{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PJYZB7JZOL3BDOLPA3PGU2SPSG","short_pith_number":"pith:PJYZB7JZ","canonical_record":{"source":{"id":"1610.06324","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T08:28:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6f36c2af22c6182916391ef4673dd2388a32beb6c26900ebe2a4db659fd3a45f","abstract_canon_sha256":"b497376fb2f339189828e916c0017d0733fe149ae1b09bc1813083f5147f5139"},"schema_version":"1.0"},"canonical_sha256":"7a7190fd3972f611b96f06de6a6a4f919f8cd1ca77f6d45a1078e02c17440723","source":{"kind":"arxiv","id":"1610.06324","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06324","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06324v3","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06324","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"PJYZB7JZOL3B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJYZB7JZOL3BDOLP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJYZB7JZ","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PJYZB7JZOL3BDOLPA3PGU2SPSG","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06324","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T08:28:57Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"6f36c2af22c6182916391ef4673dd2388a32beb6c26900ebe2a4db659fd3a45f","abstract_canon_sha256":"b497376fb2f339189828e916c0017d0733fe149ae1b09bc1813083f5147f5139"},"schema_version":"1.0"},"canonical_sha256":"7a7190fd3972f611b96f06de6a6a4f919f8cd1ca77f6d45a1078e02c17440723","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:16.122784Z","signature_b64":"TRrC58qyjBNnf15AiCkjq8Z4EBm+NRG9U0L30TIDLclE/O5WSWdX+n/r7IHcFOOwAE/qVYV+tey1KAGFYAHSDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a7190fd3972f611b96f06de6a6a4f919f8cd1ca77f6d45a1078e02c17440723","last_reissued_at":"2026-05-18T00:46:16.122167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:16.122167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06324","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5evqyaCYNpIeg9Q5rseySUcB8mwwYifUbXitaNEPv/QKGS/qumkHgptuAo11oqzpUG2bW2ypUBkIukFE+eMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:46:07.623475Z"},"content_sha256":"c71ed20d42be7a873eddda93549702d556d9c13c0f004f6c741a02909baeb7a3","schema_version":"1.0","event_id":"sha256:c71ed20d42be7a873eddda93549702d556d9c13c0f004f6c741a02909baeb7a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PJYZB7JZOL3BDOLPA3PGU2SPSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Volodymyr Flyud, Yuriy Golovaty","submitted_at":"2016-10-20T08:28:57Z","abstract_excerpt":"We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06324","kind":"arxiv","version":3},"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":"2026-05-18T00:46:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/1o6YtcrNHOAdbrevjmoIEZAaJ50kBmrzn++h/nKPJnVxKl2T2OIadko6riR0ZN2Y8Wa4As+2dvNVJAX4+tDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T09:46:07.623804Z"},"content_sha256":"734031c40b261da21d06e401e62bbc493d00dbed1bb856b468183a346490a581","schema_version":"1.0","event_id":"sha256:734031c40b261da21d06e401e62bbc493d00dbed1bb856b468183a346490a581"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/bundle.json","state_url":"https://pith.science/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/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":"2026-06-23T09:46:07Z","links":{"resolver":"https://pith.science/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG","bundle":"https://pith.science/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/bundle.json","state":"https://pith.science/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJYZB7JZOL3BDOLPA3PGU2SPSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PJYZB7JZOL3BDOLPA3PGU2SPSG","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":"b497376fb2f339189828e916c0017d0733fe149ae1b09bc1813083f5147f5139","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T08:28:57Z","title_canon_sha256":"6f36c2af22c6182916391ef4673dd2388a32beb6c26900ebe2a4db659fd3a45f"},"schema_version":"1.0","source":{"id":"1610.06324","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06324","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06324v3","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06324","created_at":"2026-05-18T00:46:16Z"},{"alias_kind":"pith_short_12","alias_value":"PJYZB7JZOL3B","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJYZB7JZOL3BDOLP","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJYZB7JZ","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:734031c40b261da21d06e401e62bbc493d00dbed1bb856b468183a346490a581","target":"graph","created_at":"2026-05-18T00:46:16Z","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 are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.","authors_text":"Volodymyr Flyud, Yuriy Golovaty","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T08:28:57Z","title":"Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06324","kind":"arxiv","version":3},"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:c71ed20d42be7a873eddda93549702d556d9c13c0f004f6c741a02909baeb7a3","target":"record","created_at":"2026-05-18T00:46:16Z","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":"b497376fb2f339189828e916c0017d0733fe149ae1b09bc1813083f5147f5139","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-20T08:28:57Z","title_canon_sha256":"6f36c2af22c6182916391ef4673dd2388a32beb6c26900ebe2a4db659fd3a45f"},"schema_version":"1.0","source":{"id":"1610.06324","kind":"arxiv","version":3}},"canonical_sha256":"7a7190fd3972f611b96f06de6a6a4f919f8cd1ca77f6d45a1078e02c17440723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a7190fd3972f611b96f06de6a6a4f919f8cd1ca77f6d45a1078e02c17440723","first_computed_at":"2026-05-18T00:46:16.122167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:16.122167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TRrC58qyjBNnf15AiCkjq8Z4EBm+NRG9U0L30TIDLclE/O5WSWdX+n/r7IHcFOOwAE/qVYV+tey1KAGFYAHSDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:16.122784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06324","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c71ed20d42be7a873eddda93549702d556d9c13c0f004f6c741a02909baeb7a3","sha256:734031c40b261da21d06e401e62bbc493d00dbed1bb856b468183a346490a581"],"state_sha256":"ab02e2c037448af43c101dd21a3bed509e5dbb25e45c29ddd9edcd849bae4ae6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N3mP3LueVqyKHo/dvoDmlMaR6AUpKanA0XepAgixNCMS0miBRZnMXhSeYZPNUV3yr1Q4uxLeZv+HJpCk2GGsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T09:46:07.625616Z","bundle_sha256":"1b2f3e1d9312c6185ff17c84065ca76da0f7032841375d6615c2535d379669b6"}}