{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HWOBLPQ7AN5ZQOBL4RYXZ3KTA6","short_pith_number":"pith:HWOBLPQ7","canonical_record":{"source":{"id":"2411.16935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T21:09:50Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6a3624514f87275a726c4a76a9bb53f42fed6ad1e8c6289d9c86deab824bebcb","abstract_canon_sha256":"d3254a1e6829bbc30ce242d6e475e992679e20d3eb1b739318b78533bc590eb9"},"schema_version":"1.0"},"canonical_sha256":"3d9c15be1f037b98382be4717ced530791e00cf38419658431445e0bf512cbc1","source":{"kind":"arxiv","id":"2411.16935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16935","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16935v1","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16935","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"HWOBLPQ7AN5Z","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"HWOBLPQ7AN5ZQOBL","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"HWOBLPQ7","created_at":"2026-07-05T09:40:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HWOBLPQ7AN5ZQOBL4RYXZ3KTA6","target":"record","payload":{"canonical_record":{"source":{"id":"2411.16935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T21:09:50Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6a3624514f87275a726c4a76a9bb53f42fed6ad1e8c6289d9c86deab824bebcb","abstract_canon_sha256":"d3254a1e6829bbc30ce242d6e475e992679e20d3eb1b739318b78533bc590eb9"},"schema_version":"1.0"},"canonical_sha256":"3d9c15be1f037b98382be4717ced530791e00cf38419658431445e0bf512cbc1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:24.812577Z","signature_b64":"ge0c0bXUt6GVGT+fLXPfu0wt0S6AiGC4Wigjenv8WuMkNt7aPUWXgaMoPWTXEKngm7rZ9NBZycK+LmFHjc9MBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d9c15be1f037b98382be4717ced530791e00cf38419658431445e0bf512cbc1","last_reissued_at":"2026-07-05T09:40:24.812131Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:24.812131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.16935","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":"2026-07-05T09:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYSJq0htxW7fj7brcW/CEpzd67kjUShNaKXu8YOKF8bKBTKPA4ijoVvJhZ6/e5Z2V+SpZjaBFw3pNn24QnkIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:05:28.071625Z"},"content_sha256":"0917030ae1d337a7a9b19847d38877d47cfd5537a5f9b95da7f370023e1e176e","schema_version":"1.0","event_id":"sha256:0917030ae1d337a7a9b19847d38877d47cfd5537a5f9b95da7f370023e1e176e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HWOBLPQ7AN5ZQOBL4RYXZ3KTA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Buffon Needle Problem Over Convex Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"A. Iosevich, G. Hart, I. Li, M. Dannenberg, N. Skerrett, T. Le, W. Hagerstrom","submitted_at":"2024-11-25T21:09:50Z","abstract_excerpt":"We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length $l$ originating in a bounded convex set $X\\subset\\mathbb{R}^2$ lies entirely within $X$. Using techniques from convex geometry, we prove an isoperimetric type inequality, showing that among sets $X$ with equal perimeter, the disk maximizes this probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16935","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/2411.16935/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":"2026-07-05T09:40:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cztWVjHuFcC7ZR1lLgDXUf96bdWU9lmedlwk3d5AkTu2AlKYOQa1XV0QbL7QU4U5aburXeXhTterawxmJc7UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T01:05:28.072510Z"},"content_sha256":"e8419d1ed938557062e7bec8959f375cf00ccc0d6db2d647968df2794b68a3ac","schema_version":"1.0","event_id":"sha256:e8419d1ed938557062e7bec8959f375cf00ccc0d6db2d647968df2794b68a3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/bundle.json","state_url":"https://pith.science/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/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":"2026-08-13T01:05:28Z","links":{"resolver":"https://pith.science/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6","bundle":"https://pith.science/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/bundle.json","state":"https://pith.science/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWOBLPQ7AN5ZQOBL4RYXZ3KTA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HWOBLPQ7AN5ZQOBL4RYXZ3KTA6","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":"d3254a1e6829bbc30ce242d6e475e992679e20d3eb1b739318b78533bc590eb9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T21:09:50Z","title_canon_sha256":"6a3624514f87275a726c4a76a9bb53f42fed6ad1e8c6289d9c86deab824bebcb"},"schema_version":"1.0","source":{"id":"2411.16935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.16935","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"arxiv_version","alias_value":"2411.16935v1","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.16935","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_12","alias_value":"HWOBLPQ7AN5Z","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_16","alias_value":"HWOBLPQ7AN5ZQOBL","created_at":"2026-07-05T09:40:24Z"},{"alias_kind":"pith_short_8","alias_value":"HWOBLPQ7","created_at":"2026-07-05T09:40:24Z"}],"graph_snapshots":[{"event_id":"sha256:e8419d1ed938557062e7bec8959f375cf00ccc0d6db2d647968df2794b68a3ac","target":"graph","created_at":"2026-07-05T09:40:24Z","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/2411.16935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length $l$ originating in a bounded convex set $X\\subset\\mathbb{R}^2$ lies entirely within $X$. Using techniques from convex geometry, we prove an isoperimetric type inequality, showing that among sets $X$ with equal perimeter, the disk maximizes this probability.","authors_text":"A. Iosevich, G. Hart, I. Li, M. Dannenberg, N. Skerrett, T. Le, W. Hagerstrom","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T21:09:50Z","title":"Buffon Needle Problem Over Convex Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.16935","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":"sha256:0917030ae1d337a7a9b19847d38877d47cfd5537a5f9b95da7f370023e1e176e","target":"record","created_at":"2026-07-05T09:40:24Z","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":"d3254a1e6829bbc30ce242d6e475e992679e20d3eb1b739318b78533bc590eb9","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2024-11-25T21:09:50Z","title_canon_sha256":"6a3624514f87275a726c4a76a9bb53f42fed6ad1e8c6289d9c86deab824bebcb"},"schema_version":"1.0","source":{"id":"2411.16935","kind":"arxiv","version":1}},"canonical_sha256":"3d9c15be1f037b98382be4717ced530791e00cf38419658431445e0bf512cbc1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d9c15be1f037b98382be4717ced530791e00cf38419658431445e0bf512cbc1","first_computed_at":"2026-07-05T09:40:24.812131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:24.812131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ge0c0bXUt6GVGT+fLXPfu0wt0S6AiGC4Wigjenv8WuMkNt7aPUWXgaMoPWTXEKngm7rZ9NBZycK+LmFHjc9MBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:24.812577Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.16935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0917030ae1d337a7a9b19847d38877d47cfd5537a5f9b95da7f370023e1e176e","sha256:e8419d1ed938557062e7bec8959f375cf00ccc0d6db2d647968df2794b68a3ac"],"state_sha256":"1d753a439bc786cd0a45a1216882a555bb56c1408dce022531d35880e0b23796"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LeFNa+unOymn0M1LeR+sV8GDlkMONduCvMp9y+xU9D020d5Ucft5e9p/tQaQps8XRvJD0brqBj/Y7oio4z63Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T01:05:28.079195Z","bundle_sha256":"cf551e8cf9363c3089cbc257eca8298e131b69b30e21d9bfd3d6422d110a2bda"}}