{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Q63Q2KCPBTLAJFDA2RER2DP6AX","short_pith_number":"pith:Q63Q2KCP","canonical_record":{"source":{"id":"1407.5554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:33:04Z","cross_cats_sorted":[],"title_canon_sha256":"66d67a6685b1390bc3c74f84ff96eb29f6742018a0247050228811aace5bd232","abstract_canon_sha256":"1d5a502e15f757da81280fb189f6dd566a1f03ee153e8d648f02f89199b37a34"},"schema_version":"1.0"},"canonical_sha256":"87b70d284f0cd6049460d4491d0dfe05cadb92379a550a5e1aa177980c8ed48e","source":{"kind":"arxiv","id":"1407.5554","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5554","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5554v1","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5554","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q63Q2KCPBTLA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q63Q2KCPBTLAJFDA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q63Q2KCP","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Q63Q2KCPBTLAJFDA2RER2DP6AX","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5554","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:33:04Z","cross_cats_sorted":[],"title_canon_sha256":"66d67a6685b1390bc3c74f84ff96eb29f6742018a0247050228811aace5bd232","abstract_canon_sha256":"1d5a502e15f757da81280fb189f6dd566a1f03ee153e8d648f02f89199b37a34"},"schema_version":"1.0"},"canonical_sha256":"87b70d284f0cd6049460d4491d0dfe05cadb92379a550a5e1aa177980c8ed48e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:13.776568Z","signature_b64":"ackhEV88ImTWZXMPfg0GXY1PIGCky5BnSvzyYycdfODOJJCxUSBwEazWDozZM2EKUNlw6YLtCTg5HTZU4ZwvAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87b70d284f0cd6049460d4491d0dfe05cadb92379a550a5e1aa177980c8ed48e","last_reissued_at":"2026-05-18T02:47:13.775961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:13.775961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5554","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":"2026-05-18T02:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sw468UxyA/jcqxva5+E+1cx1kJrra9CqsQ3qQLPUfesNQ8B8ZFYMlc+9LRXM7x4rTzyK40FAvWiNnrZfaUKkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:39:48.398849Z"},"content_sha256":"aa899a2cadb60fe055d8c63bae1fffef9b4291d3301ac6ee8467207c0ce32221","schema_version":"1.0","event_id":"sha256:aa899a2cadb60fe055d8c63bae1fffef9b4291d3301ac6ee8467207c0ce32221"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Q63Q2KCPBTLAJFDA2RER2DP6AX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jonathan D. Evans, Pablo Alvarez-Caudevilla, Victor A. Galaktionov","submitted_at":"2014-07-21T16:33:04Z","abstract_excerpt":"Fundamental global similarity solutions of the standard form u_\\g(x,t)=t^{-\\a_\\g} f_\\g(y), with the rescaled variable y= x/{t^{\\b_\\g}}, \\b_\\g= \\frac {1-n \\a_\\g}{10}, where \\a_\\g>0 are real nonlinear eigenvalues (\\g is a multiindex in R^N) of the tenth-order thin film equation (TFE-10) u_{t} = \\nabla \\cdot(|u|^{n} \\n \\D^4 u) in R^N \\times R_+, n>0, are studied. The present paper continues the study began by the authors in the previous paper\n  P. Alvarez-Caudevilla, J.D.Evans, and V.A. Galaktionov, The Cauchy problem for a tenth-order thin film equation I. Bifurcation of self-similar oscillatory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5554","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":"2026-05-18T02:47:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JlrwO3rFJGpDgejFJNmZZ/0kIOWcvAO2Jg/3gByE+4nT/+6d2Rq2kA/2x32QFtxUtx4h4tppL284JPJ5oJM0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:39:48.399204Z"},"content_sha256":"1a0c78a4daa708366449c88c1a787f5ca9b5eb3fd1986a95b82fab912bb9c6b8","schema_version":"1.0","event_id":"sha256:1a0c78a4daa708366449c88c1a787f5ca9b5eb3fd1986a95b82fab912bb9c6b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/bundle.json","state_url":"https://pith.science/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/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":"2026-07-01T23:39:48Z","links":{"resolver":"https://pith.science/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX","bundle":"https://pith.science/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/bundle.json","state":"https://pith.science/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q63Q2KCPBTLAJFDA2RER2DP6AX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q63Q2KCPBTLAJFDA2RER2DP6AX","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":"1d5a502e15f757da81280fb189f6dd566a1f03ee153e8d648f02f89199b37a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:33:04Z","title_canon_sha256":"66d67a6685b1390bc3c74f84ff96eb29f6742018a0247050228811aace5bd232"},"schema_version":"1.0","source":{"id":"1407.5554","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5554","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5554v1","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5554","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"Q63Q2KCPBTLA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q63Q2KCPBTLAJFDA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q63Q2KCP","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:1a0c78a4daa708366449c88c1a787f5ca9b5eb3fd1986a95b82fab912bb9c6b8","target":"graph","created_at":"2026-05-18T02:47:13Z","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":"Fundamental global similarity solutions of the standard form u_\\g(x,t)=t^{-\\a_\\g} f_\\g(y), with the rescaled variable y= x/{t^{\\b_\\g}}, \\b_\\g= \\frac {1-n \\a_\\g}{10}, where \\a_\\g>0 are real nonlinear eigenvalues (\\g is a multiindex in R^N) of the tenth-order thin film equation (TFE-10) u_{t} = \\nabla \\cdot(|u|^{n} \\n \\D^4 u) in R^N \\times R_+, n>0, are studied. The present paper continues the study began by the authors in the previous paper\n  P. Alvarez-Caudevilla, J.D.Evans, and V.A. Galaktionov, The Cauchy problem for a tenth-order thin film equation I. Bifurcation of self-similar oscillatory","authors_text":"Jonathan D. Evans, Pablo Alvarez-Caudevilla, Victor A. Galaktionov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:33:04Z","title":"The Cauchy problem for a tenth-order thin film equation II. Oscillatory source-type and fundamental similarity solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5554","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:aa899a2cadb60fe055d8c63bae1fffef9b4291d3301ac6ee8467207c0ce32221","target":"record","created_at":"2026-05-18T02:47:13Z","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":"1d5a502e15f757da81280fb189f6dd566a1f03ee153e8d648f02f89199b37a34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T16:33:04Z","title_canon_sha256":"66d67a6685b1390bc3c74f84ff96eb29f6742018a0247050228811aace5bd232"},"schema_version":"1.0","source":{"id":"1407.5554","kind":"arxiv","version":1}},"canonical_sha256":"87b70d284f0cd6049460d4491d0dfe05cadb92379a550a5e1aa177980c8ed48e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87b70d284f0cd6049460d4491d0dfe05cadb92379a550a5e1aa177980c8ed48e","first_computed_at":"2026-05-18T02:47:13.775961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:13.775961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ackhEV88ImTWZXMPfg0GXY1PIGCky5BnSvzyYycdfODOJJCxUSBwEazWDozZM2EKUNlw6YLtCTg5HTZU4ZwvAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:13.776568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5554","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa899a2cadb60fe055d8c63bae1fffef9b4291d3301ac6ee8467207c0ce32221","sha256:1a0c78a4daa708366449c88c1a787f5ca9b5eb3fd1986a95b82fab912bb9c6b8"],"state_sha256":"e965cb0e8e4a65e84e7ce4a411d67925f0820519cec5f3ade5b00b27f6a82bf7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLh7188UiI2yV40Lm9zwFStMbN1UZGpj5aWHVdcgz9t6zbKqWvlI+nI7j+YcEEmSZ2toNOwg2XBMyvIYAuCyBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:39:48.401497Z","bundle_sha256":"6b605cd0a9f48226794574f0c5ba5709b27675f03ee116903b503e8011b9e6cc"}}