{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RLS2SMO3KDBYNY3J7U54DTTTZJ","short_pith_number":"pith:RLS2SMO3","canonical_record":{"source":{"id":"1807.03718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T15:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"0c05b4d6e18104ecf7e20fbdfbf44331ea8f2f8f84c53d79c630e18c8e5a734b","abstract_canon_sha256":"184784e1a7b54c67e1bbfbd878071c33596a6ff7f87fe9add0f3e0c19fffc6ae"},"schema_version":"1.0"},"canonical_sha256":"8ae5a931db50c386e369fd3bc1ce73ca64ee2e4d3ef709af62cbb9704b4145a7","source":{"kind":"arxiv","id":"1807.03718","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03718","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03718v1","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03718","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"RLS2SMO3KDBY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RLS2SMO3KDBYNY3J","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RLS2SMO3","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RLS2SMO3KDBYNY3J7U54DTTTZJ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.03718","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T15:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"0c05b4d6e18104ecf7e20fbdfbf44331ea8f2f8f84c53d79c630e18c8e5a734b","abstract_canon_sha256":"184784e1a7b54c67e1bbfbd878071c33596a6ff7f87fe9add0f3e0c19fffc6ae"},"schema_version":"1.0"},"canonical_sha256":"8ae5a931db50c386e369fd3bc1ce73ca64ee2e4d3ef709af62cbb9704b4145a7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:03.456093Z","signature_b64":"+F0hZe0dq9UrQufJrB+2gaRFy8XQtQGdQMuBcxLMYwEdfEdmiMBoU/fm6W3OuQKT01XMkqEtLlYoYdpkWTxNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ae5a931db50c386e369fd3bc1ce73ca64ee2e4d3ef709af62cbb9704b4145a7","last_reissued_at":"2026-05-18T00:11:03.455369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:03.455369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.03718","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":"2026-05-18T00:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xVS7nEn0aOtb9+kO/YKyH58w9aqzBtL8VuYJV3NrpzGVKPTj0zUDRybGROCPbpdoa/vggGNb0AWX0R4BvvssAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:46:22.454736Z"},"content_sha256":"4e56ae021dd9b2d3bf1fec2aadf5441f6f03bf6fd6f4864bd82fe6bff7092bea","schema_version":"1.0","event_id":"sha256:4e56ae021dd9b2d3bf1fec2aadf5441f6f03bf6fd6f4864bd82fe6bff7092bea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RLS2SMO3KDBYNY3J7U54DTTTZJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Space-Time Tradeoffs for kSUM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ely Porat, Isaac Goldstein, Moshe Lewenstein","submitted_at":"2018-07-10T15:42:17Z","abstract_excerpt":"In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied SUBSET-SUM problem, and a special case is the 3SUM problem that is extensively used for proving conditional hardness. Several works investigated the interplay between time and space in the context of SUBSET-SUM. Recently, improved time-space tradeoffs were proven for kSUM using both randomized and deterministic algorithms.\n  In this paper we obtain an improv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03718","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":""},"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":"2026-05-18T00:11:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0bvZ/5H0SMpIQ5rZ/xdbESbhroP5ebj8wZR7/DOW5MyS6gp0x2Ewf7b9qaQ8nS9sNwzqO5yh4H436ziPp5tCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:46:22.455085Z"},"content_sha256":"630a700b56b98374202d24e43440c906c2f779d42add377080bdaa2c1ff9889a","schema_version":"1.0","event_id":"sha256:630a700b56b98374202d24e43440c906c2f779d42add377080bdaa2c1ff9889a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/bundle.json","state_url":"https://pith.science/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/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":"2026-05-30T10:46:22Z","links":{"resolver":"https://pith.science/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ","bundle":"https://pith.science/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/bundle.json","state":"https://pith.science/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RLS2SMO3KDBYNY3J7U54DTTTZJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RLS2SMO3KDBYNY3J7U54DTTTZJ","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":"184784e1a7b54c67e1bbfbd878071c33596a6ff7f87fe9add0f3e0c19fffc6ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T15:42:17Z","title_canon_sha256":"0c05b4d6e18104ecf7e20fbdfbf44331ea8f2f8f84c53d79c630e18c8e5a734b"},"schema_version":"1.0","source":{"id":"1807.03718","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03718","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03718v1","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03718","created_at":"2026-05-18T00:11:03Z"},{"alias_kind":"pith_short_12","alias_value":"RLS2SMO3KDBY","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RLS2SMO3KDBYNY3J","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RLS2SMO3","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:630a700b56b98374202d24e43440c906c2f779d42add377080bdaa2c1ff9889a","target":"graph","created_at":"2026-05-18T00:11:03Z","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":"In the kSUM problem we are given an array of numbers $a_1,a_2,...,a_n$ and we are required to determine if there are $k$ different elements in this array such that their sum is 0. This problem is a parameterized version of the well-studied SUBSET-SUM problem, and a special case is the 3SUM problem that is extensively used for proving conditional hardness. Several works investigated the interplay between time and space in the context of SUBSET-SUM. Recently, improved time-space tradeoffs were proven for kSUM using both randomized and deterministic algorithms.\n  In this paper we obtain an improv","authors_text":"Ely Porat, Isaac Goldstein, Moshe Lewenstein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T15:42:17Z","title":"Improved Space-Time Tradeoffs for kSUM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03718","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":"sha256:4e56ae021dd9b2d3bf1fec2aadf5441f6f03bf6fd6f4864bd82fe6bff7092bea","target":"record","created_at":"2026-05-18T00:11:03Z","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":"184784e1a7b54c67e1bbfbd878071c33596a6ff7f87fe9add0f3e0c19fffc6ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T15:42:17Z","title_canon_sha256":"0c05b4d6e18104ecf7e20fbdfbf44331ea8f2f8f84c53d79c630e18c8e5a734b"},"schema_version":"1.0","source":{"id":"1807.03718","kind":"arxiv","version":1}},"canonical_sha256":"8ae5a931db50c386e369fd3bc1ce73ca64ee2e4d3ef709af62cbb9704b4145a7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae5a931db50c386e369fd3bc1ce73ca64ee2e4d3ef709af62cbb9704b4145a7","first_computed_at":"2026-05-18T00:11:03.455369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:03.455369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+F0hZe0dq9UrQufJrB+2gaRFy8XQtQGdQMuBcxLMYwEdfEdmiMBoU/fm6W3OuQKT01XMkqEtLlYoYdpkWTxNDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:03.456093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03718","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e56ae021dd9b2d3bf1fec2aadf5441f6f03bf6fd6f4864bd82fe6bff7092bea","sha256:630a700b56b98374202d24e43440c906c2f779d42add377080bdaa2c1ff9889a"],"state_sha256":"4ea5ac47c4f211e91d120fb213c52d013dd8ab74af59a921a9427d5fa110667b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7rZpBd/WzmuYKcHKw7QABrFyhTZfz+AvjBwCiW7zKjG21Z6d2cGlkwYUDbvDnqsKc8It3WoYUVstcMZRqpvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:46:22.457303Z","bundle_sha256":"778c5d435e194a1cc3605d169815a4bc4bbf01ce04bad3e7058582208a876365"}}