{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:QAMSXPCH2OCHVR3UVGENL6BQRE","short_pith_number":"pith:QAMSXPCH","canonical_record":{"source":{"id":"0807.1009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-07T13:28:36Z","cross_cats_sorted":["math.CA","math.GM"],"title_canon_sha256":"e49765d99ca6205e72b64b821940d2238b190b36e4e92f6e7b3a11cd68105008","abstract_canon_sha256":"c8a71896a7b978f166031bfb5340d1d3c108e57f19ae494f8f93aa62138359cd"},"schema_version":"1.0"},"canonical_sha256":"80192bbc47d3847ac774a988d5f83089324ca8b527ce15fd1aa6a8975f2c21d4","source":{"kind":"arxiv","id":"0807.1009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1009","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1009v1","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1009","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"QAMSXPCH2OCH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QAMSXPCH2OCHVR3U","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QAMSXPCH","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:QAMSXPCH2OCHVR3UVGENL6BQRE","target":"record","payload":{"canonical_record":{"source":{"id":"0807.1009","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-07T13:28:36Z","cross_cats_sorted":["math.CA","math.GM"],"title_canon_sha256":"e49765d99ca6205e72b64b821940d2238b190b36e4e92f6e7b3a11cd68105008","abstract_canon_sha256":"c8a71896a7b978f166031bfb5340d1d3c108e57f19ae494f8f93aa62138359cd"},"schema_version":"1.0"},"canonical_sha256":"80192bbc47d3847ac774a988d5f83089324ca8b527ce15fd1aa6a8975f2c21d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:53.616174Z","signature_b64":"/+BI+3q2OVqnv967khozWpiCsSNS+1wlUBGNUbNKg2+YGV2Z5qzn0HsZAVFuGoMguN6oGvNojaC4vQ5ZRysRBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80192bbc47d3847ac774a988d5f83089324ca8b527ce15fd1aa6a8975f2c21d4","last_reissued_at":"2026-05-18T04:32:53.615775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:53.615775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.1009","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":"2026-05-18T04:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lh6vrTyxS1c/iB6GHml3UuJRBeuBsDkkBfV5HjMz/PR6NCAIbDiGv5DH5M8oXU60Bxb0stJfpdA1UrbqY9ceCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:48:04.924127Z"},"content_sha256":"0a4dcf2c20429b6fbc934607f4408af543ce75a77ba1ae3ee9ae7631acb5043b","schema_version":"1.0","event_id":"sha256:0a4dcf2c20429b6fbc934607f4408af543ce75a77ba1ae3ee9ae7631acb5043b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:QAMSXPCH2OCHVR3UVGENL6BQRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diagonalisation schemes and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.GM"],"primary_cat":"math.AP","authors_text":"Jens Wirth, Kay Jachmann","submitted_at":"2008-07-07T13:28:36Z","abstract_excerpt":"These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and eigenprojections of families of matrices depending upon real/complex parameters.\n  Applications of the schemes in different frameworks --including hyperbolic polynomials, asymptotic integration of ordinary differential equations, diagonalisation within symbolic hierarchies and pseudo-differential decoupling of hyperbolic-parabolic coupled systems-- are also discussed and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1009","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":"2026-05-18T04:32:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JaPYjQscEHpDgWTqJLMXV+mHhvEGgaZdICy5NN//oXpIEaGd39rUZ+bDk2+nMc3EA4gNXnudNCPpiM8L0U78Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:48:04.924516Z"},"content_sha256":"6d309e92d3ad7ffca22d7db3b536617f84523fbb972fd7b5837a976a2fa784d7","schema_version":"1.0","event_id":"sha256:6d309e92d3ad7ffca22d7db3b536617f84523fbb972fd7b5837a976a2fa784d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/bundle.json","state_url":"https://pith.science/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/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":"2026-06-05T12:48:04Z","links":{"resolver":"https://pith.science/pith/QAMSXPCH2OCHVR3UVGENL6BQRE","bundle":"https://pith.science/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/bundle.json","state":"https://pith.science/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QAMSXPCH2OCHVR3UVGENL6BQRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:QAMSXPCH2OCHVR3UVGENL6BQRE","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":"c8a71896a7b978f166031bfb5340d1d3c108e57f19ae494f8f93aa62138359cd","cross_cats_sorted":["math.CA","math.GM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-07T13:28:36Z","title_canon_sha256":"e49765d99ca6205e72b64b821940d2238b190b36e4e92f6e7b3a11cd68105008"},"schema_version":"1.0","source":{"id":"0807.1009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.1009","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"arxiv_version","alias_value":"0807.1009v1","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.1009","created_at":"2026-05-18T04:32:53Z"},{"alias_kind":"pith_short_12","alias_value":"QAMSXPCH2OCH","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"QAMSXPCH2OCHVR3U","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"QAMSXPCH","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:6d309e92d3ad7ffca22d7db3b536617f84523fbb972fd7b5837a976a2fa784d7","target":"graph","created_at":"2026-05-18T04:32:53Z","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":"These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and eigenprojections of families of matrices depending upon real/complex parameters.\n  Applications of the schemes in different frameworks --including hyperbolic polynomials, asymptotic integration of ordinary differential equations, diagonalisation within symbolic hierarchies and pseudo-differential decoupling of hyperbolic-parabolic coupled systems-- are also discussed and ","authors_text":"Jens Wirth, Kay Jachmann","cross_cats":["math.CA","math.GM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-07T13:28:36Z","title":"Diagonalisation schemes and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.1009","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":"sha256:0a4dcf2c20429b6fbc934607f4408af543ce75a77ba1ae3ee9ae7631acb5043b","target":"record","created_at":"2026-05-18T04:32:53Z","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":"c8a71896a7b978f166031bfb5340d1d3c108e57f19ae494f8f93aa62138359cd","cross_cats_sorted":["math.CA","math.GM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2008-07-07T13:28:36Z","title_canon_sha256":"e49765d99ca6205e72b64b821940d2238b190b36e4e92f6e7b3a11cd68105008"},"schema_version":"1.0","source":{"id":"0807.1009","kind":"arxiv","version":1}},"canonical_sha256":"80192bbc47d3847ac774a988d5f83089324ca8b527ce15fd1aa6a8975f2c21d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80192bbc47d3847ac774a988d5f83089324ca8b527ce15fd1aa6a8975f2c21d4","first_computed_at":"2026-05-18T04:32:53.615775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:53.615775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/+BI+3q2OVqnv967khozWpiCsSNS+1wlUBGNUbNKg2+YGV2Z5qzn0HsZAVFuGoMguN6oGvNojaC4vQ5ZRysRBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:53.616174Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.1009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a4dcf2c20429b6fbc934607f4408af543ce75a77ba1ae3ee9ae7631acb5043b","sha256:6d309e92d3ad7ffca22d7db3b536617f84523fbb972fd7b5837a976a2fa784d7"],"state_sha256":"261a8028393ff0d98ec72e17f2701b998b6f46385343c61cdf3d7595904db006"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4zXRgTelz8YYBDTiw9lZZL4lSNoc/bLxST3NfwHtKapW+0JtBPTdlTEMoFd1UfjoEFNxv2n5AndeO4DVhBGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:48:04.926503Z","bundle_sha256":"1b9ca9918b128dc5f23bbd7b3c591d7b23a8bbae3e181daa461feac9747f3747"}}