{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HBNXWWTKLQGWODCEAINRC352UC","short_pith_number":"pith:HBNXWWTK","canonical_record":{"source":{"id":"1706.03921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-13T06:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"bf63d4af87c8629e43f394362a6afc7feccb79115805df8c43cecf88e8300f28","abstract_canon_sha256":"ec89b48c64770abcddd11bad6eea833e9c9e6e0475e5c1650a234306637cf0d4"},"schema_version":"1.0"},"canonical_sha256":"385b7b5a6a5c0d670c44021b116fbaa09f7a20cecca9125eba31ab92e8e7fffd","source":{"kind":"arxiv","id":"1706.03921","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03921","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03921v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03921","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"HBNXWWTKLQGW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HBNXWWTKLQGWODCE","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HBNXWWTK","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HBNXWWTKLQGWODCEAINRC352UC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.03921","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-13T06:47:48Z","cross_cats_sorted":[],"title_canon_sha256":"bf63d4af87c8629e43f394362a6afc7feccb79115805df8c43cecf88e8300f28","abstract_canon_sha256":"ec89b48c64770abcddd11bad6eea833e9c9e6e0475e5c1650a234306637cf0d4"},"schema_version":"1.0"},"canonical_sha256":"385b7b5a6a5c0d670c44021b116fbaa09f7a20cecca9125eba31ab92e8e7fffd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:28.001451Z","signature_b64":"NeJva7YA6gfW/8LgdIfuEb87QSBUdL7uqX65Kt0Ga0n4ITIohN60jd4aPBNhtn2SLyrVqk2wkOK9+TyHOZJ/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"385b7b5a6a5c0d670c44021b116fbaa09f7a20cecca9125eba31ab92e8e7fffd","last_reissued_at":"2026-05-18T00:42:28.000923Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:28.000923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.03921","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":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKlu5YeSF3xD+eYxwWl1QKud6fGksyXQ+spRuZngUuiXZdwq8C+TPa3qAHKypCbPvPdWFGxdghoRyeHStM41AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:46:39.465575Z"},"content_sha256":"e2b14017ed77c577f50aa033f7279abefb60be9e073afeb93697bded3018af9f","schema_version":"1.0","event_id":"sha256:e2b14017ed77c577f50aa033f7279abefb60be9e073afeb93697bded3018af9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HBNXWWTKLQGWODCEAINRC352UC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic Solutions to Nonlinear Wave equation with $X$-dependent Coefficients under the General Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bochao Chen, Xue Yang, Yong Li","submitted_at":"2017-06-13T06:47:48Z","abstract_excerpt":"In this paper we consider a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The proofs are based on a Lyapunov-Schmidt reduction together with a differentiable Nash-Moser iteration scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03921","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":"2026-05-18T00:42:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3u2Y98xBOhBpupRsAX6JLK14gC8viMfrfla7fPtQV0mR2XWgH6lq/tmgr7ZfZCrfG1eCqfTw7NXn49nwpwXJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:46:39.465918Z"},"content_sha256":"7cc03b8bb80a1fa2edb1696c97bd9a1638150985a2710127889637da325cfe34","schema_version":"1.0","event_id":"sha256:7cc03b8bb80a1fa2edb1696c97bd9a1638150985a2710127889637da325cfe34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBNXWWTKLQGWODCEAINRC352UC/bundle.json","state_url":"https://pith.science/pith/HBNXWWTKLQGWODCEAINRC352UC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBNXWWTKLQGWODCEAINRC352UC/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":"2026-05-28T11:46:39Z","links":{"resolver":"https://pith.science/pith/HBNXWWTKLQGWODCEAINRC352UC","bundle":"https://pith.science/pith/HBNXWWTKLQGWODCEAINRC352UC/bundle.json","state":"https://pith.science/pith/HBNXWWTKLQGWODCEAINRC352UC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBNXWWTKLQGWODCEAINRC352UC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HBNXWWTKLQGWODCEAINRC352UC","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":"ec89b48c64770abcddd11bad6eea833e9c9e6e0475e5c1650a234306637cf0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-13T06:47:48Z","title_canon_sha256":"bf63d4af87c8629e43f394362a6afc7feccb79115805df8c43cecf88e8300f28"},"schema_version":"1.0","source":{"id":"1706.03921","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.03921","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"arxiv_version","alias_value":"1706.03921v1","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.03921","created_at":"2026-05-18T00:42:28Z"},{"alias_kind":"pith_short_12","alias_value":"HBNXWWTKLQGW","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HBNXWWTKLQGWODCE","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HBNXWWTK","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7cc03b8bb80a1fa2edb1696c97bd9a1638150985a2710127889637da325cfe34","target":"graph","created_at":"2026-05-18T00:42:28Z","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 a class of nonlinear wave equation with $x$-dependent coefficients and prove existence of families of time-periodic solutions under the general boundary conditions. Such a model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. The proofs are based on a Lyapunov-Schmidt reduction together with a differentiable Nash-Moser iteration scheme.","authors_text":"Bochao Chen, Xue Yang, Yong Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-13T06:47:48Z","title":"Periodic Solutions to Nonlinear Wave equation with $X$-dependent Coefficients under the General Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03921","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:e2b14017ed77c577f50aa033f7279abefb60be9e073afeb93697bded3018af9f","target":"record","created_at":"2026-05-18T00:42:28Z","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":"ec89b48c64770abcddd11bad6eea833e9c9e6e0475e5c1650a234306637cf0d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-13T06:47:48Z","title_canon_sha256":"bf63d4af87c8629e43f394362a6afc7feccb79115805df8c43cecf88e8300f28"},"schema_version":"1.0","source":{"id":"1706.03921","kind":"arxiv","version":1}},"canonical_sha256":"385b7b5a6a5c0d670c44021b116fbaa09f7a20cecca9125eba31ab92e8e7fffd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"385b7b5a6a5c0d670c44021b116fbaa09f7a20cecca9125eba31ab92e8e7fffd","first_computed_at":"2026-05-18T00:42:28.000923Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:28.000923Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NeJva7YA6gfW/8LgdIfuEb87QSBUdL7uqX65Kt0Ga0n4ITIohN60jd4aPBNhtn2SLyrVqk2wkOK9+TyHOZJ/Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:28.001451Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.03921","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2b14017ed77c577f50aa033f7279abefb60be9e073afeb93697bded3018af9f","sha256:7cc03b8bb80a1fa2edb1696c97bd9a1638150985a2710127889637da325cfe34"],"state_sha256":"1636ebd85aa8d3e4cdf462a7ebdfb15c65371750e23ffbe8cfb8108c85a05e44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpnxXlC5nw3Y3MOwZa/W2AWrdSJSz1WL9aEeVsb3LwTKfLu6PT4DayXNhIPkUMfMuSal+GxjypFbsTTXCi4RBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:46:39.467885Z","bundle_sha256":"277b5943540df96af7610aa8c1d7c9a84b0d5a007eb25c23d47963d3f0721b88"}}