{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BL6FVSXNOJ7CAOR7JQOGJ7JOB3","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":"9421c233cfa335d19fb97837591018c4c4e227bcf979b3bf740f7ed2956121ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-24T03:37:50Z","title_canon_sha256":"7835b9d53a3b8f362480a981538326c89e86b87a28798d797a3e9464c9c18b16"},"schema_version":"1.0","source":{"id":"1609.07565","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07565","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07565v1","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07565","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"BL6FVSXNOJ7C","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BL6FVSXNOJ7CAOR7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BL6FVSXN","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:b2333593f6b67f3c6169f7dac0e26ea3fb6b5327422e23c15f222992faadc4d5","target":"graph","created_at":"2026-05-18T01:03:56Z","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":"The $s$-th higher topological complexity of a space $X$, $TC_s(X)$, can be estimated from above by homotopical methods, and from below by homological methods. We give a thorough analysis of the gap between such estimates when $X=RP^m$, the real projective space of dimension $m.$ In particular, we describe a number $r(m)$, which depends on the structure of zeros and ones in the binary expansion of $m$, and with the property that $TC_s(RP^m)$ is given by $sm$ with an error of at most one provided $s \\geq r(m)$ and $m \\not\\equiv 3 \\bmod 4$ (the error vanishes for even $m$). The latter fact appear","authors_text":"Aldo Guzm\\'an-S\\'aenz, Jes\\'us Gonz\\'alez, Natalia Cadavid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-24T03:37:50Z","title":"The stability of the higher topological complexity of real projective spaces: an approach to their immersion dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07565","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":"sha256:50862882e01e08723e8df02719f687cc17f58497f302c45cb6eb7a28ed0b7812","target":"record","created_at":"2026-05-18T01:03:56Z","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":"9421c233cfa335d19fb97837591018c4c4e227bcf979b3bf740f7ed2956121ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2016-09-24T03:37:50Z","title_canon_sha256":"7835b9d53a3b8f362480a981538326c89e86b87a28798d797a3e9464c9c18b16"},"schema_version":"1.0","source":{"id":"1609.07565","kind":"arxiv","version":1}},"canonical_sha256":"0afc5acaed727e203a3f4c1c64fd2e0ef3c05c7401ee9ab132f42b10262a9e63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0afc5acaed727e203a3f4c1c64fd2e0ef3c05c7401ee9ab132f42b10262a9e63","first_computed_at":"2026-05-18T01:03:56.059723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:56.059723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/FTYMi/jcQqi/4q1yS8x0VmtzoKdp90V/lrNA0KoRby2K/pjQCQR0LeQNN4VYoqkQud1aT7FmpQ0uuz3i8nbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:56.060407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07565","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50862882e01e08723e8df02719f687cc17f58497f302c45cb6eb7a28ed0b7812","sha256:b2333593f6b67f3c6169f7dac0e26ea3fb6b5327422e23c15f222992faadc4d5"],"state_sha256":"798483fd30d439662c2b7325853aaa72b4be64210d30b6b884a8c69bf6a91283"}