{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M7XR76AWQEE5YVM7CVRNLWZZJP","short_pith_number":"pith:M7XR76AW","canonical_record":{"source":{"id":"1410.7572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-28T10:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"214046363ad09ffb83c74b36255afff0903a32acf37a517e339f97e4fe959aa2","abstract_canon_sha256":"ca063ef05080d4605cc903a070338b2ddf946d437343115492a8aab87690c55e"},"schema_version":"1.0"},"canonical_sha256":"67ef1ff8168109dc559f1562d5db394be8034c00577a687184ab4eef25b3d3af","source":{"kind":"arxiv","id":"1410.7572","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7572","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7572v2","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7572","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"pith_short_12","alias_value":"M7XR76AWQEE5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M7XR76AWQEE5YVM7","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M7XR76AW","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M7XR76AWQEE5YVM7CVRNLWZZJP","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-28T10:12:39Z","cross_cats_sorted":[],"title_canon_sha256":"214046363ad09ffb83c74b36255afff0903a32acf37a517e339f97e4fe959aa2","abstract_canon_sha256":"ca063ef05080d4605cc903a070338b2ddf946d437343115492a8aab87690c55e"},"schema_version":"1.0"},"canonical_sha256":"67ef1ff8168109dc559f1562d5db394be8034c00577a687184ab4eef25b3d3af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:18.638859Z","signature_b64":"8nmqRtKcE93cIQhqYbR8Lg9qQIvxyhTas6oxDEc8aJt7TXNlAGNNyKLFE8sGWu7swQuuOsDNrw88KEs4mPpdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ef1ff8168109dc559f1562d5db394be8034c00577a687184ab4eef25b3d3af","last_reissued_at":"2026-05-18T01:12:18.638503Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:18.638503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7572","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":"2026-05-18T01:12:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"afZ6Aa3Y/uF6aZeq0g0698JqqqAj2EXbRt7yUd9Zec3grAhkG6WswbtC0XPOdJ1WafeCDtpuU4nSymzORGsDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:12:21.238857Z"},"content_sha256":"0b789136bd7f671ac2fb82daca6f2517dd818274485dc9d705e16231ee18e7e8","schema_version":"1.0","event_id":"sha256:0b789136bd7f671ac2fb82daca6f2517dd818274485dc9d705e16231ee18e7e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M7XR76AWQEE5YVM7CVRNLWZZJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient bounds for a thin film epitaxy equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong Li, Tao Tang, Zhonghua Qiao","submitted_at":"2014-10-28T10:12:39Z","abstract_excerpt":"We consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions $d\\le 3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7572","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":"2026-05-18T01:12:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clKupLvhSbBI/YwKPYKZDNiezveluCs0Qvgn+2k40JUPqN+TRAPhXe6akYT42USxDHtYUszIDAiyfsOfejyxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:12:21.239182Z"},"content_sha256":"17442dbb7c9d50ef0ee03d0ceea8b7a056e64f182209d5d1526c09724043b191","schema_version":"1.0","event_id":"sha256:17442dbb7c9d50ef0ee03d0ceea8b7a056e64f182209d5d1526c09724043b191"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/bundle.json","state_url":"https://pith.science/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/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":"2026-06-09T11:12:21Z","links":{"resolver":"https://pith.science/pith/M7XR76AWQEE5YVM7CVRNLWZZJP","bundle":"https://pith.science/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/bundle.json","state":"https://pith.science/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7XR76AWQEE5YVM7CVRNLWZZJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M7XR76AWQEE5YVM7CVRNLWZZJP","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":"ca063ef05080d4605cc903a070338b2ddf946d437343115492a8aab87690c55e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-28T10:12:39Z","title_canon_sha256":"214046363ad09ffb83c74b36255afff0903a32acf37a517e339f97e4fe959aa2"},"schema_version":"1.0","source":{"id":"1410.7572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7572","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7572v2","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7572","created_at":"2026-05-18T01:12:18Z"},{"alias_kind":"pith_short_12","alias_value":"M7XR76AWQEE5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M7XR76AWQEE5YVM7","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M7XR76AW","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:17442dbb7c9d50ef0ee03d0ceea8b7a056e64f182209d5d1526c09724043b191","target":"graph","created_at":"2026-05-18T01:12:18Z","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 consider a gradient flow modeling the epitaxial growth of thin films with slope selection. The surface height profile satisfies a nonlinear diffusion equation with biharmonic dissipation. We establish optimal local and global wellposedness for initial data with critical regularity. To understand the mechanism of slope selection and the dependence on the dissipation coefficient, we exhibit several lower and upper bounds for the gradient of the solution in physical dimensions $d\\le 3$.","authors_text":"Dong Li, Tao Tang, Zhonghua Qiao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-28T10:12:39Z","title":"Gradient bounds for a thin film epitaxy equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7572","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":"sha256:0b789136bd7f671ac2fb82daca6f2517dd818274485dc9d705e16231ee18e7e8","target":"record","created_at":"2026-05-18T01:12:18Z","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":"ca063ef05080d4605cc903a070338b2ddf946d437343115492a8aab87690c55e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-28T10:12:39Z","title_canon_sha256":"214046363ad09ffb83c74b36255afff0903a32acf37a517e339f97e4fe959aa2"},"schema_version":"1.0","source":{"id":"1410.7572","kind":"arxiv","version":2}},"canonical_sha256":"67ef1ff8168109dc559f1562d5db394be8034c00577a687184ab4eef25b3d3af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ef1ff8168109dc559f1562d5db394be8034c00577a687184ab4eef25b3d3af","first_computed_at":"2026-05-18T01:12:18.638503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:18.638503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8nmqRtKcE93cIQhqYbR8Lg9qQIvxyhTas6oxDEc8aJt7TXNlAGNNyKLFE8sGWu7swQuuOsDNrw88KEs4mPpdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:18.638859Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b789136bd7f671ac2fb82daca6f2517dd818274485dc9d705e16231ee18e7e8","sha256:17442dbb7c9d50ef0ee03d0ceea8b7a056e64f182209d5d1526c09724043b191"],"state_sha256":"ce5dc26a6a57e2d8f089b268249d0551310d4ad7dcac2a0a423762d6a2d8587d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BzjrTtIO7ZCtLJNIb4bcPr+409mgiECRzTVoQp2XZpA26JoWGO22uj1QWa79pZz4WJAtjejmjrfG9U7t44XhBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:12:21.241028Z","bundle_sha256":"45a9336ad969281be8307dffa23f61cc29c46f4283e2e8d14931a2b6d1c55858"}}