{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZYNNJQ3SOOSI4SIF25MJHTUURP","short_pith_number":"pith:ZYNNJQ3S","canonical_record":{"source":{"id":"1705.02924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T15:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"da86c8c2151b73aff05f26a0d3e73a8bb116de01dfe31e17fe140bd969dfbb87","abstract_canon_sha256":"b5cf554388f7971fad9244906d2e4b1064bc18bf2a878bb1c2c3c32b32428e39"},"schema_version":"1.0"},"canonical_sha256":"ce1ad4c37273a48e4905d75893ce948bf697a957540694fd2960e4205ea0f648","source":{"kind":"arxiv","id":"1705.02924","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02924","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02924v2","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02924","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZYNNJQ3SOOSI","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_16","alias_value":"ZYNNJQ3SOOSI4SIF","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_8","alias_value":"ZYNNJQ3S","created_at":"2026-07-05T05:13:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZYNNJQ3SOOSI4SIF25MJHTUURP","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02924","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T15:38:14Z","cross_cats_sorted":[],"title_canon_sha256":"da86c8c2151b73aff05f26a0d3e73a8bb116de01dfe31e17fe140bd969dfbb87","abstract_canon_sha256":"b5cf554388f7971fad9244906d2e4b1064bc18bf2a878bb1c2c3c32b32428e39"},"schema_version":"1.0"},"canonical_sha256":"ce1ad4c37273a48e4905d75893ce948bf697a957540694fd2960e4205ea0f648","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:26.497879Z","signature_b64":"Pz2aVqVkw4Zd46Z3yABVBP25JikIkRYAbSQaDgRfIbKH9hIJwxJMlS7pQs6ZystNOWZ5Y9rBWu1cW3RvFfPHAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce1ad4c37273a48e4905d75893ce948bf697a957540694fd2960e4205ea0f648","last_reissued_at":"2026-07-05T05:13:26.497373Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:26.497373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02924","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":"2026-07-05T05:13:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnVz8WtECt7FvbbqV9WQfRZ4lNNZgNICZf7DzYuBLY9E4vm4x83LjyxOdSjNgMH4TYAQlBkh7dnfblsiTDppBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:25:12.586141Z"},"content_sha256":"779f5fd8b87111db2596bc485b2c7b5da1d2a870434ac91e1ae7e814f70730c7","schema_version":"1.0","event_id":"sha256:779f5fd8b87111db2596bc485b2c7b5da1d2a870434ac91e1ae7e814f70730c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZYNNJQ3SOOSI4SIF25MJHTUURP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A vicinal surface model for epitaxial growth with logarithmic free energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hangjie Ji, Jian-Guo Liu, Thomas P. Witelski, Yuan Gao","submitted_at":"2017-05-08T15:38:14Z","abstract_excerpt":"We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+\\alpha u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02924","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1705.02924/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:13:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bOKkHnqpQWn9B5X8J3xAN9cBdDLpTdopiUnxqYQoThVFlTubG53XljdI4QRYn0w70lsvz6Zc4Hu0Hs7qzoaWDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T23:25:12.586616Z"},"content_sha256":"57c83420162a19b6ddff378f19e9d6f8a9715d129cdbc52b34305198ce24b441","schema_version":"1.0","event_id":"sha256:57c83420162a19b6ddff378f19e9d6f8a9715d129cdbc52b34305198ce24b441"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/bundle.json","state_url":"https://pith.science/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/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":"2026-08-18T23:25:12Z","links":{"resolver":"https://pith.science/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP","bundle":"https://pith.science/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/bundle.json","state":"https://pith.science/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZYNNJQ3SOOSI4SIF25MJHTUURP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZYNNJQ3SOOSI4SIF25MJHTUURP","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":"b5cf554388f7971fad9244906d2e4b1064bc18bf2a878bb1c2c3c32b32428e39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T15:38:14Z","title_canon_sha256":"da86c8c2151b73aff05f26a0d3e73a8bb116de01dfe31e17fe140bd969dfbb87"},"schema_version":"1.0","source":{"id":"1705.02924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02924","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02924v2","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02924","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_12","alias_value":"ZYNNJQ3SOOSI","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_16","alias_value":"ZYNNJQ3SOOSI4SIF","created_at":"2026-07-05T05:13:26Z"},{"alias_kind":"pith_short_8","alias_value":"ZYNNJQ3S","created_at":"2026-07-05T05:13:26Z"}],"graph_snapshots":[{"event_id":"sha256:57c83420162a19b6ddff378f19e9d6f8a9715d129cdbc52b34305198ce24b441","target":"graph","created_at":"2026-07-05T05:13:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1705.02924/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t = -u^2(u^3+\\alpha u)_{hhhh}$, gives the evolution for the surface slope $u$ as a function of the local height $h$ in a monotone step train. Subject to periodic boundary conditions and positive initial conditions, we prove the existence, uniqueness and positivity of global strong solutions to this PDE using two Lyapunov energy functions. The long time behavior of $u$ co","authors_text":"Hangjie Ji, Jian-Guo Liu, Thomas P. Witelski, Yuan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T15:38:14Z","title":"A vicinal surface model for epitaxial growth with logarithmic free energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02924","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":"sha256:779f5fd8b87111db2596bc485b2c7b5da1d2a870434ac91e1ae7e814f70730c7","target":"record","created_at":"2026-07-05T05:13:26Z","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":"b5cf554388f7971fad9244906d2e4b1064bc18bf2a878bb1c2c3c32b32428e39","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-08T15:38:14Z","title_canon_sha256":"da86c8c2151b73aff05f26a0d3e73a8bb116de01dfe31e17fe140bd969dfbb87"},"schema_version":"1.0","source":{"id":"1705.02924","kind":"arxiv","version":2}},"canonical_sha256":"ce1ad4c37273a48e4905d75893ce948bf697a957540694fd2960e4205ea0f648","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce1ad4c37273a48e4905d75893ce948bf697a957540694fd2960e4205ea0f648","first_computed_at":"2026-07-05T05:13:26.497373Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:26.497373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pz2aVqVkw4Zd46Z3yABVBP25JikIkRYAbSQaDgRfIbKH9hIJwxJMlS7pQs6ZystNOWZ5Y9rBWu1cW3RvFfPHAA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:26.497879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:779f5fd8b87111db2596bc485b2c7b5da1d2a870434ac91e1ae7e814f70730c7","sha256:57c83420162a19b6ddff378f19e9d6f8a9715d129cdbc52b34305198ce24b441"],"state_sha256":"7e09e9d0a1d771356fb725f6ed29795b26fc97e5c18d44906c3e3cad90336222"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2IQCU/5T/QhISKpn1DpfrL1TNsT6kvF9bqcCYKgQAM9GT671Ys49NYRMJp9EV5GLL/wAuDvtfaz1fuRlnWeBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T23:25:12.589970Z","bundle_sha256":"90c1633c0cd66b6744df1fc7d7b313ccebf66a08c3d1bd64bbaa8fe2e32d642e"}}