{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MTEQHN736WIVAMIDAUMJOCURD2","short_pith_number":"pith:MTEQHN73","schema_version":"1.0","canonical_sha256":"64c903b7fbf5915031030518970a911e84680f6f8003785937cdb3030eb69f87","source":{"kind":"arxiv","id":"2606.10608","version":1},"attestation_state":"computed","paper":{"title":"The isoperimetric problem for the Favard length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Plakhov, Roman Karasev","submitted_at":"2026-06-09T09:10:08Z","abstract_excerpt":"The Favard length of a Borel set $E$ on the Euclidean plane is the average length of its orthogonal projections (mean shadow). Here we solve the following problem: Minimize the Favard length in the class of planar Borel sets with unit area (2-dimensional Lebesgue measure). It is shown that a circle with unit area is a solution, as expected."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.10608","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-06-09T09:10:08Z","cross_cats_sorted":[],"title_canon_sha256":"c01cc67f024c60fd2bcb9fe12530aafddcf13fea7b8dfb98b5acf562b70d86b5","abstract_canon_sha256":"658def474ef0081c7f154090af0904fbb273b840dc41938570a5c82fa99a5200"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:10:29.295265Z","signature_b64":"Eik0/ghJ7kcAZPZiScvjjRLcbHg+jxAjmU2kNMQg1w/kZoA98OAIUxJcq4DOuwVwJEACq3K8elAJTWIj89L/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64c903b7fbf5915031030518970a911e84680f6f8003785937cdb3030eb69f87","last_reissued_at":"2026-06-10T01:10:29.294350Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:10:29.294350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The isoperimetric problem for the Favard length","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Plakhov, Roman Karasev","submitted_at":"2026-06-09T09:10:08Z","abstract_excerpt":"The Favard length of a Borel set $E$ on the Euclidean plane is the average length of its orthogonal projections (mean shadow). Here we solve the following problem: Minimize the Favard length in the class of planar Borel sets with unit area (2-dimensional Lebesgue measure). It is shown that a circle with unit area is a solution, as expected."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10608","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/2606.10608/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.10608","created_at":"2026-06-10T01:10:29.294517+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.10608v1","created_at":"2026-06-10T01:10:29.294517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.10608","created_at":"2026-06-10T01:10:29.294517+00:00"},{"alias_kind":"pith_short_12","alias_value":"MTEQHN736WIV","created_at":"2026-06-10T01:10:29.294517+00:00"},{"alias_kind":"pith_short_16","alias_value":"MTEQHN736WIVAMID","created_at":"2026-06-10T01:10:29.294517+00:00"},{"alias_kind":"pith_short_8","alias_value":"MTEQHN73","created_at":"2026-06-10T01:10:29.294517+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2","json":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2.json","graph_json":"https://pith.science/api/pith-number/MTEQHN736WIVAMIDAUMJOCURD2/graph.json","events_json":"https://pith.science/api/pith-number/MTEQHN736WIVAMIDAUMJOCURD2/events.json","paper":"https://pith.science/paper/MTEQHN73"},"agent_actions":{"view_html":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2","download_json":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2.json","view_paper":"https://pith.science/paper/MTEQHN73","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.10608&json=true","fetch_graph":"https://pith.science/api/pith-number/MTEQHN736WIVAMIDAUMJOCURD2/graph.json","fetch_events":"https://pith.science/api/pith-number/MTEQHN736WIVAMIDAUMJOCURD2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2/action/storage_attestation","attest_author":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2/action/author_attestation","sign_citation":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2/action/citation_signature","submit_replication":"https://pith.science/pith/MTEQHN736WIVAMIDAUMJOCURD2/action/replication_record"}},"created_at":"2026-06-10T01:10:29.294517+00:00","updated_at":"2026-06-10T01:10:29.294517+00:00"}