{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EYYPADU3DBTYWL2XHGGQ2KTUAV","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":"93198ba2c8bc6aeb02a10b1659da8990203e57aaca22e1731da897bd244785e8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T16:39:02Z","title_canon_sha256":"d2d721b1753211a19e83b1c331b0b3a5aa651b34b684441d89d5edd5ce255d42"},"schema_version":"1.0","source":{"id":"2309.15058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.15058","created_at":"2026-07-05T07:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"2309.15058v2","created_at":"2026-07-05T07:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.15058","created_at":"2026-07-05T07:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"EYYPADU3DBTY","created_at":"2026-07-05T07:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"EYYPADU3DBTYWL2X","created_at":"2026-07-05T07:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"EYYPADU3","created_at":"2026-07-05T07:49:33Z"}],"graph_snapshots":[{"event_id":"sha256:79cfda72c2d2ebe94f2d18aa9f3818a60aee94fa35ac7414f3fd2aa9d2e28c9b","target":"graph","created_at":"2026-07-05T07:49:33Z","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/2309.15058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Orthogonal Calculus, first developed by Weiss in 1991, provides a calculus of functors for functors from real inner product spaces to spaces. Many of the functors to which Orthogonal Calculus has been applied since carry an additional lax symmetric monoidal structure which has so far been ignored. For instance, the functor $V \\mapsto \\text{BO}(V)$ admits maps $$\\text{BO}(V) \\times \\text{BO}(W) \\to \\text{BO}(V \\oplus W)$$ which determine a lax symmetric monoidal structure.\n  Our first main result, Corollary 4$.$2$.$0$.$2, states that the Taylor approximations of a lax symmetric monoidal functor","authors_text":"Leon Hendrian","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T16:39:02Z","title":"Monoidal Structures in Orthogonal Calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15058","kind":"arxiv","version":2},"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:be3832e66fbfefd0d0eff148f5eb1eb88b22f6574fb961385f6e1830deb04b11","target":"record","created_at":"2026-07-05T07:49:33Z","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":"93198ba2c8bc6aeb02a10b1659da8990203e57aaca22e1731da897bd244785e8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T16:39:02Z","title_canon_sha256":"d2d721b1753211a19e83b1c331b0b3a5aa651b34b684441d89d5edd5ce255d42"},"schema_version":"1.0","source":{"id":"2309.15058","kind":"arxiv","version":2}},"canonical_sha256":"2630f00e9b18678b2f57398d0d2a74054263304e745172f34b8656b75cbef60e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2630f00e9b18678b2f57398d0d2a74054263304e745172f34b8656b75cbef60e","first_computed_at":"2026-07-05T07:49:33.644513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:49:33.644513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vjkCw8dCLOVf5AGlB9LECilHSp9R41bx2q7u8m0I6W8B4r41iuuaGiy/kadKemy+Ft2W1JDcqOM3DdMzX39VAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:49:33.645119Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.15058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be3832e66fbfefd0d0eff148f5eb1eb88b22f6574fb961385f6e1830deb04b11","sha256:79cfda72c2d2ebe94f2d18aa9f3818a60aee94fa35ac7414f3fd2aa9d2e28c9b"],"state_sha256":"616f653d16ad3f4c1f6f2a89ef71e3e2f8a0cb94b66879fc2925723af3ed3e22"}