{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:BJMM4WJU4IOPDELJW5O5UNKCFO","short_pith_number":"pith:BJMM4WJU","schema_version":"1.0","canonical_sha256":"0a58ce5934e21cf19169b75dda35422bb3f01230a302112414b2099a71e4c330","source":{"kind":"arxiv","id":"1207.2204","version":1},"attestation_state":"computed","paper":{"title":"Projective center point and Tverberg theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Benjamin Matschke, Roman Karasev","submitted_at":"2012-07-10T01:17:10Z","abstract_excerpt":"We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called \"dual\" center point and Tverberg theorems.\n  Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space."},"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":"1207.2204","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-07-10T01:17:10Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"83e213873e2f0bc0f3d4e8cbbc7fe41a77d4241cf1a15bdb5003366de0db8d8c","abstract_canon_sha256":"3452abdb6a0baa42db1cb30ffe0032688b9655afa689a5440dbc33e23d964758"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:15.306010Z","signature_b64":"tKDAATlT4mTjml2TqSPWL5RyS0P/aR6ftTnhlr9Cj7Oz+nhmV19+3K+IPm/POXOQv+A97bwfaL/0C5PjZ9A1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a58ce5934e21cf19169b75dda35422bb3f01230a302112414b2099a71e4c330","last_reissued_at":"2026-05-18T02:42:15.305161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:15.305161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Projective center point and Tverberg theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AT","authors_text":"Benjamin Matschke, Roman Karasev","submitted_at":"2012-07-10T01:17:10Z","abstract_excerpt":"We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called \"dual\" center point and Tverberg theorems.\n  Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2204","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1207.2204","created_at":"2026-05-18T02:42:15.305287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1207.2204v1","created_at":"2026-05-18T02:42:15.305287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2204","created_at":"2026-05-18T02:42:15.305287+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJMM4WJU4IOP","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJMM4WJU4IOPDELJ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJMM4WJU","created_at":"2026-05-18T12:27:01.376967+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/BJMM4WJU4IOPDELJW5O5UNKCFO","json":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO.json","graph_json":"https://pith.science/api/pith-number/BJMM4WJU4IOPDELJW5O5UNKCFO/graph.json","events_json":"https://pith.science/api/pith-number/BJMM4WJU4IOPDELJW5O5UNKCFO/events.json","paper":"https://pith.science/paper/BJMM4WJU"},"agent_actions":{"view_html":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO","download_json":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO.json","view_paper":"https://pith.science/paper/BJMM4WJU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1207.2204&json=true","fetch_graph":"https://pith.science/api/pith-number/BJMM4WJU4IOPDELJW5O5UNKCFO/graph.json","fetch_events":"https://pith.science/api/pith-number/BJMM4WJU4IOPDELJW5O5UNKCFO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO/action/storage_attestation","attest_author":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO/action/author_attestation","sign_citation":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO/action/citation_signature","submit_replication":"https://pith.science/pith/BJMM4WJU4IOPDELJW5O5UNKCFO/action/replication_record"}},"created_at":"2026-05-18T02:42:15.305287+00:00","updated_at":"2026-05-18T02:42:15.305287+00:00"}