{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:EYYPADU3DBTYWL2XHGGQ2KTUAV","short_pith_number":"pith:EYYPADU3","canonical_record":{"source":{"id":"2309.15058","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T16:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"d2d721b1753211a19e83b1c331b0b3a5aa651b34b684441d89d5edd5ce255d42","abstract_canon_sha256":"93198ba2c8bc6aeb02a10b1659da8990203e57aaca22e1731da897bd244785e8"},"schema_version":"1.0"},"canonical_sha256":"2630f00e9b18678b2f57398d0d2a74054263304e745172f34b8656b75cbef60e","source":{"kind":"arxiv","id":"2309.15058","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:EYYPADU3DBTYWL2XHGGQ2KTUAV","target":"record","payload":{"canonical_record":{"source":{"id":"2309.15058","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.AT","submitted_at":"2023-09-26T16:39:02Z","cross_cats_sorted":[],"title_canon_sha256":"d2d721b1753211a19e83b1c331b0b3a5aa651b34b684441d89d5edd5ce255d42","abstract_canon_sha256":"93198ba2c8bc6aeb02a10b1659da8990203e57aaca22e1731da897bd244785e8"},"schema_version":"1.0"},"canonical_sha256":"2630f00e9b18678b2f57398d0d2a74054263304e745172f34b8656b75cbef60e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:49:33.645119Z","signature_b64":"vjkCw8dCLOVf5AGlB9LECilHSp9R41bx2q7u8m0I6W8B4r41iuuaGiy/kadKemy+Ft2W1JDcqOM3DdMzX39VAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2630f00e9b18678b2f57398d0d2a74054263304e745172f34b8656b75cbef60e","last_reissued_at":"2026-07-05T07:49:33.644513Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:49:33.644513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.15058","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rZxCszrQujZP81YQrKZvzzgEMMWRk5U11T1Y4rKSlyDqEWv0iS70UU9m9HfUwHlDNw26rPJmQZ4p7MHPm4KQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T12:25:00.386698Z"},"content_sha256":"be3832e66fbfefd0d0eff148f5eb1eb88b22f6574fb961385f6e1830deb04b11","schema_version":"1.0","event_id":"sha256:be3832e66fbfefd0d0eff148f5eb1eb88b22f6574fb961385f6e1830deb04b11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:EYYPADU3DBTYWL2XHGGQ2KTUAV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monoidal Structures in Orthogonal Calculus","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Leon Hendrian","submitted_at":"2023-09-26T16:39:02Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15058","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.15058/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:49:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zLh8lSRrBEeY2TRWNAvi7UyeIzIGDVktM1CXj35TTm2uV8shkcv3wgcQJ/YxfC24NH/BwIlrsM+ZK8dIOxBsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T12:25:00.387231Z"},"content_sha256":"79cfda72c2d2ebe94f2d18aa9f3818a60aee94fa35ac7414f3fd2aa9d2e28c9b","schema_version":"1.0","event_id":"sha256:79cfda72c2d2ebe94f2d18aa9f3818a60aee94fa35ac7414f3fd2aa9d2e28c9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/bundle.json","state_url":"https://pith.science/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/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":"2026-08-02T12:25:00Z","links":{"resolver":"https://pith.science/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV","bundle":"https://pith.science/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/bundle.json","state":"https://pith.science/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EYYPADU3DBTYWL2XHGGQ2KTUAV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D88wPykxk56+leuJ7QzqL2afvSWwlIGoMk7GGN8fXalbbyT/ArV+lgrF17vAdp/c7CJzzpea2Vkyuwf4CpEmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T12:25:00.393161Z","bundle_sha256":"187a71073968f2f49476d969bf731a7f6430bdcf5fdba06ccf6349b93003d9c5"}}