{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:X4YQHEZLQAHDNTQDD2HO76KXJT","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":"713da1c8c3688d9fd76da39019f3d56a6819a24e3795c50837d69f600d12fcb2","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2026-05-29T04:40:26Z","title_canon_sha256":"025b7d5763fd115603e3ac12c7ec483e3706f9690a395c1275cfc2aa55d30baf"},"schema_version":"1.0","source":{"id":"2605.30835","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.30835","created_at":"2026-06-01T01:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"2605.30835v1","created_at":"2026-06-01T01:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30835","created_at":"2026-06-01T01:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"X4YQHEZLQAHD","created_at":"2026-06-01T01:03:20Z"},{"alias_kind":"pith_short_16","alias_value":"X4YQHEZLQAHDNTQD","created_at":"2026-06-01T01:03:20Z"},{"alias_kind":"pith_short_8","alias_value":"X4YQHEZL","created_at":"2026-06-01T01:03:20Z"}],"graph_snapshots":[{"event_id":"sha256:e51a5c0fddf8441c63649266627684dbdc33e9ca8bf0c38cf759b9985574139a","target":"graph","created_at":"2026-06-01T01:03:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.30835/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The group $\\E(X)$ of homotopy self-equivalences of a topological space $X$ is a well-known group in homotopy theory and has been studied by many people since it was first introduced in the late 1950s. $\\E$ is not a functor in the usual sense. In this paper we show that $\\E$ is a Lax functor from the category $\\mathscr Top$ of topological spaces to a strict $2$-category $\\op{Corr}_{\\mathscr Gr}$ of \\emph{correspondences} of groups.","authors_text":"Shoji Yokura, Toshihiro Yamaguchi","cross_cats":["math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2026-05-29T04:40:26Z","title":"The group of homotopy self-equivalences is a Lax functor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30835","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:e8476d210dc80728995e95bcd42709f920bcb1bb018a578ac5ea86594f3260c2","target":"record","created_at":"2026-06-01T01:03:20Z","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":"713da1c8c3688d9fd76da39019f3d56a6819a24e3795c50837d69f600d12fcb2","cross_cats_sorted":["math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AT","submitted_at":"2026-05-29T04:40:26Z","title_canon_sha256":"025b7d5763fd115603e3ac12c7ec483e3706f9690a395c1275cfc2aa55d30baf"},"schema_version":"1.0","source":{"id":"2605.30835","kind":"arxiv","version":1}},"canonical_sha256":"bf3103932b800e36ce031e8eeff9574cf7964e5828a538a82409bb77038fe78f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf3103932b800e36ce031e8eeff9574cf7964e5828a538a82409bb77038fe78f","first_computed_at":"2026-06-01T01:03:20.039588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:03:20.039588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XYGxZoQ7fBmJwBn4NdIhGE5mnB6nqx4VRJPAA/3nSYndWuqG5SRvunAgiyzAsMdA5jZ7V0ufZNYaH/oWab6FCw==","signature_status":"signed_v1","signed_at":"2026-06-01T01:03:20.040674Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.30835","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8476d210dc80728995e95bcd42709f920bcb1bb018a578ac5ea86594f3260c2","sha256:e51a5c0fddf8441c63649266627684dbdc33e9ca8bf0c38cf759b9985574139a"],"state_sha256":"1184d714b4164a50ae25f630d475b096f5b6780c7029f175c9d34d7aac700570"}