{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FIOPFXUEHJ27IWVGWINRQ64OE4","short_pith_number":"pith:FIOPFXUE","schema_version":"1.0","canonical_sha256":"2a1cf2de843a75f45aa6b21b187b8e270fa36d397dea5d6cde54649b0763fa1b","source":{"kind":"arxiv","id":"1503.00190","version":3},"attestation_state":"computed","paper":{"title":"Computing with Tangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Martin Grohe, Pascal Schweitzer","submitted_at":"2015-02-28T22:21:30Z","abstract_excerpt":"Tangles of graphs have been introduced by Robertson and Seymour in the context of their graph minor theory. Tangles may be viewed as describing \"k-connected components\" of a graph (though in a twisted way). They play an important role in graph minor theory. An interesting aspect of tangles is that they cannot only be defined for graphs, but more generally for arbitrary connectivity functions (that is, integer-valued submodular and symmetric set functions).\n  However, tangles are difficult to deal with algorithmically. To start with, it is unclear how to represent them, because they are familie"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.00190","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-28T22:21:30Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"689cbd9e79bab1cc5b497fbb9b86e61a9e26f927cac183a19c3aa33a1fc1fc0a","abstract_canon_sha256":"9c8ce9b037bc5ba139d7af59bfc1e16e07492a0c9ebf61ae9f0d2c20b8eb1824"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:44.627469Z","signature_b64":"2+DpBwM4UP1y5jUSvL6BGNtJZXdurFn/Av3dvE9W+p1wZ56TYzHNZyQBvm14j4n8mvyjB9j8rvBB+qCvnAiWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a1cf2de843a75f45aa6b21b187b8e270fa36d397dea5d6cde54649b0763fa1b","last_reissued_at":"2026-05-18T01:19:44.626789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:44.626789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing with Tangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Martin Grohe, Pascal Schweitzer","submitted_at":"2015-02-28T22:21:30Z","abstract_excerpt":"Tangles of graphs have been introduced by Robertson and Seymour in the context of their graph minor theory. Tangles may be viewed as describing \"k-connected components\" of a graph (though in a twisted way). They play an important role in graph minor theory. An interesting aspect of tangles is that they cannot only be defined for graphs, but more generally for arbitrary connectivity functions (that is, integer-valued submodular and symmetric set functions).\n  However, tangles are difficult to deal with algorithmically. To start with, it is unclear how to represent them, because they are familie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00190","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.00190","created_at":"2026-05-18T01:19:44.626894+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00190v3","created_at":"2026-05-18T01:19:44.626894+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00190","created_at":"2026-05-18T01:19:44.626894+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIOPFXUEHJ27","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIOPFXUEHJ27IWVG","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIOPFXUE","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4","json":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4.json","graph_json":"https://pith.science/api/pith-number/FIOPFXUEHJ27IWVGWINRQ64OE4/graph.json","events_json":"https://pith.science/api/pith-number/FIOPFXUEHJ27IWVGWINRQ64OE4/events.json","paper":"https://pith.science/paper/FIOPFXUE"},"agent_actions":{"view_html":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4","download_json":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4.json","view_paper":"https://pith.science/paper/FIOPFXUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00190&json=true","fetch_graph":"https://pith.science/api/pith-number/FIOPFXUEHJ27IWVGWINRQ64OE4/graph.json","fetch_events":"https://pith.science/api/pith-number/FIOPFXUEHJ27IWVGWINRQ64OE4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4/action/storage_attestation","attest_author":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4/action/author_attestation","sign_citation":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4/action/citation_signature","submit_replication":"https://pith.science/pith/FIOPFXUEHJ27IWVGWINRQ64OE4/action/replication_record"}},"created_at":"2026-05-18T01:19:44.626894+00:00","updated_at":"2026-05-18T01:19:44.626894+00:00"}