{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EQMQUOU7WSD7TQZO2T7A5CS7AY","short_pith_number":"pith:EQMQUOU7","canonical_record":{"source":{"id":"1801.10401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-31T11:11:57Z","cross_cats_sorted":[],"title_canon_sha256":"052a0e247d6cc415a99576c89551ec74a675d489c4895bfabb5b8a3c7d13783e","abstract_canon_sha256":"b4bdade206394a7e5c7095f6a3619bd1e702699a1d91a01ba765bb597e84bcf6"},"schema_version":"1.0"},"canonical_sha256":"24190a3a9fb487f9c32ed4fe0e8a5f062d876fe41a60be7cf9c74a06db5c0599","source":{"kind":"arxiv","id":"1801.10401","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10401","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10401v1","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10401","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"EQMQUOU7WSD7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQMQUOU7WSD7TQZO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQMQUOU7","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EQMQUOU7WSD7TQZO2T7A5CS7AY","target":"record","payload":{"canonical_record":{"source":{"id":"1801.10401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-31T11:11:57Z","cross_cats_sorted":[],"title_canon_sha256":"052a0e247d6cc415a99576c89551ec74a675d489c4895bfabb5b8a3c7d13783e","abstract_canon_sha256":"b4bdade206394a7e5c7095f6a3619bd1e702699a1d91a01ba765bb597e84bcf6"},"schema_version":"1.0"},"canonical_sha256":"24190a3a9fb487f9c32ed4fe0e8a5f062d876fe41a60be7cf9c74a06db5c0599","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:40.911640Z","signature_b64":"+6cmgqP+H3oFOQjF3BAXHUmL92DypH/CqG12xOS47XTqPce65+tmS3kCUquD5Lywu6kgP8UFC8ixEVOyY18GBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24190a3a9fb487f9c32ed4fe0e8a5f062d876fe41a60be7cf9c74a06db5c0599","last_reissued_at":"2026-05-18T00:24:40.911073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:40.911073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.10401","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":"2026-05-18T00:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cH5dWoxScORgnn+rRR8tfYYhMtv2zXgu6RoJYS2dbiV5INme01T2gDbdQ7WqN0Hxidb9TKgDM6BCDD+2faftCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:16:32.999468Z"},"content_sha256":"c3272e080805d48b73fa5baeb5be9a128f73d625311b383f0fe0e75a137c68e3","schema_version":"1.0","event_id":"sha256:c3272e080805d48b73fa5baeb5be9a128f73d625311b383f0fe0e75a137c68e3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EQMQUOU7WSD7TQZO2T7A5CS7AY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Algorithms for Measuring the Funnel-likeness of DAGs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Hendrik Molter, Manuel Sorge, Marcelo Garlet Millani, Rolf Niedermeier","submitted_at":"2018-01-31T11:11:57Z","abstract_excerpt":"Funnels are a new natural subclass of DAGs. Intuitively, a DAG is a funnel if every source-sink path can be uniquely identified by one of its arcs. Funnels are an analog to trees for directed graphs that is more restrictive than DAGs but more expressive than in-/out-trees. Computational problems such as finding vertex-disjoint paths or tracking the origin of memes remain NP-hard on DAGs while on funnels they become solvable in polynomial time. Our main focus is the algorithmic complexity of finding out how funnel-like a given DAG is. To this end, we study the NP-hard problem of computing the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10401","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":"2026-05-18T00:24:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tIhxkPELp2bR/K0iKkjtP4+7PNiMwlJ8xbtji+luQ+B3NTmYFWBJcBT+Q1X2bvHPWt04p32OSwo6t7uKjTWbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:16:33.000134Z"},"content_sha256":"2bcbad142c31f1c097deb6f739718b4dc4d25d1a519deac9f754ca9960f33067","schema_version":"1.0","event_id":"sha256:2bcbad142c31f1c097deb6f739718b4dc4d25d1a519deac9f754ca9960f33067"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/bundle.json","state_url":"https://pith.science/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/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":"2026-06-08T18:16:33Z","links":{"resolver":"https://pith.science/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY","bundle":"https://pith.science/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/bundle.json","state":"https://pith.science/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EQMQUOU7WSD7TQZO2T7A5CS7AY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EQMQUOU7WSD7TQZO2T7A5CS7AY","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":"b4bdade206394a7e5c7095f6a3619bd1e702699a1d91a01ba765bb597e84bcf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-31T11:11:57Z","title_canon_sha256":"052a0e247d6cc415a99576c89551ec74a675d489c4895bfabb5b8a3c7d13783e"},"schema_version":"1.0","source":{"id":"1801.10401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10401","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10401v1","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10401","created_at":"2026-05-18T00:24:40Z"},{"alias_kind":"pith_short_12","alias_value":"EQMQUOU7WSD7","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EQMQUOU7WSD7TQZO","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EQMQUOU7","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:2bcbad142c31f1c097deb6f739718b4dc4d25d1a519deac9f754ca9960f33067","target":"graph","created_at":"2026-05-18T00:24:40Z","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":"Funnels are a new natural subclass of DAGs. Intuitively, a DAG is a funnel if every source-sink path can be uniquely identified by one of its arcs. Funnels are an analog to trees for directed graphs that is more restrictive than DAGs but more expressive than in-/out-trees. Computational problems such as finding vertex-disjoint paths or tracking the origin of memes remain NP-hard on DAGs while on funnels they become solvable in polynomial time. Our main focus is the algorithmic complexity of finding out how funnel-like a given DAG is. To this end, we study the NP-hard problem of computing the a","authors_text":"Hendrik Molter, Manuel Sorge, Marcelo Garlet Millani, Rolf Niedermeier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-31T11:11:57Z","title":"Efficient Algorithms for Measuring the Funnel-likeness of DAGs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10401","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:c3272e080805d48b73fa5baeb5be9a128f73d625311b383f0fe0e75a137c68e3","target":"record","created_at":"2026-05-18T00:24:40Z","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":"b4bdade206394a7e5c7095f6a3619bd1e702699a1d91a01ba765bb597e84bcf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-31T11:11:57Z","title_canon_sha256":"052a0e247d6cc415a99576c89551ec74a675d489c4895bfabb5b8a3c7d13783e"},"schema_version":"1.0","source":{"id":"1801.10401","kind":"arxiv","version":1}},"canonical_sha256":"24190a3a9fb487f9c32ed4fe0e8a5f062d876fe41a60be7cf9c74a06db5c0599","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24190a3a9fb487f9c32ed4fe0e8a5f062d876fe41a60be7cf9c74a06db5c0599","first_computed_at":"2026-05-18T00:24:40.911073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:40.911073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+6cmgqP+H3oFOQjF3BAXHUmL92DypH/CqG12xOS47XTqPce65+tmS3kCUquD5Lywu6kgP8UFC8ixEVOyY18GBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:40.911640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3272e080805d48b73fa5baeb5be9a128f73d625311b383f0fe0e75a137c68e3","sha256:2bcbad142c31f1c097deb6f739718b4dc4d25d1a519deac9f754ca9960f33067"],"state_sha256":"b3dd81eab41eeb7d59315cd93d4ec12d53db5ba748a5942f60aa01537beeacca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niT80WAVH/J+vR57fw0yUe9cBvt0Zf8PeE5yndjrRSPWdYVifUbkH0P+v4KdRM4X4le/XJ8+tueMXPf1/8aJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:16:33.004733Z","bundle_sha256":"6517857b76e851044df79c1cce8a6391ac7fdf3ea469e86e5ad0792122d8ea10"}}