{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:F4DYWA36S6T4BAMN73LXKJVD7R","short_pith_number":"pith:F4DYWA36","canonical_record":{"source":{"id":"1702.07669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-24T17:18:02Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"be85b86bd7e39ef1004d4f3cd327cc6b3699a2c74413a860d81e93ad919eef3b","abstract_canon_sha256":"af173d2c833be3b43df60e54879336b7aa1ee2bad3f41c2797fb4a2489833968"},"schema_version":"1.0"},"canonical_sha256":"2f078b037e97a7c0818dfed77526a3fc550a5f060c8d6835dd0e0062e2f27467","source":{"kind":"arxiv","id":"1702.07669","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07669","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07669v2","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07669","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"F4DYWA36S6T4","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F4DYWA36S6T4BAMN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F4DYWA36","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:F4DYWA36S6T4BAMN73LXKJVD7R","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07669","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-24T17:18:02Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"be85b86bd7e39ef1004d4f3cd327cc6b3699a2c74413a860d81e93ad919eef3b","abstract_canon_sha256":"af173d2c833be3b43df60e54879336b7aa1ee2bad3f41c2797fb4a2489833968"},"schema_version":"1.0"},"canonical_sha256":"2f078b037e97a7c0818dfed77526a3fc550a5f060c8d6835dd0e0062e2f27467","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:03.966740Z","signature_b64":"YMZAOP85ZeQVY7mkonWt9E5fq8mOFkylbex8LfUA9TcaSZmcHS3YLk2Vc4oMmjiGP5y0TLS8fz5zUkyXw3eGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f078b037e97a7c0818dfed77526a3fc550a5f060c8d6835dd0e0062e2f27467","last_reissued_at":"2026-05-17T23:47:03.966064Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:03.966064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07669","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":"2026-05-17T23:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hjCpmM1QDKHapc3T8I0YJfnTz4//b0hF3DKl6oCPwLMaxUbIvi6/uYBMJ6lx0ZvtqffY4D2+JfWJBAPB84FBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:26:10.343483Z"},"content_sha256":"066db742ea24539ff4cf948335ad6d5d2eb47437a0f95b77defcaf3bbc5e7f30","schema_version":"1.0","event_id":"sha256:066db742ea24539ff4cf948335ad6d5d2eb47437a0f95b77defcaf3bbc5e7f30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:F4DYWA36S6T4BAMN73LXKJVD7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On problems equivalent to (min,+)-convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Karol W\\k{e}grzycki, Marcin Mucha, Marek Cygan, Micha{\\l} W{\\l}odarczyk","submitted_at":"2017-02-24T17:18:02Z","abstract_excerpt":"In recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower bounds -- reductions from a problem assumed to be hard. The hard problems include 3SUM, All-Pairs Shortest Path, SAT, Orthogonal Vectors, and others.\n  In the $(\\min,+)$-convolution problem, the goal is to compute a sequence $(c[i])^{n-1}_{i=0}$, where $c[k] = $ $\\min_{i=0,\\ldots,k} $ $\\{a[i] $ $+$ $b[k-i]\\}$, given sequences $(a[i])^{n-1}_{i=0}$ and $(b[i])_{i=0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07669","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":"2026-05-17T23:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kURYGyMcpq2wX3qXguMCaffQUDgkQHC/ndoiILufmbyMQnoflpfZt471UnuLutno7iqj6oLFliujPaHyDqHVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:26:10.344135Z"},"content_sha256":"a37e661c7af09087374d32fabec130a6373c3619b8b38c709aa5f31f0900984d","schema_version":"1.0","event_id":"sha256:a37e661c7af09087374d32fabec130a6373c3619b8b38c709aa5f31f0900984d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F4DYWA36S6T4BAMN73LXKJVD7R/bundle.json","state_url":"https://pith.science/pith/F4DYWA36S6T4BAMN73LXKJVD7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F4DYWA36S6T4BAMN73LXKJVD7R/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":"2026-06-11T03:26:10Z","links":{"resolver":"https://pith.science/pith/F4DYWA36S6T4BAMN73LXKJVD7R","bundle":"https://pith.science/pith/F4DYWA36S6T4BAMN73LXKJVD7R/bundle.json","state":"https://pith.science/pith/F4DYWA36S6T4BAMN73LXKJVD7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F4DYWA36S6T4BAMN73LXKJVD7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:F4DYWA36S6T4BAMN73LXKJVD7R","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":"af173d2c833be3b43df60e54879336b7aa1ee2bad3f41c2797fb4a2489833968","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-24T17:18:02Z","title_canon_sha256":"be85b86bd7e39ef1004d4f3cd327cc6b3699a2c74413a860d81e93ad919eef3b"},"schema_version":"1.0","source":{"id":"1702.07669","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07669","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07669v2","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07669","created_at":"2026-05-17T23:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"F4DYWA36S6T4","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"F4DYWA36S6T4BAMN","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"F4DYWA36","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:a37e661c7af09087374d32fabec130a6373c3619b8b38c709aa5f31f0900984d","target":"graph","created_at":"2026-05-17T23:47:03Z","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 recent years, significant progress has been made in explaining the apparent hardness of improving upon the naive solutions for many fundamental polynomially solvable problems. This progress has come in the form of conditional lower bounds -- reductions from a problem assumed to be hard. The hard problems include 3SUM, All-Pairs Shortest Path, SAT, Orthogonal Vectors, and others.\n  In the $(\\min,+)$-convolution problem, the goal is to compute a sequence $(c[i])^{n-1}_{i=0}$, where $c[k] = $ $\\min_{i=0,\\ldots,k} $ $\\{a[i] $ $+$ $b[k-i]\\}$, given sequences $(a[i])^{n-1}_{i=0}$ and $(b[i])_{i=0","authors_text":"Karol W\\k{e}grzycki, Marcin Mucha, Marek Cygan, Micha{\\l} W{\\l}odarczyk","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-24T17:18:02Z","title":"On problems equivalent to (min,+)-convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07669","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":"sha256:066db742ea24539ff4cf948335ad6d5d2eb47437a0f95b77defcaf3bbc5e7f30","target":"record","created_at":"2026-05-17T23:47:03Z","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":"af173d2c833be3b43df60e54879336b7aa1ee2bad3f41c2797fb4a2489833968","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-24T17:18:02Z","title_canon_sha256":"be85b86bd7e39ef1004d4f3cd327cc6b3699a2c74413a860d81e93ad919eef3b"},"schema_version":"1.0","source":{"id":"1702.07669","kind":"arxiv","version":2}},"canonical_sha256":"2f078b037e97a7c0818dfed77526a3fc550a5f060c8d6835dd0e0062e2f27467","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f078b037e97a7c0818dfed77526a3fc550a5f060c8d6835dd0e0062e2f27467","first_computed_at":"2026-05-17T23:47:03.966064Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:03.966064Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMZAOP85ZeQVY7mkonWt9E5fq8mOFkylbex8LfUA9TcaSZmcHS3YLk2Vc4oMmjiGP5y0TLS8fz5zUkyXw3eGAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:03.966740Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07669","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:066db742ea24539ff4cf948335ad6d5d2eb47437a0f95b77defcaf3bbc5e7f30","sha256:a37e661c7af09087374d32fabec130a6373c3619b8b38c709aa5f31f0900984d"],"state_sha256":"fcb8cd6264128845a238a70776e01df9f2e2eb59e52cc1231c1eb69dca982f67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNAWy8NpjkUQWJrCFZwfRRKPUftE0sQLli+cPE4LkANocXWBHb1sH7AhLAdTo4SbX6sL4/UQhP6rpWp8M2qnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:26:10.348302Z","bundle_sha256":"21cacb4c0e6c2e047c4cf940206928e506007eedf8f6f438642c6db3985e3aed"}}