{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VX4YQK35ZYX7X27WYZAVTKI5UF","short_pith_number":"pith:VX4YQK35","canonical_record":{"source":{"id":"1903.07034","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-17T06:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"e43971b0fd1f3687488d8a785fd4013da712baf40ff31a88a4cd028617238904","abstract_canon_sha256":"a78776caa3c29955838169cfeaf476751345d733d4833b664488b6e5510d2196"},"schema_version":"1.0"},"canonical_sha256":"adf9882b7dce2ffbebf6c64159a91da168b6c90736a27702b2a6ba7006323530","source":{"kind":"arxiv","id":"1903.07034","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07034","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07034v2","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07034","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"pith_short_12","alias_value":"VX4YQK35ZYX7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VX4YQK35ZYX7X27W","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VX4YQK35","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VX4YQK35ZYX7X27WYZAVTKI5UF","target":"record","payload":{"canonical_record":{"source":{"id":"1903.07034","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-17T06:27:52Z","cross_cats_sorted":[],"title_canon_sha256":"e43971b0fd1f3687488d8a785fd4013da712baf40ff31a88a4cd028617238904","abstract_canon_sha256":"a78776caa3c29955838169cfeaf476751345d733d4833b664488b6e5510d2196"},"schema_version":"1.0"},"canonical_sha256":"adf9882b7dce2ffbebf6c64159a91da168b6c90736a27702b2a6ba7006323530","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:48.321084Z","signature_b64":"cP6xTO2MQZzF0whBQkm9dI1jPB6dLXj4rTtLk0hwkGOyAQUBe1XgenVQMr9L87IN4nusL22XqoUHCxLSZJVZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adf9882b7dce2ffbebf6c64159a91da168b6c90736a27702b2a6ba7006323530","last_reissued_at":"2026-05-17T23:42:48.320569Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:48.320569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.07034","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":"2026-05-17T23:42:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8e295U5uCY9YGzBvF9bHmrMUSURdR/q01TWN81RzScSgXfqNHV+G05aYKb2BANtX754Y8thhwVNqfV9f/f4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:21:15.604233Z"},"content_sha256":"113cb8a27c99750d978d15eca6a3fc4f70439892ca06340ee55a6e1952428fb0","schema_version":"1.0","event_id":"sha256:113cb8a27c99750d978d15eca6a3fc4f70439892ca06340ee55a6e1952428fb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VX4YQK35ZYX7X27WYZAVTKI5UF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstruction for the coefficients of a quasilinear elliptic partial differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C\\u{a}t\\u{a}lin I. C\\^arstea, Gen Nakamura, Manmohan Vashisth","submitted_at":"2019-03-17T06:27:52Z","abstract_excerpt":"In this paper we consider an inverse coefficients problem for a quasilinear elliptic equation of divergence form $\\nabla\\cdot\\vec{C}(x,\\nabla u(x))=0$, in a bounded smooth domain $\\Omega$. We assume that $\\overrightarrow{C}(x,\\vec{p})=\\gamma(x)\\vec{p}+\\vec{b}(x)|\\vec{p}|^2+\\mathcal{O}(|\\vec{p}|^3)$, by expanding $\\overrightarrow{C}(x,\\vec{p})$ around $\\vec{p}=0$. We give a reconstruction method for $\\gamma$ and $\\vec{b}$ from the Dirichlet to Neumann map defined on $\\partial\\Omega$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07034","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":"2026-05-17T23:42:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vNNdt/y9i0eE8NzqXkdJzElCXW76k7900ZYQIxdEWY2Vt+i27E5xW2TVaDknlP2dlMNjKUVNiPMBkT13DRe5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:21:15.604815Z"},"content_sha256":"a67d3f3870aa25d97c0f13d44a0ab0d732bef3a4d681a6ff9a3e697de7302576","schema_version":"1.0","event_id":"sha256:a67d3f3870aa25d97c0f13d44a0ab0d732bef3a4d681a6ff9a3e697de7302576"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/bundle.json","state_url":"https://pith.science/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/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":"2026-06-24T11:21:15Z","links":{"resolver":"https://pith.science/pith/VX4YQK35ZYX7X27WYZAVTKI5UF","bundle":"https://pith.science/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/bundle.json","state":"https://pith.science/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VX4YQK35ZYX7X27WYZAVTKI5UF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VX4YQK35ZYX7X27WYZAVTKI5UF","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":"a78776caa3c29955838169cfeaf476751345d733d4833b664488b6e5510d2196","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-17T06:27:52Z","title_canon_sha256":"e43971b0fd1f3687488d8a785fd4013da712baf40ff31a88a4cd028617238904"},"schema_version":"1.0","source":{"id":"1903.07034","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07034","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07034v2","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07034","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"pith_short_12","alias_value":"VX4YQK35ZYX7","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VX4YQK35ZYX7X27W","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VX4YQK35","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:a67d3f3870aa25d97c0f13d44a0ab0d732bef3a4d681a6ff9a3e697de7302576","target":"graph","created_at":"2026-05-17T23:42:48Z","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 this paper we consider an inverse coefficients problem for a quasilinear elliptic equation of divergence form $\\nabla\\cdot\\vec{C}(x,\\nabla u(x))=0$, in a bounded smooth domain $\\Omega$. We assume that $\\overrightarrow{C}(x,\\vec{p})=\\gamma(x)\\vec{p}+\\vec{b}(x)|\\vec{p}|^2+\\mathcal{O}(|\\vec{p}|^3)$, by expanding $\\overrightarrow{C}(x,\\vec{p})$ around $\\vec{p}=0$. We give a reconstruction method for $\\gamma$ and $\\vec{b}$ from the Dirichlet to Neumann map defined on $\\partial\\Omega$.","authors_text":"C\\u{a}t\\u{a}lin I. C\\^arstea, Gen Nakamura, Manmohan Vashisth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-17T06:27:52Z","title":"Reconstruction for the coefficients of a quasilinear elliptic partial differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07034","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":"sha256:113cb8a27c99750d978d15eca6a3fc4f70439892ca06340ee55a6e1952428fb0","target":"record","created_at":"2026-05-17T23:42:48Z","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":"a78776caa3c29955838169cfeaf476751345d733d4833b664488b6e5510d2196","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-17T06:27:52Z","title_canon_sha256":"e43971b0fd1f3687488d8a785fd4013da712baf40ff31a88a4cd028617238904"},"schema_version":"1.0","source":{"id":"1903.07034","kind":"arxiv","version":2}},"canonical_sha256":"adf9882b7dce2ffbebf6c64159a91da168b6c90736a27702b2a6ba7006323530","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adf9882b7dce2ffbebf6c64159a91da168b6c90736a27702b2a6ba7006323530","first_computed_at":"2026-05-17T23:42:48.320569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:48.320569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cP6xTO2MQZzF0whBQkm9dI1jPB6dLXj4rTtLk0hwkGOyAQUBe1XgenVQMr9L87IN4nusL22XqoUHCxLSZJVZCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:48.321084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07034","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:113cb8a27c99750d978d15eca6a3fc4f70439892ca06340ee55a6e1952428fb0","sha256:a67d3f3870aa25d97c0f13d44a0ab0d732bef3a4d681a6ff9a3e697de7302576"],"state_sha256":"07fbf92e89384eab3070e4c42680783750d9b318ade8dc2c64312385171a5a7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5P1a7ftaAb8qKDzAzultSMlrLJrHghgDhPZ7KEZcB+ytpw6lAUMkYrOhUZovFe+xacxC8RLnhkmzGy1XyO61AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:21:15.608762Z","bundle_sha256":"b5adf09e4fe8fb50ab6c267c6e61906b5b65fa520aeba2713a0b771bd6418664"}}