{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:4W2K26ZKNZWKHM3YULQ7CROCSW","short_pith_number":"pith:4W2K26ZK","canonical_record":{"source":{"id":"1510.08919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-29T21:42:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"7c066d0cb0485058b971646cab1dd14ae474ac8d44e46828fe3501fc27ab7d63","abstract_canon_sha256":"324d45dcacb1633a42dfa5abc013f8b99706f083c82582adfc1a71b1444e60c2"},"schema_version":"1.0"},"canonical_sha256":"e5b4ad7b2a6e6ca3b378a2e1f145c295a3ace6f2bbc26ab8facda0d934d5b7c7","source":{"kind":"arxiv","id":"1510.08919","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08919","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08919v2","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08919","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"4W2K26ZKNZWK","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4W2K26ZKNZWKHM3Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4W2K26ZK","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:4W2K26ZKNZWKHM3YULQ7CROCSW","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08919","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-29T21:42:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"7c066d0cb0485058b971646cab1dd14ae474ac8d44e46828fe3501fc27ab7d63","abstract_canon_sha256":"324d45dcacb1633a42dfa5abc013f8b99706f083c82582adfc1a71b1444e60c2"},"schema_version":"1.0"},"canonical_sha256":"e5b4ad7b2a6e6ca3b378a2e1f145c295a3ace6f2bbc26ab8facda0d934d5b7c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:40.516780Z","signature_b64":"TfJtQMzuIEIKhw+s8XanMW4g81tLDgPPSxyvGFrH9jNaYOoxx4lbGb/IM6p7oQaBq42FMm/HC77q9THcjtEmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5b4ad7b2a6e6ca3b378a2e1f145c295a3ace6f2bbc26ab8facda0d934d5b7c7","last_reissued_at":"2026-05-18T00:50:40.516161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:40.516161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08919","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JbTuytrC6R7hhGoludCVtnXdDaQPK5gjdcMJxp1FNqsERbLx2uAJ9QZMMwM9Ul3rx3rsQoxe/vje9YgrIU9MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:45:10.347701Z"},"content_sha256":"55a68c9d06e741bdb9e317802c328c83294fc4c181a83e29e762aa96b99699a2","schema_version":"1.0","event_id":"sha256:55a68c9d06e741bdb9e317802c328c83294fc4c181a83e29e762aa96b99699a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:4W2K26ZKNZWKHM3YULQ7CROCSW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Ilya Pavlyukevich, Navaratnam Sri Namachchivaya, Nishanth Lingala","submitted_at":"2015-10-29T21:42:32Z","abstract_excerpt":"The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\\varepsilon$. It is well known that, as $\\varepsilon \\to 0$, the measure of the set of initial conditions which lead to 'capture in a resonance zone' goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08919","kind":"arxiv","version":2},"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":"2026-05-18T00:50:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5O8j5OVYlUKptgakMokZB7V2FO5oSu/1IxynVX++svoPQMkTztf8x4GSkIahl0Jm8E25ffwGjCv5ApG0VA9RCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:45:10.348263Z"},"content_sha256":"9a73bbd98ec1bb7d79c711e37df35f690a0cd290ff392c6a0f770ac5c93d8b4e","schema_version":"1.0","event_id":"sha256:9a73bbd98ec1bb7d79c711e37df35f690a0cd290ff392c6a0f770ac5c93d8b4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/bundle.json","state_url":"https://pith.science/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/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":"2026-06-05T08:45:10Z","links":{"resolver":"https://pith.science/pith/4W2K26ZKNZWKHM3YULQ7CROCSW","bundle":"https://pith.science/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/bundle.json","state":"https://pith.science/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4W2K26ZKNZWKHM3YULQ7CROCSW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4W2K26ZKNZWKHM3YULQ7CROCSW","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":"324d45dcacb1633a42dfa5abc013f8b99706f083c82582adfc1a71b1444e60c2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-29T21:42:32Z","title_canon_sha256":"7c066d0cb0485058b971646cab1dd14ae474ac8d44e46828fe3501fc27ab7d63"},"schema_version":"1.0","source":{"id":"1510.08919","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08919","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08919v2","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08919","created_at":"2026-05-18T00:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"4W2K26ZKNZWK","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4W2K26ZKNZWKHM3Y","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4W2K26ZK","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:9a73bbd98ec1bb7d79c711e37df35f690a0cd290ff392c6a0f770ac5c93d8b4e","target":"graph","created_at":"2026-05-18T00:50:40Z","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":"The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\\varepsilon$. It is well known that, as $\\varepsilon \\to 0$, the measure of the set of initial conditions which lead to 'capture in a resonance zone' goes to zero. In this paper we study the effect of weak noise on the escape from a resonance zone.","authors_text":"Ilya Pavlyukevich, Navaratnam Sri Namachchivaya, Nishanth Lingala","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-29T21:42:32Z","title":"Random Perturbations of a Periodically Driven Nonlinear Oscillator: Escape from a resonance zone"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08919","kind":"arxiv","version":2},"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":"sha256:55a68c9d06e741bdb9e317802c328c83294fc4c181a83e29e762aa96b99699a2","target":"record","created_at":"2026-05-18T00:50:40Z","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":"324d45dcacb1633a42dfa5abc013f8b99706f083c82582adfc1a71b1444e60c2","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-29T21:42:32Z","title_canon_sha256":"7c066d0cb0485058b971646cab1dd14ae474ac8d44e46828fe3501fc27ab7d63"},"schema_version":"1.0","source":{"id":"1510.08919","kind":"arxiv","version":2}},"canonical_sha256":"e5b4ad7b2a6e6ca3b378a2e1f145c295a3ace6f2bbc26ab8facda0d934d5b7c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5b4ad7b2a6e6ca3b378a2e1f145c295a3ace6f2bbc26ab8facda0d934d5b7c7","first_computed_at":"2026-05-18T00:50:40.516161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:40.516161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TfJtQMzuIEIKhw+s8XanMW4g81tLDgPPSxyvGFrH9jNaYOoxx4lbGb/IM6p7oQaBq42FMm/HC77q9THcjtEmAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:40.516780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08919","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55a68c9d06e741bdb9e317802c328c83294fc4c181a83e29e762aa96b99699a2","sha256:9a73bbd98ec1bb7d79c711e37df35f690a0cd290ff392c6a0f770ac5c93d8b4e"],"state_sha256":"fd4454a2f9dac09d63e31ef588053f4009cd900e5f65aab941b0902c8bddc760"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pTAXoZJ9DzSqJSTs2r865y4FcMNXnOBVQFuICQtfRCRSHs821wN0NRvdmoKrhG0aDVwbzwj878XDo/aJDxA9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:45:10.351208Z","bundle_sha256":"f622bd2d15347b4eb383ffcf8c5eccc9003d6b3d70300ba114af58da2f38705e"}}