{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:3N2BNAHGSEXMDHE65CXFZQECB2","short_pith_number":"pith:3N2BNAHG","canonical_record":{"source":{"id":"1710.06457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T18:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"63af99e6b9c6b1477aa0ac3315efb6005d3ec65516aa46f1f1af5abaf87b29a2","abstract_canon_sha256":"ce530a223afcd2353bfae3732a5d883f14b0e103a284d9784d056891ce455c6c"},"schema_version":"1.0"},"canonical_sha256":"db741680e6912ec19c9ee8ae5cc0820e89866f6a0069c359d26d896904a1bdd5","source":{"kind":"arxiv","id":"1710.06457","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06457","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06457v2","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06457","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"3N2BNAHGSEXM","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3N2BNAHGSEXMDHE6","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3N2BNAHG","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:3N2BNAHGSEXMDHE65CXFZQECB2","target":"record","payload":{"canonical_record":{"source":{"id":"1710.06457","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T18:16:53Z","cross_cats_sorted":[],"title_canon_sha256":"63af99e6b9c6b1477aa0ac3315efb6005d3ec65516aa46f1f1af5abaf87b29a2","abstract_canon_sha256":"ce530a223afcd2353bfae3732a5d883f14b0e103a284d9784d056891ce455c6c"},"schema_version":"1.0"},"canonical_sha256":"db741680e6912ec19c9ee8ae5cc0820e89866f6a0069c359d26d896904a1bdd5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:10.642857Z","signature_b64":"ggMpldNMm8X25FymsSoGtZHW76k8mvCBagVwNMZcwgoU+aMI4vryu7uAJI16NXAMoLrCwHA52Koc33bJuqntAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db741680e6912ec19c9ee8ae5cc0820e89866f6a0069c359d26d896904a1bdd5","last_reissued_at":"2026-05-18T00:22:10.642264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:10.642264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.06457","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":"2026-05-18T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XZh1ttcDYBziJ+eC2k/xpm3gcOiHoXDS0sT8Wusx/tKG5THD8KFNTMGwlC2LJrkFAuxKL5+AxwcRXzObVtcWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:23:20.604218Z"},"content_sha256":"f0c5deeeb841b8d7c278c1de7272061f86d1838161b9bddacbeb16ffb455f5c9","schema_version":"1.0","event_id":"sha256:f0c5deeeb841b8d7c278c1de7272061f86d1838161b9bddacbeb16ffb455f5c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:3N2BNAHGSEXMDHE65CXFZQECB2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear acoustics: Blackstock-Crighton equations with a periodic forcing term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aday Celik, Mads Kyed","submitted_at":"2017-10-17T18:16:53Z","abstract_excerpt":"The Blackstock-Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into account. In this article, a mathematical analysis of the Blackstock-Crighton equations with a time-periodic forcing term is carried out. For arbitrary time-periodic data (sufficiently restricted in size) it is shown that a time-periodic solution of the same period always exists. This implies that the dissipative effects are sufficient to avoid resonance within the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06457","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":"2026-05-18T00:22:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OiSVQqQwVQ07diX6r1BOuCUQCk/K4G7XB8xhJsCd7iCthHEWRQuo8hyliwFbf3xcnn5VuRfsURsr2aBMXX+aCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:23:20.604833Z"},"content_sha256":"5a88bcb2aa61e3b52df4a052dfc968214fed95f99c6b32172aa4c3661dde194c","schema_version":"1.0","event_id":"sha256:5a88bcb2aa61e3b52df4a052dfc968214fed95f99c6b32172aa4c3661dde194c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3N2BNAHGSEXMDHE65CXFZQECB2/bundle.json","state_url":"https://pith.science/pith/3N2BNAHGSEXMDHE65CXFZQECB2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3N2BNAHGSEXMDHE65CXFZQECB2/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":"2026-06-08T00:23:20Z","links":{"resolver":"https://pith.science/pith/3N2BNAHGSEXMDHE65CXFZQECB2","bundle":"https://pith.science/pith/3N2BNAHGSEXMDHE65CXFZQECB2/bundle.json","state":"https://pith.science/pith/3N2BNAHGSEXMDHE65CXFZQECB2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3N2BNAHGSEXMDHE65CXFZQECB2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3N2BNAHGSEXMDHE65CXFZQECB2","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":"ce530a223afcd2353bfae3732a5d883f14b0e103a284d9784d056891ce455c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T18:16:53Z","title_canon_sha256":"63af99e6b9c6b1477aa0ac3315efb6005d3ec65516aa46f1f1af5abaf87b29a2"},"schema_version":"1.0","source":{"id":"1710.06457","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.06457","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"arxiv_version","alias_value":"1710.06457v2","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.06457","created_at":"2026-05-18T00:22:10Z"},{"alias_kind":"pith_short_12","alias_value":"3N2BNAHGSEXM","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3N2BNAHGSEXMDHE6","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3N2BNAHG","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:5a88bcb2aa61e3b52df4a052dfc968214fed95f99c6b32172aa4c3661dde194c","target":"graph","created_at":"2026-05-18T00:22:10Z","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 Blackstock-Crighton equations describe the motion of a viscous, heat-conducting, compressible fluid. They are used as models for acoustic wave propagation in a medium in which both nonlinear and dissipative effects are taken into account. In this article, a mathematical analysis of the Blackstock-Crighton equations with a time-periodic forcing term is carried out. For arbitrary time-periodic data (sufficiently restricted in size) it is shown that a time-periodic solution of the same period always exists. This implies that the dissipative effects are sufficient to avoid resonance within the","authors_text":"Aday Celik, Mads Kyed","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T18:16:53Z","title":"Nonlinear acoustics: Blackstock-Crighton equations with a periodic forcing term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06457","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:f0c5deeeb841b8d7c278c1de7272061f86d1838161b9bddacbeb16ffb455f5c9","target":"record","created_at":"2026-05-18T00:22:10Z","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":"ce530a223afcd2353bfae3732a5d883f14b0e103a284d9784d056891ce455c6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-17T18:16:53Z","title_canon_sha256":"63af99e6b9c6b1477aa0ac3315efb6005d3ec65516aa46f1f1af5abaf87b29a2"},"schema_version":"1.0","source":{"id":"1710.06457","kind":"arxiv","version":2}},"canonical_sha256":"db741680e6912ec19c9ee8ae5cc0820e89866f6a0069c359d26d896904a1bdd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db741680e6912ec19c9ee8ae5cc0820e89866f6a0069c359d26d896904a1bdd5","first_computed_at":"2026-05-18T00:22:10.642264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:10.642264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggMpldNMm8X25FymsSoGtZHW76k8mvCBagVwNMZcwgoU+aMI4vryu7uAJI16NXAMoLrCwHA52Koc33bJuqntAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:10.642857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.06457","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0c5deeeb841b8d7c278c1de7272061f86d1838161b9bddacbeb16ffb455f5c9","sha256:5a88bcb2aa61e3b52df4a052dfc968214fed95f99c6b32172aa4c3661dde194c"],"state_sha256":"53db30b407366b14eaac63c7a44818c9115432af45f521aa7c09551f1fa71d3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PrEC4gbRT2cwt5H/p6Hfpy2rLW6OO262Vd0FivGxlPPLUr8QOCnie2xoHY+OZez9hnmSQeC4jDFNCZbfNbYzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:23:20.608198Z","bundle_sha256":"86490318453fe94d78dd923a4711e36f6986eda2f54583789c08f4da52b8b563"}}