{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5JHTYJBRVHMKXNJPFUUSOEPSH4","short_pith_number":"pith:5JHTYJBR","canonical_record":{"source":{"id":"1703.09821","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-28T21:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b874369b3a25181f1165cbab6c6cd0858a10c10857c88119c4bd01ccc0ee0985","abstract_canon_sha256":"4cec736d04396e8e2187d8a1f7a046fe16d80c26a36b3a9d336a00bff7b48e3e"},"schema_version":"1.0"},"canonical_sha256":"ea4f3c2431a9d8abb52f2d292711f23f210ecc29df3ded49a1716f40a1855d95","source":{"kind":"arxiv","id":"1703.09821","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09821","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09821v3","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09821","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"5JHTYJBRVHMK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5JHTYJBRVHMKXNJP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5JHTYJBR","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5JHTYJBRVHMKXNJPFUUSOEPSH4","target":"record","payload":{"canonical_record":{"source":{"id":"1703.09821","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-28T21:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b874369b3a25181f1165cbab6c6cd0858a10c10857c88119c4bd01ccc0ee0985","abstract_canon_sha256":"4cec736d04396e8e2187d8a1f7a046fe16d80c26a36b3a9d336a00bff7b48e3e"},"schema_version":"1.0"},"canonical_sha256":"ea4f3c2431a9d8abb52f2d292711f23f210ecc29df3ded49a1716f40a1855d95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:30.355512Z","signature_b64":"CLS4bEMdCsYeiTgR7S1yx5LLgW84y4GJv3PCSRXEYfC0jCw8itEcxLzExg1/+cHvsU8Ffv6/pYWk79WIZo7sBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea4f3c2431a9d8abb52f2d292711f23f210ecc29df3ded49a1716f40a1855d95","last_reissued_at":"2026-05-18T00:40:30.354955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:30.354955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.09821","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":"2026-05-18T00:40:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/aoBcpAvh2Uer/W9zUiu7QVR/hk5BXXfPGd/1ksR02IB1nIFGE4RrEySjDIIpnaL9UDR41J2QDem6TIrEwjgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:43:05.391797Z"},"content_sha256":"e37cd117aaa50f81eca5056d63c814d9015989e8c97aa36b7c893ac359fed4bf","schema_version":"1.0","event_id":"sha256:e37cd117aaa50f81eca5056d63c814d9015989e8c97aa36b7c893ac359fed4bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5JHTYJBRVHMKXNJPFUUSOEPSH4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularity formation for the 1D compressible Euler equation with variable damping coefficient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yuusuke Sugiyama","submitted_at":"2017-03-28T21:51:37Z","abstract_excerpt":"In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping for the occurrence of the finite time blow-up. In particular, our sufficient conditions ensure that the derivative blow-up occurs in finite time with the solution itself and the pressure bounded. Our method is based on simple estimates with Riemann invariants. Furthermore, we give sharp lower and upper estimates of the lifespan of solutions, when initial dat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09821","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":"2026-05-18T00:40:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tr2gsLjsXfeCCB7LFMHa2Wpzogjlac0W5h2/TBSmMj/mp8hjqkMnMGWjV5ZjuFvyuGOBHVhR34uEX6dmIBjbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:43:05.392453Z"},"content_sha256":"47177be5788541fef64e3c5ff3d6d66da78931aa9838d0a784b8769ac7db8bef","schema_version":"1.0","event_id":"sha256:47177be5788541fef64e3c5ff3d6d66da78931aa9838d0a784b8769ac7db8bef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/bundle.json","state_url":"https://pith.science/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/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":"2026-06-08T20:43:05Z","links":{"resolver":"https://pith.science/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4","bundle":"https://pith.science/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/bundle.json","state":"https://pith.science/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JHTYJBRVHMKXNJPFUUSOEPSH4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5JHTYJBRVHMKXNJPFUUSOEPSH4","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":"4cec736d04396e8e2187d8a1f7a046fe16d80c26a36b3a9d336a00bff7b48e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-28T21:51:37Z","title_canon_sha256":"b874369b3a25181f1165cbab6c6cd0858a10c10857c88119c4bd01ccc0ee0985"},"schema_version":"1.0","source":{"id":"1703.09821","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.09821","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.09821v3","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.09821","created_at":"2026-05-18T00:40:30Z"},{"alias_kind":"pith_short_12","alias_value":"5JHTYJBRVHMK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5JHTYJBRVHMKXNJP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5JHTYJBR","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:47177be5788541fef64e3c5ff3d6d66da78931aa9838d0a784b8769ac7db8bef","target":"graph","created_at":"2026-05-18T00:40:30Z","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 some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping for the occurrence of the finite time blow-up. In particular, our sufficient conditions ensure that the derivative blow-up occurs in finite time with the solution itself and the pressure bounded. Our method is based on simple estimates with Riemann invariants. Furthermore, we give sharp lower and upper estimates of the lifespan of solutions, when initial dat","authors_text":"Yuusuke Sugiyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-28T21:51:37Z","title":"Singularity formation for the 1D compressible Euler equation with variable damping coefficient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.09821","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:e37cd117aaa50f81eca5056d63c814d9015989e8c97aa36b7c893ac359fed4bf","target":"record","created_at":"2026-05-18T00:40:30Z","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":"4cec736d04396e8e2187d8a1f7a046fe16d80c26a36b3a9d336a00bff7b48e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-28T21:51:37Z","title_canon_sha256":"b874369b3a25181f1165cbab6c6cd0858a10c10857c88119c4bd01ccc0ee0985"},"schema_version":"1.0","source":{"id":"1703.09821","kind":"arxiv","version":3}},"canonical_sha256":"ea4f3c2431a9d8abb52f2d292711f23f210ecc29df3ded49a1716f40a1855d95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea4f3c2431a9d8abb52f2d292711f23f210ecc29df3ded49a1716f40a1855d95","first_computed_at":"2026-05-18T00:40:30.354955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:30.354955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLS4bEMdCsYeiTgR7S1yx5LLgW84y4GJv3PCSRXEYfC0jCw8itEcxLzExg1/+cHvsU8Ffv6/pYWk79WIZo7sBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:30.355512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.09821","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37cd117aaa50f81eca5056d63c814d9015989e8c97aa36b7c893ac359fed4bf","sha256:47177be5788541fef64e3c5ff3d6d66da78931aa9838d0a784b8769ac7db8bef"],"state_sha256":"8144f4ef755271b6d11dddba948944dd2996cbdace4d65d7cfc0f4821fef74bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6mepuKXwoGJgC41aoWDaqqYb+b2o80AAiIGJZISygwKsBjgmHvSocPxmVQQuoYJzDY+yW9R2NNJZRRPL3MbBCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:43:05.395958Z","bundle_sha256":"0ede40c5591bff4d4827438526e1cd7124c1e9174a34dce051476c752bec8ab3"}}