{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5M46MH3C6IQNTMVON7ODUPHFTO","short_pith_number":"pith:5M46MH3C","canonical_record":{"source":{"id":"1311.0712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T14:30:07Z","cross_cats_sorted":[],"title_canon_sha256":"0d8a64ac4e4cecbfeefbccaa9b9a7084b699e4596bbe8961c14893140f92692f","abstract_canon_sha256":"53d3428b380259d46d0d506d13c854911ad5e547fc53986e09356174c906b983"},"schema_version":"1.0"},"canonical_sha256":"eb39e61f62f220d9b2ae6fdc3a3ce59bb55a0e54798ddc31f6c7e83e85b9b6a4","source":{"kind":"arxiv","id":"1311.0712","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0712","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0712v2","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0712","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"5M46MH3C6IQN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5M46MH3C6IQNTMVO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5M46MH3C","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5M46MH3C6IQNTMVON7ODUPHFTO","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0712","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T14:30:07Z","cross_cats_sorted":[],"title_canon_sha256":"0d8a64ac4e4cecbfeefbccaa9b9a7084b699e4596bbe8961c14893140f92692f","abstract_canon_sha256":"53d3428b380259d46d0d506d13c854911ad5e547fc53986e09356174c906b983"},"schema_version":"1.0"},"canonical_sha256":"eb39e61f62f220d9b2ae6fdc3a3ce59bb55a0e54798ddc31f6c7e83e85b9b6a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:50.407077Z","signature_b64":"RR5g5X4RyZuNOpKZas5fI5G+IGyUwsOXvf6PmrYsVNVqR7YCot4wJStWDQ512iZ+Bu9It67v7s+JBjG6yjO1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb39e61f62f220d9b2ae6fdc3a3ce59bb55a0e54798ddc31f6c7e83e85b9b6a4","last_reissued_at":"2026-05-18T02:50:50.406573Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:50.406573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0712","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":"2026-05-18T02:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"64PdcPOGOTPIJJZkNLY+JRlH8JRddXoSmZlP8yGGbXHGFpbiIzpUjXijLy1V1JgwbZTuocvq7W8RM/U0CEO7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:21:05.707643Z"},"content_sha256":"d0f7362609e5887f57d1396c3e70caac36530d3d4e68833ddb514b3b1254479f","schema_version":"1.0","event_id":"sha256:d0f7362609e5887f57d1396c3e70caac36530d3d4e68833ddb514b3b1254479f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5M46MH3C6IQNTMVON7ODUPHFTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pablo Alvarez-Caudevilla, Victor A. Galaktionov","submitted_at":"2013-11-04T14:30:07Z","abstract_excerpt":"This paper is devoted to some aspects of well-posedness of the Cauchy problem for a quasilinear degenerate fourth-order parabolic thin film equation u_{t} = -\\nabla \\cdot(|u|^{n} \\nabla\\D u) in \\ren \\times \\re_+, \\quad u(x,0)=u_0(x) in \\ren, where $n>0$ is a fixed exponent, with bounded smooth compactly supported initial data. Dealing with the CP (for, at least, $n \\in (0, \\frac 32)$) requires introducing classes of infinitely changing sign solutions that are oscillatory close to finite interfaces.\n  The main goal of the paper is to detect proper solutions of the CP for the degenerate TFE--4 b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0712","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":"2026-05-18T02:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SZQRHnWl5it0rXfUR4G5xpcOGnSgQ3VX69oQdwc41HrAXVy4HOfsu0osU/6kCf64pgqjxdYkcqU3QMYhv9FAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:21:05.707996Z"},"content_sha256":"3cd8eaa2ba3d700bd6e9bbe36f93ad57e96912049d53b7fe677d0ff359a6c833","schema_version":"1.0","event_id":"sha256:3cd8eaa2ba3d700bd6e9bbe36f93ad57e96912049d53b7fe677d0ff359a6c833"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5M46MH3C6IQNTMVON7ODUPHFTO/bundle.json","state_url":"https://pith.science/pith/5M46MH3C6IQNTMVON7ODUPHFTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5M46MH3C6IQNTMVON7ODUPHFTO/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":"2026-07-02T04:21:05Z","links":{"resolver":"https://pith.science/pith/5M46MH3C6IQNTMVON7ODUPHFTO","bundle":"https://pith.science/pith/5M46MH3C6IQNTMVON7ODUPHFTO/bundle.json","state":"https://pith.science/pith/5M46MH3C6IQNTMVON7ODUPHFTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5M46MH3C6IQNTMVON7ODUPHFTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5M46MH3C6IQNTMVON7ODUPHFTO","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":"53d3428b380259d46d0d506d13c854911ad5e547fc53986e09356174c906b983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T14:30:07Z","title_canon_sha256":"0d8a64ac4e4cecbfeefbccaa9b9a7084b699e4596bbe8961c14893140f92692f"},"schema_version":"1.0","source":{"id":"1311.0712","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0712","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0712v2","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0712","created_at":"2026-05-18T02:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"5M46MH3C6IQN","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5M46MH3C6IQNTMVO","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5M46MH3C","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:3cd8eaa2ba3d700bd6e9bbe36f93ad57e96912049d53b7fe677d0ff359a6c833","target":"graph","created_at":"2026-05-18T02:50:50Z","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":"This paper is devoted to some aspects of well-posedness of the Cauchy problem for a quasilinear degenerate fourth-order parabolic thin film equation u_{t} = -\\nabla \\cdot(|u|^{n} \\nabla\\D u) in \\ren \\times \\re_+, \\quad u(x,0)=u_0(x) in \\ren, where $n>0$ is a fixed exponent, with bounded smooth compactly supported initial data. Dealing with the CP (for, at least, $n \\in (0, \\frac 32)$) requires introducing classes of infinitely changing sign solutions that are oscillatory close to finite interfaces.\n  The main goal of the paper is to detect proper solutions of the CP for the degenerate TFE--4 b","authors_text":"Pablo Alvarez-Caudevilla, Victor A. Galaktionov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T14:30:07Z","title":"Well-posedness of the Cauchy problem for a fourth-order thin film equation via regularization approaches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0712","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:d0f7362609e5887f57d1396c3e70caac36530d3d4e68833ddb514b3b1254479f","target":"record","created_at":"2026-05-18T02:50:50Z","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":"53d3428b380259d46d0d506d13c854911ad5e547fc53986e09356174c906b983","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-11-04T14:30:07Z","title_canon_sha256":"0d8a64ac4e4cecbfeefbccaa9b9a7084b699e4596bbe8961c14893140f92692f"},"schema_version":"1.0","source":{"id":"1311.0712","kind":"arxiv","version":2}},"canonical_sha256":"eb39e61f62f220d9b2ae6fdc3a3ce59bb55a0e54798ddc31f6c7e83e85b9b6a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb39e61f62f220d9b2ae6fdc3a3ce59bb55a0e54798ddc31f6c7e83e85b9b6a4","first_computed_at":"2026-05-18T02:50:50.406573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:50.406573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RR5g5X4RyZuNOpKZas5fI5G+IGyUwsOXvf6PmrYsVNVqR7YCot4wJStWDQ512iZ+Bu9It67v7s+JBjG6yjO1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:50.407077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0712","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0f7362609e5887f57d1396c3e70caac36530d3d4e68833ddb514b3b1254479f","sha256:3cd8eaa2ba3d700bd6e9bbe36f93ad57e96912049d53b7fe677d0ff359a6c833"],"state_sha256":"86dea55e2e56c3aa2fc8502d8f3e0a01c37beb870e6e3ebcf7c913986896b0d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7SxdLPJmgzu21gx1vq2KVapxC8dq+gsJ86kqRxtoU+XIYKDWS26SSGkU98aoAwbpOAebaQuIWd4NUFKpQiQdCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T04:21:05.709980Z","bundle_sha256":"912f9f5ac2efaf3bd3c816403849bf4a7f37f1ebb9cf779d2c91b81f98e9935b"}}