{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ZI4F4266YWKLVWYXZXVQXPXXJF","short_pith_number":"pith:ZI4F4266","canonical_record":{"source":{"id":"1101.3261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-17T16:38:03Z","cross_cats_sorted":["math.NA","physics.flu-dyn"],"title_canon_sha256":"e141939d7e84ebdf749e9e80b5d9c12d9597502d5864ef7a4f299ee848b3f8a0","abstract_canon_sha256":"5c513ce247b49ea690dde2fc8a39adb488ab385043a616335202e07d419ec3ba"},"schema_version":"1.0"},"canonical_sha256":"ca385e6bdec594badb17cdeb0bbef749410a56fb0e687d67b510e1852b1538f5","source":{"kind":"arxiv","id":"1101.3261","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3261","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3261v2","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3261","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZI4F4266YWKL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZI4F4266YWKLVWYX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZI4F4266","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ZI4F4266YWKLVWYXZXVQXPXXJF","target":"record","payload":{"canonical_record":{"source":{"id":"1101.3261","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-17T16:38:03Z","cross_cats_sorted":["math.NA","physics.flu-dyn"],"title_canon_sha256":"e141939d7e84ebdf749e9e80b5d9c12d9597502d5864ef7a4f299ee848b3f8a0","abstract_canon_sha256":"5c513ce247b49ea690dde2fc8a39adb488ab385043a616335202e07d419ec3ba"},"schema_version":"1.0"},"canonical_sha256":"ca385e6bdec594badb17cdeb0bbef749410a56fb0e687d67b510e1852b1538f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:08.905113Z","signature_b64":"q3Zmt1bucnvVCuFIFaTqw4QFDwg5biiGkacDCVqqc3SUBKLT4hWMJE/xlqfeAWlULh5RyAShQCyhEWbeyudnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca385e6bdec594badb17cdeb0bbef749410a56fb0e687d67b510e1852b1538f5","last_reissued_at":"2026-05-18T04:10:08.902861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:08.902861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.3261","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":"2026-05-18T04:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29AiLDXRRXna0GDXLbOG6MpYZu54y05LDTnn/cgzJaTggtcGQ6f4smwY/MX5FpfJMBPmz6ie66tcTvFm2Cf4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:10:13.686524Z"},"content_sha256":"a70cd0cd66ddd8c1818e067cd8091e5b98672ffa52c15f399e561b74e6cc006c","schema_version":"1.0","event_id":"sha256:a70cd0cd66ddd8c1818e067cd8091e5b98672ffa52c15f399e561b74e6cc006c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ZI4F4266YWKLVWYXZXVQXPXXJF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Daniel Ginsberg, Gideon Simpson","submitted_at":"2011-01-17T16:38:03Z","abstract_excerpt":"We consider an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate an iterative spectral algorithm for computing these steady states. Finally, we explore a non-existence inequality for steady state solutions from the recent work of Chugunova, Pugh, & Taranets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3261","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":"2026-05-18T04:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FVHyyHPW3c2glMS1vUQEX+qkNnrHoAUv5eMKq9yzoY8HCyG3q1FxbsorEW8/jIQeFM6NKCPhZ6bU1sIWLN2GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:10:13.686868Z"},"content_sha256":"c9570afe9773ace65d4d5e9afa7fe46504df49db7a47ced90ed47768b9c48924","schema_version":"1.0","event_id":"sha256:c9570afe9773ace65d4d5e9afa7fe46504df49db7a47ced90ed47768b9c48924"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/bundle.json","state_url":"https://pith.science/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/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":"2026-06-29T00:10:13Z","links":{"resolver":"https://pith.science/pith/ZI4F4266YWKLVWYXZXVQXPXXJF","bundle":"https://pith.science/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/bundle.json","state":"https://pith.science/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZI4F4266YWKLVWYXZXVQXPXXJF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZI4F4266YWKLVWYXZXVQXPXXJF","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":"5c513ce247b49ea690dde2fc8a39adb488ab385043a616335202e07d419ec3ba","cross_cats_sorted":["math.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-17T16:38:03Z","title_canon_sha256":"e141939d7e84ebdf749e9e80b5d9c12d9597502d5864ef7a4f299ee848b3f8a0"},"schema_version":"1.0","source":{"id":"1101.3261","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.3261","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1101.3261v2","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3261","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZI4F4266YWKL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZI4F4266YWKLVWYX","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZI4F4266","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:c9570afe9773ace65d4d5e9afa7fe46504df49db7a47ced90ed47768b9c48924","target":"graph","created_at":"2026-05-18T04:10:08Z","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 an equation for a thin-film of fluid on a rotating cylinder and present several new analytical and numerical results on steady state solutions. First, we provide an elementary proof that both weak and classical steady states must be strictly positive so long as the speed of rotation is nonzero. Next, we formulate an iterative spectral algorithm for computing these steady states. Finally, we explore a non-existence inequality for steady state solutions from the recent work of Chugunova, Pugh, & Taranets.","authors_text":"Daniel Ginsberg, Gideon Simpson","cross_cats":["math.NA","physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-17T16:38:03Z","title":"Analytical and Numerical Results on the Positivity of Steady State Solutions of a Thin Film Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3261","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:a70cd0cd66ddd8c1818e067cd8091e5b98672ffa52c15f399e561b74e6cc006c","target":"record","created_at":"2026-05-18T04:10:08Z","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":"5c513ce247b49ea690dde2fc8a39adb488ab385043a616335202e07d419ec3ba","cross_cats_sorted":["math.NA","physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-17T16:38:03Z","title_canon_sha256":"e141939d7e84ebdf749e9e80b5d9c12d9597502d5864ef7a4f299ee848b3f8a0"},"schema_version":"1.0","source":{"id":"1101.3261","kind":"arxiv","version":2}},"canonical_sha256":"ca385e6bdec594badb17cdeb0bbef749410a56fb0e687d67b510e1852b1538f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca385e6bdec594badb17cdeb0bbef749410a56fb0e687d67b510e1852b1538f5","first_computed_at":"2026-05-18T04:10:08.902861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:08.902861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3Zmt1bucnvVCuFIFaTqw4QFDwg5biiGkacDCVqqc3SUBKLT4hWMJE/xlqfeAWlULh5RyAShQCyhEWbeyudnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:08.905113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.3261","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a70cd0cd66ddd8c1818e067cd8091e5b98672ffa52c15f399e561b74e6cc006c","sha256:c9570afe9773ace65d4d5e9afa7fe46504df49db7a47ced90ed47768b9c48924"],"state_sha256":"0c24b6505ba62891ffbdb6c35771c737396b1c54de7fb21526638d90459fe612"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eH3NwMC0O28SQ0RPU1RXdS5fyxsYbqQcstRblJRQ+5l9vAyDDifZQU/ZLOxgeOq0sHD5RE6ydBPLmevOhu48CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:10:13.688734Z","bundle_sha256":"c7bc86d9b805dc3c950f662c5d6956cdcd3c37857a985760643e33ab7e212c56"}}