{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WNYCH5JONSAJLDKPK75O7WUHY7","short_pith_number":"pith:WNYCH5JO","canonical_record":{"source":{"id":"1504.03861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-15T11:19:06Z","cross_cats_sorted":[],"title_canon_sha256":"9689c2012b652886ab91672760f0cd74f3004882ec8ab7414438742d194c975e","abstract_canon_sha256":"2b27cc0a057daae4fb7128789667f0059fc368b45c85bea16d0bd32b35681ac0"},"schema_version":"1.0"},"canonical_sha256":"b37023f52e6c80958d4f57faefda87c7f6bfe6bca6d2d0f7ae8edd9621fd46fe","source":{"kind":"arxiv","id":"1504.03861","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03861","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03861v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03861","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"WNYCH5JONSAJ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WNYCH5JONSAJLDKP","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WNYCH5JO","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WNYCH5JONSAJLDKPK75O7WUHY7","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-15T11:19:06Z","cross_cats_sorted":[],"title_canon_sha256":"9689c2012b652886ab91672760f0cd74f3004882ec8ab7414438742d194c975e","abstract_canon_sha256":"2b27cc0a057daae4fb7128789667f0059fc368b45c85bea16d0bd32b35681ac0"},"schema_version":"1.0"},"canonical_sha256":"b37023f52e6c80958d4f57faefda87c7f6bfe6bca6d2d0f7ae8edd9621fd46fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:41.899424Z","signature_b64":"DNB4BWuc/5zkOZIDOQIW/nC3p1mzQweVmJPO7MmMa0ZXmbstOvzgP8bLCsETqSqsVTFc6LVuE/OtbfaVa9EZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b37023f52e6c80958d4f57faefda87c7f6bfe6bca6d2d0f7ae8edd9621fd46fe","last_reissued_at":"2026-05-18T02:18:41.898675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:41.898675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03861","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WbdNKBHgwT0212rSgpxTG2CSnjDzt6GP2r1wK6kHxAC8S9hvM+4t+A6r43yVnQb3o75qNtg2byxZkM36SsONAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:11:43.763402Z"},"content_sha256":"a4fabb6934fe2e5a9c37b4fdd3c537e719dbe60bb13921ed70f622d30de02a8e","schema_version":"1.0","event_id":"sha256:a4fabb6934fe2e5a9c37b4fdd3c537e719dbe60bb13921ed70f622d30de02a8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WNYCH5JONSAJLDKPK75O7WUHY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"H\\\"older regularity at the boundary of two-dimensional sliding almost minimal sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Yangqin Fang","submitted_at":"2015-04-15T11:19:06Z","abstract_excerpt":"In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in $\\mathbb{R}^{3}$. It is quite important for understanding the soap films and the solutions of Plateau's problem away from boundary. In this paper, we will give a regularity result on the boundary for two dimensional sliding almost minimal sets in $\\mathbb{R}^{3}$. It will be of use for understanding their boundary behavior."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03861","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":"2026-05-18T02:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5R7iyVbSPFI9u3JQAeY9B7V4nuq853fvoXG3MqMz9TMDR+wVqljiXy9yVshnkir0S6xxY2ABQp/lmRdXm4xNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T10:11:43.763743Z"},"content_sha256":"1d7ec5bf91176105e69007d93261c8315ed6c50dbfeefbe37cfbaaa67a7ca9a2","schema_version":"1.0","event_id":"sha256:1d7ec5bf91176105e69007d93261c8315ed6c50dbfeefbe37cfbaaa67a7ca9a2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WNYCH5JONSAJLDKPK75O7WUHY7/bundle.json","state_url":"https://pith.science/pith/WNYCH5JONSAJLDKPK75O7WUHY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WNYCH5JONSAJLDKPK75O7WUHY7/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":"2026-06-24T10:11:43Z","links":{"resolver":"https://pith.science/pith/WNYCH5JONSAJLDKPK75O7WUHY7","bundle":"https://pith.science/pith/WNYCH5JONSAJLDKPK75O7WUHY7/bundle.json","state":"https://pith.science/pith/WNYCH5JONSAJLDKPK75O7WUHY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WNYCH5JONSAJLDKPK75O7WUHY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WNYCH5JONSAJLDKPK75O7WUHY7","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":"2b27cc0a057daae4fb7128789667f0059fc368b45c85bea16d0bd32b35681ac0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-15T11:19:06Z","title_canon_sha256":"9689c2012b652886ab91672760f0cd74f3004882ec8ab7414438742d194c975e"},"schema_version":"1.0","source":{"id":"1504.03861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03861","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03861v1","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03861","created_at":"2026-05-18T02:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"WNYCH5JONSAJ","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WNYCH5JONSAJLDKP","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WNYCH5JO","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:1d7ec5bf91176105e69007d93261c8315ed6c50dbfeefbe37cfbaaa67a7ca9a2","target":"graph","created_at":"2026-05-18T02:18:41Z","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":"In [15], Jean Taylor has proved a regularity theorem away from boundary for Almgren almost minimal sets of dimension two in $\\mathbb{R}^{3}$. It is quite important for understanding the soap films and the solutions of Plateau's problem away from boundary. In this paper, we will give a regularity result on the boundary for two dimensional sliding almost minimal sets in $\\mathbb{R}^{3}$. It will be of use for understanding their boundary behavior.","authors_text":"Yangqin Fang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-15T11:19:06Z","title":"H\\\"older regularity at the boundary of two-dimensional sliding almost minimal sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03861","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:a4fabb6934fe2e5a9c37b4fdd3c537e719dbe60bb13921ed70f622d30de02a8e","target":"record","created_at":"2026-05-18T02:18:41Z","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":"2b27cc0a057daae4fb7128789667f0059fc368b45c85bea16d0bd32b35681ac0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-04-15T11:19:06Z","title_canon_sha256":"9689c2012b652886ab91672760f0cd74f3004882ec8ab7414438742d194c975e"},"schema_version":"1.0","source":{"id":"1504.03861","kind":"arxiv","version":1}},"canonical_sha256":"b37023f52e6c80958d4f57faefda87c7f6bfe6bca6d2d0f7ae8edd9621fd46fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b37023f52e6c80958d4f57faefda87c7f6bfe6bca6d2d0f7ae8edd9621fd46fe","first_computed_at":"2026-05-18T02:18:41.898675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:41.898675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DNB4BWuc/5zkOZIDOQIW/nC3p1mzQweVmJPO7MmMa0ZXmbstOvzgP8bLCsETqSqsVTFc6LVuE/OtbfaVa9EZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:41.899424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4fabb6934fe2e5a9c37b4fdd3c537e719dbe60bb13921ed70f622d30de02a8e","sha256:1d7ec5bf91176105e69007d93261c8315ed6c50dbfeefbe37cfbaaa67a7ca9a2"],"state_sha256":"dbe6cdd55238c9b6d26bf372760a3f9d2e37f5574e61c2d17ef2065f86bfa7f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJU+hk2IqKPc3noWl2mOiVOIzC7hYi9z7t/ZmPZapyk59A6wjy7gj7yQm++1wfMNB6PtVOOwOUYZXbdAD9X5BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T10:11:43.765621Z","bundle_sha256":"cf3c4a3b4a563f884a9b38534dc5bcfb19d2e0e02b0823dfc285d0546cf4f15f"}}