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A complex $K$ is $r$-unavoidable if $\\pi(K)\\leq r$. Motivated by the problems of Tverberg-Van Kampen-Flores type, and inspired by the `constraint method' of Blagojevi\\'{c}, Frick, and Ziegler, arXiv:1401.0690 [math.CO], we study the combinatorics of $r$-unavoidable complexes."},"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":"1612.09487","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-30T13:33:17Z","cross_cats_sorted":[],"title_canon_sha256":"e18f171225b6cf0805f0c4a2d79fe5a74cd63391d0fd0e7c89d0f99dd6249ae2","abstract_canon_sha256":"0cb7c3872ac95b131ba7cfb20f0ba9beda5380fd4c49805ef5ad418d8cc7650b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.247767Z","signature_b64":"7/WC0PPiHQcN3evcdRUAx6hhl9vJQn3SfcGea0njnb9hzoahwM8Z9Oz9xcOl0b0100XxW+41GFCnzqz/j4NeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a631f8abb2218024de59f5dbc8d485cfaa424253cf3d6bd9332621b6e2db6c8","last_reissued_at":"2026-05-17T23:46:31.247123Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.247123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combinatorics of `unavoidable complexes'","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Du\\v{s}ko Joji\\'c, Marija Jeli\\'c Milutinovi\\'c, Marinko Timotijevi\\'c, Rade T. \\v{Z}ivaljevi\\'c, Sini\\v{s}a T. 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Motivated by the problems of Tverberg-Van Kampen-Flores type, and inspired by the `constraint method' of Blagojevi\\'{c}, Frick, and Ziegler, arXiv:1401.0690 [math.CO], we study the combinatorics of $r$-unavoidable complexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09487","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1612.09487","created_at":"2026-05-17T23:46:31.247230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.09487v2","created_at":"2026-05-17T23:46:31.247230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09487","created_at":"2026-05-17T23:46:31.247230+00:00"},{"alias_kind":"pith_short_12","alias_value":"FJRR7CV3EIMA","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FJRR7CV3EIMAETPF","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FJRR7CV3","created_at":"2026-05-18T12:30:15.759754+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/FJRR7CV3EIMAETPFT5O3ZDKILT","json":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT.json","graph_json":"https://pith.science/api/pith-number/FJRR7CV3EIMAETPFT5O3ZDKILT/graph.json","events_json":"https://pith.science/api/pith-number/FJRR7CV3EIMAETPFT5O3ZDKILT/events.json","paper":"https://pith.science/paper/FJRR7CV3"},"agent_actions":{"view_html":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT","download_json":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT.json","view_paper":"https://pith.science/paper/FJRR7CV3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.09487&json=true","fetch_graph":"https://pith.science/api/pith-number/FJRR7CV3EIMAETPFT5O3ZDKILT/graph.json","fetch_events":"https://pith.science/api/pith-number/FJRR7CV3EIMAETPFT5O3ZDKILT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT/action/storage_attestation","attest_author":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT/action/author_attestation","sign_citation":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT/action/citation_signature","submit_replication":"https://pith.science/pith/FJRR7CV3EIMAETPFT5O3ZDKILT/action/replication_record"}},"created_at":"2026-05-17T23:46:31.247230+00:00","updated_at":"2026-05-17T23:46:31.247230+00:00"}