWbbiVAFOf6A1x/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:39:39.853190Z"},"content_sha256":"306e2398b7cd72392327b8e8c7e65c0fe99eabc39c6b37ffdfbcdfec0d6e93d9","schema_version":"1.0","event_id":"sha256:306e2398b7cd72392327b8e8c7e65c0fe99eabc39c6b37ffdfbcdfec0d6e93d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/bundle.json","state_url":"https://pith.science/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/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":"2026-07-04T14:39:39Z","links":{"resolver":"https://pith.science/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ","bundle":"https://pith.science/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/bundle.json","state":"https://pith.science/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EREMMNUUIXCPEJWXWF5AP2QUHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:EREMMNUUIXCPEJWXWF5AP2QUHQ","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":"22731e6c705760083f370792b486b57872b289f583d14dc869d298fd306634ef","cross_cats_sorted":["math.FA","math.SP"],"license":"","primary_cat":"math.AP","submitted_at":"2006-05-22T12:02:21Z","title_canon_sha256":"9e3c8c671267c90f91732ced1e845f8f32faf34f3c1d3c2a1aed69a043b9b8db"},"schema_version":"1.0","source":{"id":"math/0605584","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0605584","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"arxiv_version","alias_value":"math/0605584v1","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0605584","created_at":"2026-05-18T02:57:45Z"},{"alias_kind":"pith_short_12","alias_value":"EREMMNUUIXCP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"EREMMNUUIXCPEJWX","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"EREMMNUU","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:306e2398b7cd72392327b8e8c7e65c0fe99eabc39c6b37ffdfbcdfec0d6e93d9","target":"graph","created_at":"2026-05-18T02:57:45Z","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 introduce a new perturbation for the operator curl related to connections with nonabelian gauge groups. We also prove that the perturbed operator is unitary equivalent to the operator curl if the corresponding connection is close enough to the trivial one with respect to a certain topology on the space of connections.","authors_text":"A. Sevostyanov","cross_cats":["math.FA","math.SP"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-05-22T12:02:21Z","title":"An analogue of the operator curl for nonabelian gauge groups and scattering theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0605584","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":"sha256:0cdbd03af180f41e704c4ea150b49b15025a1a9fd83af102a04f24e88bb53c27","target":"record","created_at":"2026-05-18T02:57:45Z","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":"22731e6c705760083f370792b486b57872b289f583d14dc869d298fd306634ef","cross_cats_sorted":["math.FA","math.SP"],"license":"","primary_cat":"math.AP","submitted_at":"2006-05-22T12:02:21Z","title_canon_sha256":"9e3c8c671267c90f91732ced1e845f8f32faf34f3c1d3c2a1aed69a043b9b8db"},"schema_version":"1.0","source":{"id":"math/0605584","kind":"arxiv","version":1}},"canonical_sha256":"2448c6369445c4f226d7b17a07ea143c27802391637e17e5f7b3d8368be9422f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2448c6369445c4f226d7b17a07ea143c27802391637e17e5f7b3d8368be9422f","first_computed_at":"2026-05-18T02:57:45.587427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:45.587427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6nz7rgVxcNcuWE/GhDZCAce0BB1Jzp5g3W8mCqLm0bxPaSb81WCi1iMrr7g6bSN3WxQ8kfzUViHeY4suDLZ6CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:45.587848Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0605584","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cdbd03af180f41e704c4ea150b49b15025a1a9fd83af102a04f24e88bb53c27","sha256:306e2398b7cd72392327b8e8c7e65c0fe99eabc39c6b37ffdfbcdfec0d6e93d9"],"state_sha256":"2e42c9d457121f522777384e203c351b3180dfae966c4c3765dc612af16db6f5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vIa3o075rVIFxwHiatvoc1f7dNX31J9bx2nOUbvFK7/tX1VL2Y1iKk94vo4Q7pMv1m7F52uo5MpIdgnp9iKMDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T14:39:39.855093Z","bundle_sha256":"49f184946fda94249405ae2f7832880bd36241cac8d7d2131d66de78242b919b"}}