{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MS5TQRTBQBCCSWDIDW57BWJDSH","short_pith_number":"pith:MS5TQRTB","canonical_record":{"source":{"id":"1409.2899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-09T21:15:19Z","cross_cats_sorted":[],"title_canon_sha256":"f28d3421258ffb272377e5a2433486b3d32b8fb8171e203eaa63c01df7560a27","abstract_canon_sha256":"30763b5bdcbbac28bf2081e85df836a404185bc30f97460218d610502d7e9b12"},"schema_version":"1.0"},"canonical_sha256":"64bb38466180442958681dbbf0d92391f2ee12f830945edb813d3374a206a06e","source":{"kind":"arxiv","id":"1409.2899","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2899","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2899v1","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2899","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"MS5TQRTBQBCC","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS5TQRTBQBCCSWDI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS5TQRTB","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MS5TQRTBQBCCSWDIDW57BWJDSH","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2899","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-09T21:15:19Z","cross_cats_sorted":[],"title_canon_sha256":"f28d3421258ffb272377e5a2433486b3d32b8fb8171e203eaa63c01df7560a27","abstract_canon_sha256":"30763b5bdcbbac28bf2081e85df836a404185bc30f97460218d610502d7e9b12"},"schema_version":"1.0"},"canonical_sha256":"64bb38466180442958681dbbf0d92391f2ee12f830945edb813d3374a206a06e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:08.796575Z","signature_b64":"CLBJpL9InaJnJZMWZ/a8VfOy4RLO5fyI30Gv5MmuPtJ+KLMUkIJmBisgg5KcdvwOHwgLzXfcgGNMMvSZehpaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64bb38466180442958681dbbf0d92391f2ee12f830945edb813d3374a206a06e","last_reissued_at":"2026-05-18T02:43:08.796136Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:08.796136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2899","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":"2026-05-18T02:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6adKfVF/IHqBt8zv6JEKkTbAbwroOHJIU790aGQ5pGuWSE3MsKI1Ew9MG0m6i432yqUjaEFoFVfes7VVreXRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:26:49.140663Z"},"content_sha256":"8e6f0a071ed3198f8408a6aac8fa103d0d581eadac9f9ae64d45038df11b563a","schema_version":"1.0","event_id":"sha256:8e6f0a071ed3198f8408a6aac8fa103d0d581eadac9f9ae64d45038df11b563a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MS5TQRTBQBCCSWDIDW57BWJDSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong General Position","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Micha A. Perles, Moriah Sigron","submitted_at":"2014-09-09T21:15:19Z","abstract_excerpt":"We say that a finite set S of points in R^d is in \"strong general position\" if for any collection {F_1,..., F_r} of r pairwise disjoint subsets of S (1 <= r <= |S|) we have: d-dim (the intersection of aff F_1,aff F_2,...,aff F_r) = min{d+1, (d-dim aff F_1)+(d-dim aff F_2)+...+(d-dim aff F_r)}. In this paper we reduce the set of conditions that one has to check in order to determine if S is in \"strong general position\"."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2899","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":"2026-05-18T02:43:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mywaSzYL9lCHJhv9oD+a3CX3m7vAtyk2dV2xNCdEKOV5mIffh1A132FMgeJ5AD/EZ7ZzVH0NpovaM+fKhIw0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:26:49.141266Z"},"content_sha256":"2092fde2b2e60624df153974003723003cbb003278d84f17781d73a14f5c0c1e","schema_version":"1.0","event_id":"sha256:2092fde2b2e60624df153974003723003cbb003278d84f17781d73a14f5c0c1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/bundle.json","state_url":"https://pith.science/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/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":"2026-06-22T21:26:49Z","links":{"resolver":"https://pith.science/pith/MS5TQRTBQBCCSWDIDW57BWJDSH","bundle":"https://pith.science/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/bundle.json","state":"https://pith.science/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MS5TQRTBQBCCSWDIDW57BWJDSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MS5TQRTBQBCCSWDIDW57BWJDSH","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":"30763b5bdcbbac28bf2081e85df836a404185bc30f97460218d610502d7e9b12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-09T21:15:19Z","title_canon_sha256":"f28d3421258ffb272377e5a2433486b3d32b8fb8171e203eaa63c01df7560a27"},"schema_version":"1.0","source":{"id":"1409.2899","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2899","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2899v1","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2899","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"MS5TQRTBQBCC","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MS5TQRTBQBCCSWDI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MS5TQRTB","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:2092fde2b2e60624df153974003723003cbb003278d84f17781d73a14f5c0c1e","target":"graph","created_at":"2026-05-18T02:43:08Z","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":"We say that a finite set S of points in R^d is in \"strong general position\" if for any collection {F_1,..., F_r} of r pairwise disjoint subsets of S (1 <= r <= |S|) we have: d-dim (the intersection of aff F_1,aff F_2,...,aff F_r) = min{d+1, (d-dim aff F_1)+(d-dim aff F_2)+...+(d-dim aff F_r)}. In this paper we reduce the set of conditions that one has to check in order to determine if S is in \"strong general position\".","authors_text":"Micha A. Perles, Moriah Sigron","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-09T21:15:19Z","title":"Strong General Position"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2899","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":"sha256:8e6f0a071ed3198f8408a6aac8fa103d0d581eadac9f9ae64d45038df11b563a","target":"record","created_at":"2026-05-18T02:43:08Z","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":"30763b5bdcbbac28bf2081e85df836a404185bc30f97460218d610502d7e9b12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-09T21:15:19Z","title_canon_sha256":"f28d3421258ffb272377e5a2433486b3d32b8fb8171e203eaa63c01df7560a27"},"schema_version":"1.0","source":{"id":"1409.2899","kind":"arxiv","version":1}},"canonical_sha256":"64bb38466180442958681dbbf0d92391f2ee12f830945edb813d3374a206a06e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64bb38466180442958681dbbf0d92391f2ee12f830945edb813d3374a206a06e","first_computed_at":"2026-05-18T02:43:08.796136Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:08.796136Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CLBJpL9InaJnJZMWZ/a8VfOy4RLO5fyI30Gv5MmuPtJ+KLMUkIJmBisgg5KcdvwOHwgLzXfcgGNMMvSZehpaAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:08.796575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2899","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e6f0a071ed3198f8408a6aac8fa103d0d581eadac9f9ae64d45038df11b563a","sha256:2092fde2b2e60624df153974003723003cbb003278d84f17781d73a14f5c0c1e"],"state_sha256":"cc7de32264dcb4d25d1f07c5332d2bc2cd3c3bc42b761adb4b418ded4f6b9ec3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWkyBN7FtXLZkfmkXgEWeAPH7wODiGK+ChtaZBAkeE/harzuadTwajUmfZDQnTh0bKTFiGhsmRsAaPiV6sE2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:26:49.144381Z","bundle_sha256":"87218ad32d987693d0d60ccd0414d0a5ada516f8c8cc602c8ed3c11e1cc463cc"}}