{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PBOT36GOHN5DMYLRQVTDVZVMXX","short_pith_number":"pith:PBOT36GO","canonical_record":{"source":{"id":"2606.30348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T14:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"df04363d1b9406a899a0d727826994c833938c68f6d925a0cb2ec702eef5bd36","abstract_canon_sha256":"087d7b1e81fc7784fb48c71872c2bd8a21e862cac0abad376e2f412d6711b8e8"},"schema_version":"1.0"},"canonical_sha256":"785d3df8ce3b7a36617185663ae6acbdf4d9d358368f60f6ef23bd9376d67f20","source":{"kind":"arxiv","id":"2606.30348","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30348","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30348v1","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30348","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBOT36GOHN5D","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"PBOT36GOHN5DMYLR","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"PBOT36GO","created_at":"2026-06-30T02:18:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PBOT36GOHN5DMYLRQVTDVZVMXX","target":"record","payload":{"canonical_record":{"source":{"id":"2606.30348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T14:21:54Z","cross_cats_sorted":[],"title_canon_sha256":"df04363d1b9406a899a0d727826994c833938c68f6d925a0cb2ec702eef5bd36","abstract_canon_sha256":"087d7b1e81fc7784fb48c71872c2bd8a21e862cac0abad376e2f412d6711b8e8"},"schema_version":"1.0"},"canonical_sha256":"785d3df8ce3b7a36617185663ae6acbdf4d9d358368f60f6ef23bd9376d67f20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:11.366598Z","signature_b64":"+u+WKQZCo47Ncy++XcIv78YeCw/7HkrAfQOP9WdPowy8ouIY2CjFZ9o+RXXFv1WQutsWTsTKv6nUCrNHxm2gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"785d3df8ce3b7a36617185663ae6acbdf4d9d358368f60f6ef23bd9376d67f20","last_reissued_at":"2026-06-30T02:18:11.366092Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:11.366092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.30348","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":"2026-06-30T02:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d1Fqa5RGy8dDRzf8CnNuo8+FaFOPn/KjO3osuMOGoUafT+JKTdLB+f3aKfwBOqOWJtdx0FbWEeIEEyT1cEFOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:15:24.689236Z"},"content_sha256":"ebf60879bb03755824c7d8ee8c8544d521654f9085c89fb433d118ce456c3af9","schema_version":"1.0","event_id":"sha256:ebf60879bb03755824c7d8ee8c8544d521654f9085c89fb433d118ce456c3af9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PBOT36GOHN5DMYLRQVTDVZVMXX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Stable Coresets for Geometric Median via Uniform Sampling","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amir Carmel, Nir Petruschka, Robert Krauthgamer","submitted_at":"2026-06-29T14:21:54Z","abstract_excerpt":"The geometric median problem asks to find a point in $\\mathbb{R}^d$ that minimizes the sum of Euclidean distances to an input set. It is a classical problem in computational geometry and appears as a subroutine in numerous optimization tasks, many of which require the solution to satisfy additional structural constraints. A common approach to reduce the input size is to construct a coreset, which is a small weighted subset that faithfully represents the input for a specific optimization problem. Strong coresets preserve the cost of every candidate solution but require linear time to construct;"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30348","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/2606.30348/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":"2026-06-30T02:18:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umTLHxU5R0KbBCDurQIy2p4AG5Y0rYHk3bxenoPLxvokvDlhrmWDvKdKA/K7IAltWt6t68KxWOHT908IuqCJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T08:15:24.694771Z"},"content_sha256":"e7f70131f9a92e48988e81ceb8fe0e80e81440870637c6d8b8ce42d58535ea8e","schema_version":"1.0","event_id":"sha256:e7f70131f9a92e48988e81ceb8fe0e80e81440870637c6d8b8ce42d58535ea8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/bundle.json","state_url":"https://pith.science/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/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":"2026-07-01T08:15:24Z","links":{"resolver":"https://pith.science/pith/PBOT36GOHN5DMYLRQVTDVZVMXX","bundle":"https://pith.science/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/bundle.json","state":"https://pith.science/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBOT36GOHN5DMYLRQVTDVZVMXX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PBOT36GOHN5DMYLRQVTDVZVMXX","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":"087d7b1e81fc7784fb48c71872c2bd8a21e862cac0abad376e2f412d6711b8e8","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T14:21:54Z","title_canon_sha256":"df04363d1b9406a899a0d727826994c833938c68f6d925a0cb2ec702eef5bd36"},"schema_version":"1.0","source":{"id":"2606.30348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30348","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30348v1","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30348","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_12","alias_value":"PBOT36GOHN5D","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_16","alias_value":"PBOT36GOHN5DMYLR","created_at":"2026-06-30T02:18:11Z"},{"alias_kind":"pith_short_8","alias_value":"PBOT36GO","created_at":"2026-06-30T02:18:11Z"}],"graph_snapshots":[{"event_id":"sha256:e7f70131f9a92e48988e81ceb8fe0e80e81440870637c6d8b8ce42d58535ea8e","target":"graph","created_at":"2026-06-30T02:18:11Z","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/2606.30348/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The geometric median problem asks to find a point in $\\mathbb{R}^d$ that minimizes the sum of Euclidean distances to an input set. It is a classical problem in computational geometry and appears as a subroutine in numerous optimization tasks, many of which require the solution to satisfy additional structural constraints. A common approach to reduce the input size is to construct a coreset, which is a small weighted subset that faithfully represents the input for a specific optimization problem. Strong coresets preserve the cost of every candidate solution but require linear time to construct;","authors_text":"Amir Carmel, Nir Petruschka, Robert Krauthgamer","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T14:21:54Z","title":"Optimal Stable Coresets for Geometric Median via Uniform Sampling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30348","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:ebf60879bb03755824c7d8ee8c8544d521654f9085c89fb433d118ce456c3af9","target":"record","created_at":"2026-06-30T02:18:11Z","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":"087d7b1e81fc7784fb48c71872c2bd8a21e862cac0abad376e2f412d6711b8e8","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T14:21:54Z","title_canon_sha256":"df04363d1b9406a899a0d727826994c833938c68f6d925a0cb2ec702eef5bd36"},"schema_version":"1.0","source":{"id":"2606.30348","kind":"arxiv","version":1}},"canonical_sha256":"785d3df8ce3b7a36617185663ae6acbdf4d9d358368f60f6ef23bd9376d67f20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"785d3df8ce3b7a36617185663ae6acbdf4d9d358368f60f6ef23bd9376d67f20","first_computed_at":"2026-06-30T02:18:11.366092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:18:11.366092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+u+WKQZCo47Ncy++XcIv78YeCw/7HkrAfQOP9WdPowy8ouIY2CjFZ9o+RXXFv1WQutsWTsTKv6nUCrNHxm2gCg==","signature_status":"signed_v1","signed_at":"2026-06-30T02:18:11.366598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebf60879bb03755824c7d8ee8c8544d521654f9085c89fb433d118ce456c3af9","sha256:e7f70131f9a92e48988e81ceb8fe0e80e81440870637c6d8b8ce42d58535ea8e"],"state_sha256":"cc311131fee84ff8ab60762f00bfe0114dde0ae15bbc3bf5222b5e3367b4d1b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qieG982S5Gnf3Mn0zKgBj2nHQ6aoEqO7juF5mUbh7CD8RKdSfQBMZ5ElNoemoB8auNuOiLaVqfHfsSMkA2NxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T08:15:24.704506Z","bundle_sha256":"a61e32db532fe46e3897430530412628ebf0ec156044bd4cffc1a62359dcd287"}}