{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GZBV7WEV62QEQ7DKASMPCCUW32","short_pith_number":"pith:GZBV7WEV","canonical_record":{"source":{"id":"1702.01136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-03T19:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"b7cb8d75854c14e17a0857559e2888fe7474cdb2c06e18d64c594a67e117f305","abstract_canon_sha256":"e0a7a9bf235f7e1d9b50eae431957bd01b6fa6efd2dab87c1b8eb796cc47ce34"},"schema_version":"1.0"},"canonical_sha256":"36435fd895f6a0487c6a0498f10a96deacc2a1a0f47d0aa97c4f87e2e2bc9d70","source":{"kind":"arxiv","id":"1702.01136","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01136","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01136v2","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01136","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"pith_short_12","alias_value":"GZBV7WEV62QE","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZBV7WEV62QEQ7DK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZBV7WEV","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GZBV7WEV62QEQ7DKASMPCCUW32","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-03T19:35:00Z","cross_cats_sorted":[],"title_canon_sha256":"b7cb8d75854c14e17a0857559e2888fe7474cdb2c06e18d64c594a67e117f305","abstract_canon_sha256":"e0a7a9bf235f7e1d9b50eae431957bd01b6fa6efd2dab87c1b8eb796cc47ce34"},"schema_version":"1.0"},"canonical_sha256":"36435fd895f6a0487c6a0498f10a96deacc2a1a0f47d0aa97c4f87e2e2bc9d70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:09.695905Z","signature_b64":"jNpAtdRjiyDJitxS3BbxkjYgnwtRpM8jjdgkJ+f4jHLa4YF2YqMpFZpFIkjDLR7uacftJJV3zqWpoaO7+CZABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36435fd895f6a0487c6a0498f10a96deacc2a1a0f47d0aa97c4f87e2e2bc9d70","last_reissued_at":"2026-05-18T00:27:09.695151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:09.695151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01136","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:27:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8x/AlFtN4Q2jBlzPzJx7rartMImUjfo9zNhlEF89CVsN4LFHER16lHXxCU5sc+ygSbp6y6IxWP8VAE4e3zb5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:31:52.452100Z"},"content_sha256":"c31f4e4c340b71bf79875c6085fe70189e7b47c701bcfb0ac705c2112f8b2096","schema_version":"1.0","event_id":"sha256:c31f4e4c340b71bf79875c6085fe70189e7b47c701bcfb0ac705c2112f8b2096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GZBV7WEV62QEQ7DKASMPCCUW32","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Guarantees for Vertex Sparsification in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Gramoz Goranci, Monika Henzinger, Pan Peng","submitted_at":"2017-02-03T19:35:00Z","abstract_excerpt":"Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of vertices. We focus on the following notions:\n  (1) Given a digraph $G=(V,E)$ and terminal vertices $K \\subset V$ with $|K| = k$, a (vertex) reachability sparsifier of $G$ is a digraph $H=(V_H,E_H)$, $K \\subset V_H$ that preserves all reachability information among terminal pairs. In this work we introduce the notion of reachability-preserving minors (RPMs) , i.e., "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01136","kind":"arxiv","version":2},"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":"2026-05-18T00:27:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SThhGE5at+phbTJGn7zLUKwFnCTRmEi4uQKRaoTgAh5IFfcqVb2KalYvJIsb3WCwEaU3LxqmmDWbx7dUsoqvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:31:52.452852Z"},"content_sha256":"cee8fb210d04f7af62063eb67dfd9faba9fec872269da7a953dc57f2ec5e2315","schema_version":"1.0","event_id":"sha256:cee8fb210d04f7af62063eb67dfd9faba9fec872269da7a953dc57f2ec5e2315"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZBV7WEV62QEQ7DKASMPCCUW32/bundle.json","state_url":"https://pith.science/pith/GZBV7WEV62QEQ7DKASMPCCUW32/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZBV7WEV62QEQ7DKASMPCCUW32/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":"2026-06-10T22:31:52Z","links":{"resolver":"https://pith.science/pith/GZBV7WEV62QEQ7DKASMPCCUW32","bundle":"https://pith.science/pith/GZBV7WEV62QEQ7DKASMPCCUW32/bundle.json","state":"https://pith.science/pith/GZBV7WEV62QEQ7DKASMPCCUW32/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZBV7WEV62QEQ7DKASMPCCUW32/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GZBV7WEV62QEQ7DKASMPCCUW32","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":"e0a7a9bf235f7e1d9b50eae431957bd01b6fa6efd2dab87c1b8eb796cc47ce34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-03T19:35:00Z","title_canon_sha256":"b7cb8d75854c14e17a0857559e2888fe7474cdb2c06e18d64c594a67e117f305"},"schema_version":"1.0","source":{"id":"1702.01136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01136","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01136v2","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01136","created_at":"2026-05-18T00:27:09Z"},{"alias_kind":"pith_short_12","alias_value":"GZBV7WEV62QE","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GZBV7WEV62QEQ7DK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GZBV7WEV","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:cee8fb210d04f7af62063eb67dfd9faba9fec872269da7a953dc57f2ec5e2315","target":"graph","created_at":"2026-05-18T00:27:09Z","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":"Graph Sparsification aims at compressing large graphs into smaller ones while preserving important characteristics of the input graph. In this work we study Vertex Sparsifiers, i.e., sparsifiers whose goal is to reduce the number of vertices. We focus on the following notions:\n  (1) Given a digraph $G=(V,E)$ and terminal vertices $K \\subset V$ with $|K| = k$, a (vertex) reachability sparsifier of $G$ is a digraph $H=(V_H,E_H)$, $K \\subset V_H$ that preserves all reachability information among terminal pairs. In this work we introduce the notion of reachability-preserving minors (RPMs) , i.e., ","authors_text":"Gramoz Goranci, Monika Henzinger, Pan Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-03T19:35:00Z","title":"Improved Guarantees for Vertex Sparsification in Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01136","kind":"arxiv","version":2},"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:c31f4e4c340b71bf79875c6085fe70189e7b47c701bcfb0ac705c2112f8b2096","target":"record","created_at":"2026-05-18T00:27:09Z","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":"e0a7a9bf235f7e1d9b50eae431957bd01b6fa6efd2dab87c1b8eb796cc47ce34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-03T19:35:00Z","title_canon_sha256":"b7cb8d75854c14e17a0857559e2888fe7474cdb2c06e18d64c594a67e117f305"},"schema_version":"1.0","source":{"id":"1702.01136","kind":"arxiv","version":2}},"canonical_sha256":"36435fd895f6a0487c6a0498f10a96deacc2a1a0f47d0aa97c4f87e2e2bc9d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36435fd895f6a0487c6a0498f10a96deacc2a1a0f47d0aa97c4f87e2e2bc9d70","first_computed_at":"2026-05-18T00:27:09.695151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:09.695151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jNpAtdRjiyDJitxS3BbxkjYgnwtRpM8jjdgkJ+f4jHLa4YF2YqMpFZpFIkjDLR7uacftJJV3zqWpoaO7+CZABg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:09.695905Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c31f4e4c340b71bf79875c6085fe70189e7b47c701bcfb0ac705c2112f8b2096","sha256:cee8fb210d04f7af62063eb67dfd9faba9fec872269da7a953dc57f2ec5e2315"],"state_sha256":"342d67884d3dcc60df21002de5530f1e2e0a11d65b74b6f854c6d511f1b76374"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JR1mnbZy23kAb2ejzwk1xkNK5o38CDDaK/ZM+JZRtLvuB8xkAOI6MPuP2Gu3juLcfosmZcrCMaLeFGfvdgNeDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:31:52.456935Z","bundle_sha256":"eaa28350bbbf93765d0498fc28b2877860cbed8fa765d46f7c682077727abb09"}}