{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GBMACKGXQO3GJJW7WI3SY75A5T","short_pith_number":"pith:GBMACKGX","canonical_record":{"source":{"id":"2506.00392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-31T04:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"e08e3975475a25cec82637b8ad619ba24149f767cb808354224954761f5a7880","abstract_canon_sha256":"5d661f6c41cffb25557fb42a6874d9521ebf717cdc99cd01616ee1e54d9364e6"},"schema_version":"1.0"},"canonical_sha256":"30580128d783b664a6dfb2372c7fa0ecf3354050111102c962f3ca2ee6da440e","source":{"kind":"arxiv","id":"2506.00392","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00392","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00392v1","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00392","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"GBMACKGXQO3G","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_16","alias_value":"GBMACKGXQO3GJJW7","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_8","alias_value":"GBMACKGX","created_at":"2026-07-05T11:13:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GBMACKGXQO3GJJW7WI3SY75A5T","target":"record","payload":{"canonical_record":{"source":{"id":"2506.00392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-31T04:52:12Z","cross_cats_sorted":[],"title_canon_sha256":"e08e3975475a25cec82637b8ad619ba24149f767cb808354224954761f5a7880","abstract_canon_sha256":"5d661f6c41cffb25557fb42a6874d9521ebf717cdc99cd01616ee1e54d9364e6"},"schema_version":"1.0"},"canonical_sha256":"30580128d783b664a6dfb2372c7fa0ecf3354050111102c962f3ca2ee6da440e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:33.854917Z","signature_b64":"xsedRMVosvTnDQylGueYCO9tz6a0MgMr4e1aqeP/+U2vXbjXqeVk7if6WzVriM2ABaJQlp8MX8F8M38KQoBdAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30580128d783b664a6dfb2372c7fa0ecf3354050111102c962f3ca2ee6da440e","last_reissued_at":"2026-07-05T11:13:33.854470Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:33.854470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.00392","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":"2026-07-05T11:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"epmdA2cp/SbW+Fmf2NaGpp/WN7CMGgDHY2PNQEnODraZ/kBKZIZqdXWW0c9+VjUhzFQJVgC1A5ZQQImxEEDCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:34:02.909345Z"},"content_sha256":"9f5c0f84ef2bdf013025665aa13fc2566ae34115230c22f1689338422dd01ef8","schema_version":"1.0","event_id":"sha256:9f5c0f84ef2bdf013025665aa13fc2566ae34115230c22f1689338422dd01ef8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GBMACKGXQO3GJJW7WI3SY75A5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Xingyu Wang","submitted_at":"2025-05-31T04:52:12Z","abstract_excerpt":"This work investigates the vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions. We establish local-in-time convergence of solutions to mean curvature flow with a fixed contact angle $0<\\alpha\\leq 90^\\circ$, for a broad class of boundary energy densities and well-prepared initial data. The limiting sharp-interface system is derived, comprising harmonic heat flows in the bulk and minimal pair conditions at phase boundaries. The analysis combines the relative entropy method with gradient flow calibrations and weak convergence techniqu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00392","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.00392/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":"2026-07-05T11:13:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tAbFgpyfvT9+TxpnU9HvMV+sB3XKrZ/lPW2yNgzCMsFvyf4A6YQa651HMvbXreWCG3aHBWxtfeSmQ1OW0QTvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:34:02.910014Z"},"content_sha256":"e5cba880cbc8ef5c769f49f0c7049065dacc1817052a2aa01dd1b51e30a80376","schema_version":"1.0","event_id":"sha256:e5cba880cbc8ef5c769f49f0c7049065dacc1817052a2aa01dd1b51e30a80376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBMACKGXQO3GJJW7WI3SY75A5T/bundle.json","state_url":"https://pith.science/pith/GBMACKGXQO3GJJW7WI3SY75A5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBMACKGXQO3GJJW7WI3SY75A5T/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":"2026-08-18T18:34:02Z","links":{"resolver":"https://pith.science/pith/GBMACKGXQO3GJJW7WI3SY75A5T","bundle":"https://pith.science/pith/GBMACKGXQO3GJJW7WI3SY75A5T/bundle.json","state":"https://pith.science/pith/GBMACKGXQO3GJJW7WI3SY75A5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBMACKGXQO3GJJW7WI3SY75A5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GBMACKGXQO3GJJW7WI3SY75A5T","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":"5d661f6c41cffb25557fb42a6874d9521ebf717cdc99cd01616ee1e54d9364e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-31T04:52:12Z","title_canon_sha256":"e08e3975475a25cec82637b8ad619ba24149f767cb808354224954761f5a7880"},"schema_version":"1.0","source":{"id":"2506.00392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00392","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00392v1","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00392","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_12","alias_value":"GBMACKGXQO3G","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_16","alias_value":"GBMACKGXQO3GJJW7","created_at":"2026-07-05T11:13:33Z"},{"alias_kind":"pith_short_8","alias_value":"GBMACKGX","created_at":"2026-07-05T11:13:33Z"}],"graph_snapshots":[{"event_id":"sha256:e5cba880cbc8ef5c769f49f0c7049065dacc1817052a2aa01dd1b51e30a80376","target":"graph","created_at":"2026-07-05T11:13:33Z","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/2506.00392/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work investigates the vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions. We establish local-in-time convergence of solutions to mean curvature flow with a fixed contact angle $0<\\alpha\\leq 90^\\circ$, for a broad class of boundary energy densities and well-prepared initial data. The limiting sharp-interface system is derived, comprising harmonic heat flows in the bulk and minimal pair conditions at phase boundaries. The analysis combines the relative entropy method with gradient flow calibrations and weak convergence techniqu","authors_text":"Xingyu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-31T04:52:12Z","title":"The vector-valued Allen-Cahn equation with potentials of high-dimensional double-wells under Robin boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00392","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":"sha256:9f5c0f84ef2bdf013025665aa13fc2566ae34115230c22f1689338422dd01ef8","target":"record","created_at":"2026-07-05T11:13:33Z","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":"5d661f6c41cffb25557fb42a6874d9521ebf717cdc99cd01616ee1e54d9364e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-05-31T04:52:12Z","title_canon_sha256":"e08e3975475a25cec82637b8ad619ba24149f767cb808354224954761f5a7880"},"schema_version":"1.0","source":{"id":"2506.00392","kind":"arxiv","version":1}},"canonical_sha256":"30580128d783b664a6dfb2372c7fa0ecf3354050111102c962f3ca2ee6da440e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30580128d783b664a6dfb2372c7fa0ecf3354050111102c962f3ca2ee6da440e","first_computed_at":"2026-07-05T11:13:33.854470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:33.854470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xsedRMVosvTnDQylGueYCO9tz6a0MgMr4e1aqeP/+U2vXbjXqeVk7if6WzVriM2ABaJQlp8MX8F8M38KQoBdAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:33.854917Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f5c0f84ef2bdf013025665aa13fc2566ae34115230c22f1689338422dd01ef8","sha256:e5cba880cbc8ef5c769f49f0c7049065dacc1817052a2aa01dd1b51e30a80376"],"state_sha256":"3a85f8553ce500ca431e0b86a060df537bc992ea91d303f63dae39e81226b038"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oTGmoEh5FE8yDw2mqcleUPs7g1rexML1FF6kiWuJYqrWHkxNlYhtd5BgWaO5LN3AMFYTtlpweU18h+uKWuWsCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:34:02.915267Z","bundle_sha256":"2f8cec0e76115547d4fdac6122fa335b476f95afa98b06d0cf4e7675bd9c268a"}}