{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I7PLR6QBVZMVCLHK3TJZBEEOIO","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":"7ddc21286cd5b11b75cbd5b8ed1295c3550092fd7a994ec49795a634ee33b117","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-17T13:34:58Z","title_canon_sha256":"16ce703695188c5025452ac4b6d1dd70723f90c02f89cf600a62dd6140975cb2"},"schema_version":"1.0","source":{"id":"2509.13962","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.13962","created_at":"2026-06-19T16:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"2509.13962v3","created_at":"2026-06-19T16:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.13962","created_at":"2026-06-19T16:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"I7PLR6QBVZMV","created_at":"2026-06-19T16:12:47Z"},{"alias_kind":"pith_short_16","alias_value":"I7PLR6QBVZMVCLHK","created_at":"2026-06-19T16:12:47Z"},{"alias_kind":"pith_short_8","alias_value":"I7PLR6QB","created_at":"2026-06-19T16:12:47Z"}],"graph_snapshots":[{"event_id":"sha256:f7b9badbe3a75c380f98c11882168843aed712f52f443f024d40bea3c37a43c6","target":"graph","created_at":"2026-06-19T16:12:47Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We derive sufficient conditions on the initial data that guarantee the stability and uniqueness of the solution obtained from a one-point measurement. Moreover, we present more general uniqueness theorems, which also cover the identification of the initial data, the coefficient of the zero order term and the degeneracy power, using measurements taken over time."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The analysis assumes that the solution admits an explicit representation in terms of Bessel functions for the spectral problem associated with the degenerate diffusion operator, which is invoked to obtain the uniqueness and stability results."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Sufficient conditions on initial data guarantee unique and stable reconstruction of the degeneracy point, power, and related coefficients in strongly degenerate 1D parabolic equations and systems from one-point or time-dependent boundary observations."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Sufficient initial data conditions guarantee unique and stable recovery of the degeneracy point from one boundary measurement in degenerate parabolic equations."}],"snapshot_sha256":"d00066a84dd1da05e737ecc303a5edacf832a1ab2b9da9ecd71fb946d7a4642b"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2ece858a2ea2c78b9839a38f255eaa477fe0d3917a54db56daf9735f764c1ab3"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.13962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address the inverse problem of recovering a degeneracy point within the diffusion coefficient of a one-dimensional complex parabolic equation by observing the normal derivative at one point of the boundary. The strongly degenerate case is analyzed. In particular, we derive sufficient conditions on the initial data that guarantee the stability and uniqueness of the solution obtained from a one-point measurement. Moreover, we present more general uniqueness theorems, which also cover the identification of the initial data, the coefficient of the zero order term and the degeneracy power, using","authors_text":"Anna Doubova, Piermarco Cannarsa, Veronica Danesi","cross_cats":[],"headline":"Sufficient initial data conditions guarantee unique and stable recovery of the degeneracy point from one boundary measurement in degenerate parabolic equations.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-17T13:34:58Z","title":"Reconstruction of degeneracy region and power for parabolic equations and systems"},"references":{"count":33,"internal_anchors":0,"resolved_work":33,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"M. Abramowitz, I. A. Stegun. Handbook of Mathematical Funct ions with Formulas, Graphs, and Mathematical Tables. vol. 55, U. S. Government Printing Oﬃce, Washington (1964)","work_id":"ef79a828-5840-4ca4-9f34-5a626aeaca71","year":1964},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"F. Alabau-Boussouira, P. Cannarsa, G. Fragnelli. Carleman estim ates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ., 6 (20 06), pp. 161–204","work_id":"90322f3f-36af-4dba-aed5-78ec842db5f1","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"J. Apraiz, J. Cheng, A. Doubova, E. Fern´ andez-Cara, M. Yam amoto. Uniqueness and nu- merical reconstruction for inverse problems dealing with interval s ize search. Inverse Probl. Imaging 16 (2022) ","work_id":"3f31ae92-4936-45cf-aeee-ed6ece86f480","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"F. Black, M. Scholes. The pricing of options and corporate liabilities . J. Polit. Econ. 81 (1973) 637–54","work_id":"f8a77a4f-5647-4b6a-9720-6b7c564e89da","year":1973},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"M. Campiti, G. Metafune, D. Pallara. Degenerate self-adjoint ev olution equations on the unit interval. Semigroup Forum, 57 (1998), pp. 1–36","work_id":"2618c254-1a6e-41e3-a99f-9d589b0bff7a","year":1998}],"snapshot_sha256":"7ec3e4eb0e14a3ec11d2f6e25b2306bb3183e2e765ceb79229aff24c54069d28"},"source":{"id":"2509.13962","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-18T16:25:08.547905Z","id":"8a5bd8aa-8fb6-4c8e-a532-68574148df8a","model_set":{"reader":"grok-4.3"},"one_line_summary":"Sufficient conditions on initial data guarantee unique and stable reconstruction of the degeneracy point, power, and related coefficients in strongly degenerate 1D parabolic equations and systems from one-point or time-dependent boundary observations.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Sufficient initial data conditions guarantee unique and stable recovery of the degeneracy point from one boundary measurement in degenerate parabolic equations.","strongest_claim":"We derive sufficient conditions on the initial data that guarantee the stability and uniqueness of the solution obtained from a one-point measurement. Moreover, we present more general uniqueness theorems, which also cover the identification of the initial data, the coefficient of the zero order term and the degeneracy power, using measurements taken over time.","weakest_assumption":"The analysis assumes that the solution admits an explicit representation in terms of Bessel functions for the spectral problem associated with the degenerate diffusion operator, which is invoked to obtain the uniqueness and stability results."}},"verdict_id":"8a5bd8aa-8fb6-4c8e-a532-68574148df8a"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b7e4c7d8b9e91e78b182a39322b198f637c5d49171f1f6e1858b4363919bcc33","target":"record","created_at":"2026-06-19T16:12:47Z","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":"7ddc21286cd5b11b75cbd5b8ed1295c3550092fd7a994ec49795a634ee33b117","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-17T13:34:58Z","title_canon_sha256":"16ce703695188c5025452ac4b6d1dd70723f90c02f89cf600a62dd6140975cb2"},"schema_version":"1.0","source":{"id":"2509.13962","kind":"arxiv","version":3}},"canonical_sha256":"47deb8fa01ae59512ceadcd390908e43b8320f6958819e849350c84942b720a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47deb8fa01ae59512ceadcd390908e43b8320f6958819e849350c84942b720a4","first_computed_at":"2026-06-19T16:12:47.788061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:47.788061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DKNZ7mEmppzG0D3juCkTZ2xP5MF+BJP/Bjpe0W4Kx5gn2GrMKCZUYqv+Go2ogAb4mXpU6sz6/ytV2nA3ZpUbCg==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:47.788530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.13962","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7e4c7d8b9e91e78b182a39322b198f637c5d49171f1f6e1858b4363919bcc33","sha256:f7b9badbe3a75c380f98c11882168843aed712f52f443f024d40bea3c37a43c6"],"state_sha256":"dd931519b6b08e8c3e38ebefb1d00f588b5b6033920ecfd15f5b4f3ee3545343"}