{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SVCH3LXSQKFU7CI7Y7POH34BGN","short_pith_number":"pith:SVCH3LXS","canonical_record":{"source":{"id":"2608.09105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-10T04:23:36Z","cross_cats_sorted":[],"title_canon_sha256":"3cf2c0e6fa0195d31628a488c13a1c60b3a60610909c054be23b2e0bcdc66a9d","abstract_canon_sha256":"d339da2ba98479a75aeb25058f5e5a2dc6838138ab92d9c68ca80914199184de"},"schema_version":"1.0"},"canonical_sha256":"95447daef2828b4f891fc7dee3ef813352ba285b865f12b4bbd6f57b7ca768ce","source":{"kind":"arxiv","id":"2608.09105","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09105","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09105v1","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09105","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_12","alias_value":"SVCH3LXSQKFU","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_16","alias_value":"SVCH3LXSQKFU7CI7","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_8","alias_value":"SVCH3LXS","created_at":"2026-08-11T02:21:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SVCH3LXSQKFU7CI7Y7POH34BGN","target":"record","payload":{"canonical_record":{"source":{"id":"2608.09105","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-10T04:23:36Z","cross_cats_sorted":[],"title_canon_sha256":"3cf2c0e6fa0195d31628a488c13a1c60b3a60610909c054be23b2e0bcdc66a9d","abstract_canon_sha256":"d339da2ba98479a75aeb25058f5e5a2dc6838138ab92d9c68ca80914199184de"},"schema_version":"1.0"},"canonical_sha256":"95447daef2828b4f891fc7dee3ef813352ba285b865f12b4bbd6f57b7ca768ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-11T02:21:48.507715Z","signature_b64":"FEwg3ddT6+Gp2iA/Taboxoh2o5hx4Hz5Jq9qGlZ8m8aJu+yvO3AiCoidr9T596fPiyuVruFj5r7X0NcNxh1FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95447daef2828b4f891fc7dee3ef813352ba285b865f12b4bbd6f57b7ca768ce","last_reissued_at":"2026-08-11T02:21:48.505820Z","signature_status":"signed_v1","first_computed_at":"2026-08-11T02:21:48.505820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.09105","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":"2026-08-11T02:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xjGt9qp90Rui13GmawmznF2bjMpBxIkH8Dwno6P/bS8guq35nyOdE5hSAFhXvlhNcIol7hHxFIGsPHUFeAGzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T13:31:02.982732Z"},"content_sha256":"4d3e9c5c6d030196b5ed792bc3b7041f14ea8e8d4040f759cba700b112af5d67","schema_version":"1.0","event_id":"sha256:4d3e9c5c6d030196b5ed792bc3b7041f14ea8e8d4040f759cba700b112af5d67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SVCH3LXSQKFU7CI7Y7POH34BGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Longest convex chains with i.i.d. points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arnab Sen, Erik Bates","submitted_at":"2026-08-10T04:23:36Z","abstract_excerpt":"Sample $n$ i.i.d. points from a triangle, according to some bounded density function. Given two vertices $A,B$ of the triangle, what is the maximum number of samples that form a convex chain with initial point $A$ and terminal point $B$? We show that to leading order, the answer is $cn^{1/3}$, generalizing a result of Ambrus and B\\'ar\\'any that considered uniformly distributed points. Furthermore, we express the constant $c$ using a variational formula whose maximizer (if unique) gives the limiting curve formed by the longest convex chain. By comparison, for $n$ i.i.d. samples from the unit sq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09105","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/2608.09105/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":"2026-08-11T02:21:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IVRBrVmvvOrDQxg2+chCnCS0++Y92hCcLi124+TpX81YlEHtRsLJTqnucWXDT24OV6nEWIXu/oy1MdQ74qI/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T13:31:02.983303Z"},"content_sha256":"218c12622e3bba21229e61890c14a771e0d2c14bd55c125f5695d1d5d8659718","schema_version":"1.0","event_id":"sha256:218c12622e3bba21229e61890c14a771e0d2c14bd55c125f5695d1d5d8659718"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/bundle.json","state_url":"https://pith.science/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/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":"2026-08-20T13:31:02Z","links":{"resolver":"https://pith.science/pith/SVCH3LXSQKFU7CI7Y7POH34BGN","bundle":"https://pith.science/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/bundle.json","state":"https://pith.science/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SVCH3LXSQKFU7CI7Y7POH34BGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SVCH3LXSQKFU7CI7Y7POH34BGN","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":"d339da2ba98479a75aeb25058f5e5a2dc6838138ab92d9c68ca80914199184de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-10T04:23:36Z","title_canon_sha256":"3cf2c0e6fa0195d31628a488c13a1c60b3a60610909c054be23b2e0bcdc66a9d"},"schema_version":"1.0","source":{"id":"2608.09105","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.09105","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"arxiv_version","alias_value":"2608.09105v1","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.09105","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_12","alias_value":"SVCH3LXSQKFU","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_16","alias_value":"SVCH3LXSQKFU7CI7","created_at":"2026-08-11T02:21:48Z"},{"alias_kind":"pith_short_8","alias_value":"SVCH3LXS","created_at":"2026-08-11T02:21:48Z"}],"graph_snapshots":[{"event_id":"sha256:218c12622e3bba21229e61890c14a771e0d2c14bd55c125f5695d1d5d8659718","target":"graph","created_at":"2026-08-11T02:21:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.09105/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sample $n$ i.i.d. points from a triangle, according to some bounded density function. Given two vertices $A,B$ of the triangle, what is the maximum number of samples that form a convex chain with initial point $A$ and terminal point $B$? We show that to leading order, the answer is $cn^{1/3}$, generalizing a result of Ambrus and B\\'ar\\'any that considered uniformly distributed points. Furthermore, we express the constant $c$ using a variational formula whose maximizer (if unique) gives the limiting curve formed by the longest convex chain. By comparison, for $n$ i.i.d. samples from the unit sq","authors_text":"Arnab Sen, Erik Bates","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-10T04:23:36Z","title":"Longest convex chains with i.i.d. points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.09105","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":"sha256:4d3e9c5c6d030196b5ed792bc3b7041f14ea8e8d4040f759cba700b112af5d67","target":"record","created_at":"2026-08-11T02:21:48Z","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":"d339da2ba98479a75aeb25058f5e5a2dc6838138ab92d9c68ca80914199184de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-08-10T04:23:36Z","title_canon_sha256":"3cf2c0e6fa0195d31628a488c13a1c60b3a60610909c054be23b2e0bcdc66a9d"},"schema_version":"1.0","source":{"id":"2608.09105","kind":"arxiv","version":1}},"canonical_sha256":"95447daef2828b4f891fc7dee3ef813352ba285b865f12b4bbd6f57b7ca768ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95447daef2828b4f891fc7dee3ef813352ba285b865f12b4bbd6f57b7ca768ce","first_computed_at":"2026-08-11T02:21:48.505820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-11T02:21:48.505820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FEwg3ddT6+Gp2iA/Taboxoh2o5hx4Hz5Jq9qGlZ8m8aJu+yvO3AiCoidr9T596fPiyuVruFj5r7X0NcNxh1FBQ==","signature_status":"signed_v1","signed_at":"2026-08-11T02:21:48.507715Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.09105","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d3e9c5c6d030196b5ed792bc3b7041f14ea8e8d4040f759cba700b112af5d67","sha256:218c12622e3bba21229e61890c14a771e0d2c14bd55c125f5695d1d5d8659718"],"state_sha256":"edabb7c58b1a583dde910d0db78c5dbc31d69246c70299d7c10329fbca5dc16b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3icCWabklehPCiT96hJeKym6VUaVebGjcxsjoGGcskScF/F82Wc6s/zJkfeNPz0cQhrhvc8b6/ww9oXHPSUcCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T13:31:02.988720Z","bundle_sha256":"1f5387b3c7cb24e4bdefb1beeb1bb41d292b11bdf0dfa9d2faeb5da1ca7be50b"}}