{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NO4QX5QJ73FHVSDKVQ2V2IKMM5","short_pith_number":"pith:NO4QX5QJ","canonical_record":{"source":{"id":"2411.15498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T09:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"0605a5ff216bb2c1dd9e985c4fff13b03919deddf0bb9e78926d8f5f1d4e274b","abstract_canon_sha256":"2eaea68b0018e18c61d84ce82b2f037c93376d74820f0b06aa7357aa7f2bf7b3"},"schema_version":"1.0"},"canonical_sha256":"6bb90bf609feca7ac86aac355d214c674bafbc9c4c01249e84ac7013c7ba8cf7","source":{"kind":"arxiv","id":"2411.15498","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15498","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15498v1","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15498","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"NO4QX5QJ73FH","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_16","alias_value":"NO4QX5QJ73FHVSDK","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_8","alias_value":"NO4QX5QJ","created_at":"2026-07-05T09:39:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NO4QX5QJ73FHVSDKVQ2V2IKMM5","target":"record","payload":{"canonical_record":{"source":{"id":"2411.15498","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T09:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"0605a5ff216bb2c1dd9e985c4fff13b03919deddf0bb9e78926d8f5f1d4e274b","abstract_canon_sha256":"2eaea68b0018e18c61d84ce82b2f037c93376d74820f0b06aa7357aa7f2bf7b3"},"schema_version":"1.0"},"canonical_sha256":"6bb90bf609feca7ac86aac355d214c674bafbc9c4c01249e84ac7013c7ba8cf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:39:35.904945Z","signature_b64":"D6EJCgpbhVn5R4H1arnef8HAEWaGAOYNvog8iRsX4C25qr9ruHgGo7flEU7lHOgQIK7iJ9d0XMR6Fz09wAQADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6bb90bf609feca7ac86aac355d214c674bafbc9c4c01249e84ac7013c7ba8cf7","last_reissued_at":"2026-07-05T09:39:35.904565Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:39:35.904565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.15498","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":"2026-07-05T09:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifcbnbsuiZX1A9b9Kf39J6Nsu5FTU7Lt71MjEoWNdFxFP5pnqVqPK82iRux9ruyXaMkVigfKnMcFTQBuds5/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:09:00.806093Z"},"content_sha256":"3e49b6278c21bb6c2d7bea3a1eab1499cc5a66ad6918d9fb8074389503cdef51","schema_version":"1.0","event_id":"sha256:3e49b6278c21bb6c2d7bea3a1eab1499cc5a66ad6918d9fb8074389503cdef51"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NO4QX5QJ73FHVSDKVQ2V2IKMM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal higher derivative estimates for solutions of the Lam\\'e system with closely spaced hard inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Haigang Li, Hongjie Dong, Huaijun Teng, Peihao Zhang","submitted_at":"2024-11-23T09:20:32Z","abstract_excerpt":"We investigate higher derivative estimates for the Lam\\'e system with hard inclusions embedded in a bounded domain in $\\mathbb{R}^{d}$. As the distance $\\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in the narrow regions between the inclusions increases significantly. This stress is captured by the gradient of the solution. The key contribution of this paper is a detailed characterization of this singularity, achieved by deriving higher derivative estimates for solutions to the Lam\\'e system with partially infinite coefficients. These upper bounds are show"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15498","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/2411.15498/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":"2026-07-05T09:39:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IM2Bpipg7Z6OfYlmJbXFKLuc8CmPaRYkWNS0tHyqATobfrUJl+p897eW1KB6bBPPYvi3agfuaq9hQsW1Z1wLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T02:09:00.807160Z"},"content_sha256":"90f9b3598cec25112b1cd95b263b004f1e8f733c72eaa36903027bd3d888cba3","schema_version":"1.0","event_id":"sha256:90f9b3598cec25112b1cd95b263b004f1e8f733c72eaa36903027bd3d888cba3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/bundle.json","state_url":"https://pith.science/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/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":"2026-08-13T02:09:00Z","links":{"resolver":"https://pith.science/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5","bundle":"https://pith.science/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/bundle.json","state":"https://pith.science/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NO4QX5QJ73FHVSDKVQ2V2IKMM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NO4QX5QJ73FHVSDKVQ2V2IKMM5","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":"2eaea68b0018e18c61d84ce82b2f037c93376d74820f0b06aa7357aa7f2bf7b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T09:20:32Z","title_canon_sha256":"0605a5ff216bb2c1dd9e985c4fff13b03919deddf0bb9e78926d8f5f1d4e274b"},"schema_version":"1.0","source":{"id":"2411.15498","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.15498","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.15498v1","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.15498","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_12","alias_value":"NO4QX5QJ73FH","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_16","alias_value":"NO4QX5QJ73FHVSDK","created_at":"2026-07-05T09:39:35Z"},{"alias_kind":"pith_short_8","alias_value":"NO4QX5QJ","created_at":"2026-07-05T09:39:35Z"}],"graph_snapshots":[{"event_id":"sha256:90f9b3598cec25112b1cd95b263b004f1e8f733c72eaa36903027bd3d888cba3","target":"graph","created_at":"2026-07-05T09:39:35Z","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/2411.15498/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate higher derivative estimates for the Lam\\'e system with hard inclusions embedded in a bounded domain in $\\mathbb{R}^{d}$. As the distance $\\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in the narrow regions between the inclusions increases significantly. This stress is captured by the gradient of the solution. The key contribution of this paper is a detailed characterization of this singularity, achieved by deriving higher derivative estimates for solutions to the Lam\\'e system with partially infinite coefficients. These upper bounds are show","authors_text":"Haigang Li, Hongjie Dong, Huaijun Teng, Peihao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T09:20:32Z","title":"Optimal higher derivative estimates for solutions of the Lam\\'e system with closely spaced hard inclusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.15498","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":"sha256:3e49b6278c21bb6c2d7bea3a1eab1499cc5a66ad6918d9fb8074389503cdef51","target":"record","created_at":"2026-07-05T09:39:35Z","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":"2eaea68b0018e18c61d84ce82b2f037c93376d74820f0b06aa7357aa7f2bf7b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-11-23T09:20:32Z","title_canon_sha256":"0605a5ff216bb2c1dd9e985c4fff13b03919deddf0bb9e78926d8f5f1d4e274b"},"schema_version":"1.0","source":{"id":"2411.15498","kind":"arxiv","version":1}},"canonical_sha256":"6bb90bf609feca7ac86aac355d214c674bafbc9c4c01249e84ac7013c7ba8cf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bb90bf609feca7ac86aac355d214c674bafbc9c4c01249e84ac7013c7ba8cf7","first_computed_at":"2026-07-05T09:39:35.904565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:39:35.904565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D6EJCgpbhVn5R4H1arnef8HAEWaGAOYNvog8iRsX4C25qr9ruHgGo7flEU7lHOgQIK7iJ9d0XMR6Fz09wAQADA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:39:35.904945Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.15498","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e49b6278c21bb6c2d7bea3a1eab1499cc5a66ad6918d9fb8074389503cdef51","sha256:90f9b3598cec25112b1cd95b263b004f1e8f733c72eaa36903027bd3d888cba3"],"state_sha256":"d0276bf908f7a89e02835778afab32b21f7a34823864e32e349e44e9f79d67b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7q6o4VqPDzxMPVmLnhWi9WleqbE8FhttqHH+NtW5mIazAPTDZZz8K9YUMbOoCf5gzC1tn4VG20hbxQKNrxseBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T02:09:00.815177Z","bundle_sha256":"c6a174ed6954199764d59f14010621079216267d237cdaf4b0e150fc6bdda7f7"}}