{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PCWLKJ7XG53IQ44GJ2E24PKQHX","short_pith_number":"pith:PCWLKJ7X","canonical_record":{"source":{"id":"1303.3345","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-14T05:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"d014f7f83c6d7618863618e271915a7d339bbfb69a9b6cd694e85c66219503fc","abstract_canon_sha256":"532f184d71529d1f07f3744b551444dd30d29ec0c6ce142a157b1aa47ab07d81"},"schema_version":"1.0"},"canonical_sha256":"78acb527f737768873864e89ae3d503dde07147bc84ad9776c57f864e1723553","source":{"kind":"arxiv","id":"1303.3345","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3345","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3345v4","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3345","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"PCWLKJ7XG53I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PCWLKJ7XG53IQ44G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PCWLKJ7X","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PCWLKJ7XG53IQ44GJ2E24PKQHX","target":"record","payload":{"canonical_record":{"source":{"id":"1303.3345","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-14T05:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"d014f7f83c6d7618863618e271915a7d339bbfb69a9b6cd694e85c66219503fc","abstract_canon_sha256":"532f184d71529d1f07f3744b551444dd30d29ec0c6ce142a157b1aa47ab07d81"},"schema_version":"1.0"},"canonical_sha256":"78acb527f737768873864e89ae3d503dde07147bc84ad9776c57f864e1723553","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:18.744382Z","signature_b64":"3Dcyl9uJS17B/WRtiAsC7xg6I7ZH5EvnHsKlSFMsJtW2e/aTCFdVAG37l9waiFYhW5OiyPCBehQBYws6KdKSAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78acb527f737768873864e89ae3d503dde07147bc84ad9776c57f864e1723553","last_reissued_at":"2026-05-18T01:11:18.743945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:18.743945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.3345","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ztye/BQVUmwlKaZ8eD6ksSr0qn4j5Q5CkUJaPrt3c3Yst9A5GUkfZs7w+5GnUIYdgCTskLZR/s3H1Ht26HsRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:38:11.331167Z"},"content_sha256":"b5e3c17289250e9dae9faf8ce8687fcd555345b9b1c3402e6848b7f9ff244d1b","schema_version":"1.0","event_id":"sha256:b5e3c17289250e9dae9faf8ce8687fcd555345b9b1c3402e6848b7f9ff244d1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PCWLKJ7XG53IQ44GJ2E24PKQHX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification of convergence rates of solutions of perturbed ordinary differential equations with regularly varying nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Denis D. Patterson, John A. D. Appleby","submitted_at":"2013-03-14T05:30:51Z","abstract_excerpt":"In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear mean reverting force, we demonstrate that the convergence rate is preserved when the perturbation decays more rapidly than a critical rate. At the critical rate, the convergence to equilibrium is slightly slower than the unperturbed equation, and when the perturbation decays more slowly than the critical rate, the convergence to equilibrium is strictly slower t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3345","kind":"arxiv","version":4},"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":"2026-05-18T01:11:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJsGFhV56xfz1Kdia5WY4D2aIaEUVXrCPUDKKiVprMwPThStxNvt6dwM4kPtY6tQZkedqmAATJOPAQviod5bDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:38:11.331530Z"},"content_sha256":"f8e0591d29d4bfcda916b3aaf264048f470be05f14f75554605fe61919e0d789","schema_version":"1.0","event_id":"sha256:f8e0591d29d4bfcda916b3aaf264048f470be05f14f75554605fe61919e0d789"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/bundle.json","state_url":"https://pith.science/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/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":"2026-06-25T08:38:11Z","links":{"resolver":"https://pith.science/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX","bundle":"https://pith.science/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/bundle.json","state":"https://pith.science/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PCWLKJ7XG53IQ44GJ2E24PKQHX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PCWLKJ7XG53IQ44GJ2E24PKQHX","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":"532f184d71529d1f07f3744b551444dd30d29ec0c6ce142a157b1aa47ab07d81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-14T05:30:51Z","title_canon_sha256":"d014f7f83c6d7618863618e271915a7d339bbfb69a9b6cd694e85c66219503fc"},"schema_version":"1.0","source":{"id":"1303.3345","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.3345","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"arxiv_version","alias_value":"1303.3345v4","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.3345","created_at":"2026-05-18T01:11:18Z"},{"alias_kind":"pith_short_12","alias_value":"PCWLKJ7XG53I","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PCWLKJ7XG53IQ44G","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PCWLKJ7X","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:f8e0591d29d4bfcda916b3aaf264048f470be05f14f75554605fe61919e0d789","target":"graph","created_at":"2026-05-18T01:11:18Z","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":"In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear mean reverting force, we demonstrate that the convergence rate is preserved when the perturbation decays more rapidly than a critical rate. At the critical rate, the convergence to equilibrium is slightly slower than the unperturbed equation, and when the perturbation decays more slowly than the critical rate, the convergence to equilibrium is strictly slower t","authors_text":"Denis D. Patterson, John A. D. Appleby","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-14T05:30:51Z","title":"Classification of convergence rates of solutions of perturbed ordinary differential equations with regularly varying nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3345","kind":"arxiv","version":4},"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:b5e3c17289250e9dae9faf8ce8687fcd555345b9b1c3402e6848b7f9ff244d1b","target":"record","created_at":"2026-05-18T01:11:18Z","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":"532f184d71529d1f07f3744b551444dd30d29ec0c6ce142a157b1aa47ab07d81","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-03-14T05:30:51Z","title_canon_sha256":"d014f7f83c6d7618863618e271915a7d339bbfb69a9b6cd694e85c66219503fc"},"schema_version":"1.0","source":{"id":"1303.3345","kind":"arxiv","version":4}},"canonical_sha256":"78acb527f737768873864e89ae3d503dde07147bc84ad9776c57f864e1723553","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78acb527f737768873864e89ae3d503dde07147bc84ad9776c57f864e1723553","first_computed_at":"2026-05-18T01:11:18.743945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:18.743945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3Dcyl9uJS17B/WRtiAsC7xg6I7ZH5EvnHsKlSFMsJtW2e/aTCFdVAG37l9waiFYhW5OiyPCBehQBYws6KdKSAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:18.744382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.3345","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5e3c17289250e9dae9faf8ce8687fcd555345b9b1c3402e6848b7f9ff244d1b","sha256:f8e0591d29d4bfcda916b3aaf264048f470be05f14f75554605fe61919e0d789"],"state_sha256":"1d97f501361d4eb2c22191e23521f65b33889aa33fee1b38f390c4ef1fea1f07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VC+eQEhmzWbCZ313CoZVYaOT3Rw8VM1qoLZqih1pkNaIjylD120NCTJ9QJT6i80CDIssMXHt7vGKEYuqQRa5AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:38:11.333546Z","bundle_sha256":"f29f7ebab6494a30d3e51f6566a3a8e97b5e388a75d4231559d777c55de76cf1"}}