{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DWQYFK3L3BLVTIIDRK6OKRXVK4","short_pith_number":"pith:DWQYFK3L","canonical_record":{"source":{"id":"1707.01368","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-05T12:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"57812c744881589b83b4926ca644d6e2e65f273c397c461bdcbd58734d1dcd02","abstract_canon_sha256":"63fd2a6e195712e40d99d768260b1af922e6babef86717e7d415146f0ec86ea8"},"schema_version":"1.0"},"canonical_sha256":"1da182ab6bd85759a1038abce546f55720ffc4fca9f534650593108a4b4c98ed","source":{"kind":"arxiv","id":"1707.01368","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01368","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01368v3","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01368","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"pith_short_12","alias_value":"DWQYFK3L3BLV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DWQYFK3L3BLVTIID","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DWQYFK3L","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DWQYFK3L3BLVTIIDRK6OKRXVK4","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01368","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-05T12:44:20Z","cross_cats_sorted":[],"title_canon_sha256":"57812c744881589b83b4926ca644d6e2e65f273c397c461bdcbd58734d1dcd02","abstract_canon_sha256":"63fd2a6e195712e40d99d768260b1af922e6babef86717e7d415146f0ec86ea8"},"schema_version":"1.0"},"canonical_sha256":"1da182ab6bd85759a1038abce546f55720ffc4fca9f534650593108a4b4c98ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:32.519938Z","signature_b64":"ZqZydTdeKXqiJwGHfBHyknKcwuU/c3uqjHBqmiKO0EKO/A4nOYZ41ihZBfDahL91kJB2OixUKbgOzeBl6YqlDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1da182ab6bd85759a1038abce546f55720ffc4fca9f534650593108a4b4c98ed","last_reissued_at":"2026-05-18T00:11:32.519347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:32.519347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01368","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2uraLuOHzCS+9O4HXCYpvScbLrU3DuE3umA2gRp8HsUkL0jkrHp4apJQ9LO1xsGC1jaaktrwjp2gBn1OVd6ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:45:13.769956Z"},"content_sha256":"90e4a5747f6b138d526ae670b0dbc46644a3e558c3aa18be2459e4acd008a059","schema_version":"1.0","event_id":"sha256:90e4a5747f6b138d526ae670b0dbc46644a3e558c3aa18be2459e4acd008a059"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DWQYFK3L3BLVTIIDRK6OKRXVK4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to place an obstacle having a dihedral symmetry centered at a given point inside a disk so as to optimize the fundamental Dirichlet eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anisa M.H. Chorwadwala, Souvik Roy","submitted_at":"2017-07-05T12:44:20Z","abstract_excerpt":"A generic model for the shape optimization problems we consider in this paper is the optimization of the Dirichlet eigenvalues of the Laplace operator with a volume constraint. We deal with an obstacle placement problem which can be formulated as the following eigenvalue optimization problem: Fix two positive real numbers $r_1$ and $A$. We consider a disk $B\\subset \\mathbb{R}^2$ having radius $r_1$. We want to place an obstacle $P$ of area $A$ within $B$ so as to maximize or minimize the fundamental Dirichlet eigenvalue $\\lambda_1$ for the Laplacian on $B\\setminus P$. That is, we want to study"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01368","kind":"arxiv","version":3},"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":"2026-05-18T00:11:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zL0PkVQhdI0l8Lu1qeg1nkUDOVunemBvjKU9PebV3Pyd7+xYM6AhaWaNmCIkDY7QZUHoGXdCegn6bjcvUSrqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T01:45:13.770278Z"},"content_sha256":"ea130eec26a317828e429c07e7c914cde72fdafc07d0b041c907997f2ce52e87","schema_version":"1.0","event_id":"sha256:ea130eec26a317828e429c07e7c914cde72fdafc07d0b041c907997f2ce52e87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/bundle.json","state_url":"https://pith.science/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/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":"2026-06-27T01:45:13Z","links":{"resolver":"https://pith.science/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4","bundle":"https://pith.science/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/bundle.json","state":"https://pith.science/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWQYFK3L3BLVTIIDRK6OKRXVK4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DWQYFK3L3BLVTIIDRK6OKRXVK4","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":"63fd2a6e195712e40d99d768260b1af922e6babef86717e7d415146f0ec86ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-05T12:44:20Z","title_canon_sha256":"57812c744881589b83b4926ca644d6e2e65f273c397c461bdcbd58734d1dcd02"},"schema_version":"1.0","source":{"id":"1707.01368","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01368","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01368v3","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01368","created_at":"2026-05-18T00:11:32Z"},{"alias_kind":"pith_short_12","alias_value":"DWQYFK3L3BLV","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DWQYFK3L3BLVTIID","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DWQYFK3L","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:ea130eec26a317828e429c07e7c914cde72fdafc07d0b041c907997f2ce52e87","target":"graph","created_at":"2026-05-18T00:11:32Z","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":"A generic model for the shape optimization problems we consider in this paper is the optimization of the Dirichlet eigenvalues of the Laplace operator with a volume constraint. We deal with an obstacle placement problem which can be formulated as the following eigenvalue optimization problem: Fix two positive real numbers $r_1$ and $A$. We consider a disk $B\\subset \\mathbb{R}^2$ having radius $r_1$. We want to place an obstacle $P$ of area $A$ within $B$ so as to maximize or minimize the fundamental Dirichlet eigenvalue $\\lambda_1$ for the Laplacian on $B\\setminus P$. That is, we want to study","authors_text":"Anisa M.H. Chorwadwala, Souvik Roy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-05T12:44:20Z","title":"How to place an obstacle having a dihedral symmetry centered at a given point inside a disk so as to optimize the fundamental Dirichlet eigenvalue"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01368","kind":"arxiv","version":3},"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":"sha256:90e4a5747f6b138d526ae670b0dbc46644a3e558c3aa18be2459e4acd008a059","target":"record","created_at":"2026-05-18T00:11:32Z","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":"63fd2a6e195712e40d99d768260b1af922e6babef86717e7d415146f0ec86ea8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-07-05T12:44:20Z","title_canon_sha256":"57812c744881589b83b4926ca644d6e2e65f273c397c461bdcbd58734d1dcd02"},"schema_version":"1.0","source":{"id":"1707.01368","kind":"arxiv","version":3}},"canonical_sha256":"1da182ab6bd85759a1038abce546f55720ffc4fca9f534650593108a4b4c98ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1da182ab6bd85759a1038abce546f55720ffc4fca9f534650593108a4b4c98ed","first_computed_at":"2026-05-18T00:11:32.519347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:32.519347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZqZydTdeKXqiJwGHfBHyknKcwuU/c3uqjHBqmiKO0EKO/A4nOYZ41ihZBfDahL91kJB2OixUKbgOzeBl6YqlDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:32.519938Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01368","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e4a5747f6b138d526ae670b0dbc46644a3e558c3aa18be2459e4acd008a059","sha256:ea130eec26a317828e429c07e7c914cde72fdafc07d0b041c907997f2ce52e87"],"state_sha256":"8fe1513b1f18d7cdf6474f69a274390d4a8c3b4f2a1a09e3fec9eec69fc6de44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9bPf64xEuXTC7MN3PoMQxlXzJBb2Jk2t5ivAW+k/ZUnDfZb/FgWpar7Q4dr+WF1L1q3OF1/JsdCE5p2wlpEkBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T01:45:13.772048Z","bundle_sha256":"4b968c8b0e142928865c2f55d31dae14a15a0744a1d2d066a0cc8fb874164fb5"}}