{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:AZITDB5V3XUGAEGTCH4AIDRHZG","short_pith_number":"pith:AZITDB5V","canonical_record":{"source":{"id":"2403.07676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-12T14:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"d078a54e21f469858b3c9f8a095f1aa01b8e0dde0400b45c82783308c8bac8f1","abstract_canon_sha256":"b8ed3a5f9afc36d40d5e76f4fe098ba9fbb1793addbf5cea7d012d88e3e4224e"},"schema_version":"1.0"},"canonical_sha256":"06513187b5dde86010d311f8040e27c9ae0d93622309e7a60227f36cb030c27e","source":{"kind":"arxiv","id":"2403.07676","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.07676","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"2403.07676v3","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.07676","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"AZITDB5V3XUG","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_16","alias_value":"AZITDB5V3XUGAEGT","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_8","alias_value":"AZITDB5V","created_at":"2026-07-05T11:07:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:AZITDB5V3XUGAEGTCH4AIDRHZG","target":"record","payload":{"canonical_record":{"source":{"id":"2403.07676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-12T14:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"d078a54e21f469858b3c9f8a095f1aa01b8e0dde0400b45c82783308c8bac8f1","abstract_canon_sha256":"b8ed3a5f9afc36d40d5e76f4fe098ba9fbb1793addbf5cea7d012d88e3e4224e"},"schema_version":"1.0"},"canonical_sha256":"06513187b5dde86010d311f8040e27c9ae0d93622309e7a60227f36cb030c27e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:57.088485Z","signature_b64":"hqRXzwR4ML73YrcmgnOopmj8a9xDsW8NPug+7yNjIjjF3SoiQKnsaeizFIjvxD7TsLcrX2FkHj/axOBneFIcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06513187b5dde86010d311f8040e27c9ae0d93622309e7a60227f36cb030c27e","last_reissued_at":"2026-07-05T11:07:57.087927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:57.087927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.07676","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RQPfsKuqQqeWbkwdSH1KsdzeOBBHxNu9/kazVL+dQYQZwrwVHLhq2M4ipFgfjAfJ4i1xUwrB1YowvhHcOC/nBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:22:04.101675Z"},"content_sha256":"9c9bb004911d080f5620751d16e7476b49a8f06ec1fa0df61c2efbd66816cc9b","schema_version":"1.0","event_id":"sha256:9c9bb004911d080f5620751d16e7476b49a8f06ec1fa0df61c2efbd66816cc9b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:AZITDB5V3XUGAEGTCH4AIDRHZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parametrized (higher) semiadditivity and the universality of spans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bastiaan Cnossen, Sil Linskens, Tobias Lenz","submitted_at":"2024-03-12T14:12:17Z","abstract_excerpt":"Semiadditivity of an $\\infty$-category, i.e. the existence of biproducts, provides it with useful algebraic structure in the form of a canonical enrichment in commutative monoids. This ultimately comes from the fact that the $\\infty$-category of commutative monoids is the universal semiadditive $\\infty$-category equipped with a finite-product-preserving functor to spaces, or equivalently that the $(2,1)$-category of spans of finite sets is the universal semiadditive $\\infty$-category. In this article, we prove a vast generalization of these facts in the context of parametrized semiadditivity, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07676","kind":"arxiv","version":3},"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/2403.07676/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":"2026-07-05T11:07:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vmQzGxoL8eORuZZKJufbd6iTfAR5kgoW7JrZ22VCzRvpOf8KINUS1+wtwcsf2TkN3hraw7KDa8gryEUhaHExCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:22:04.102173Z"},"content_sha256":"dd052bf88f5ccf40f123d4d4d5ad28519a5fc24920db5c8002c059def485d095","schema_version":"1.0","event_id":"sha256:dd052bf88f5ccf40f123d4d4d5ad28519a5fc24920db5c8002c059def485d095"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/bundle.json","state_url":"https://pith.science/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/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":"2026-08-13T03:22:04Z","links":{"resolver":"https://pith.science/pith/AZITDB5V3XUGAEGTCH4AIDRHZG","bundle":"https://pith.science/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/bundle.json","state":"https://pith.science/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AZITDB5V3XUGAEGTCH4AIDRHZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:AZITDB5V3XUGAEGTCH4AIDRHZG","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":"b8ed3a5f9afc36d40d5e76f4fe098ba9fbb1793addbf5cea7d012d88e3e4224e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-12T14:12:17Z","title_canon_sha256":"d078a54e21f469858b3c9f8a095f1aa01b8e0dde0400b45c82783308c8bac8f1"},"schema_version":"1.0","source":{"id":"2403.07676","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.07676","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"arxiv_version","alias_value":"2403.07676v3","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.07676","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_12","alias_value":"AZITDB5V3XUG","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_16","alias_value":"AZITDB5V3XUGAEGT","created_at":"2026-07-05T11:07:57Z"},{"alias_kind":"pith_short_8","alias_value":"AZITDB5V","created_at":"2026-07-05T11:07:57Z"}],"graph_snapshots":[{"event_id":"sha256:dd052bf88f5ccf40f123d4d4d5ad28519a5fc24920db5c8002c059def485d095","target":"graph","created_at":"2026-07-05T11:07:57Z","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/2403.07676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Semiadditivity of an $\\infty$-category, i.e. the existence of biproducts, provides it with useful algebraic structure in the form of a canonical enrichment in commutative monoids. This ultimately comes from the fact that the $\\infty$-category of commutative monoids is the universal semiadditive $\\infty$-category equipped with a finite-product-preserving functor to spaces, or equivalently that the $(2,1)$-category of spans of finite sets is the universal semiadditive $\\infty$-category. In this article, we prove a vast generalization of these facts in the context of parametrized semiadditivity, ","authors_text":"Bastiaan Cnossen, Sil Linskens, Tobias Lenz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-12T14:12:17Z","title":"Parametrized (higher) semiadditivity and the universality of spans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07676","kind":"arxiv","version":3},"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":"sha256:9c9bb004911d080f5620751d16e7476b49a8f06ec1fa0df61c2efbd66816cc9b","target":"record","created_at":"2026-07-05T11:07:57Z","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":"b8ed3a5f9afc36d40d5e76f4fe098ba9fbb1793addbf5cea7d012d88e3e4224e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2024-03-12T14:12:17Z","title_canon_sha256":"d078a54e21f469858b3c9f8a095f1aa01b8e0dde0400b45c82783308c8bac8f1"},"schema_version":"1.0","source":{"id":"2403.07676","kind":"arxiv","version":3}},"canonical_sha256":"06513187b5dde86010d311f8040e27c9ae0d93622309e7a60227f36cb030c27e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06513187b5dde86010d311f8040e27c9ae0d93622309e7a60227f36cb030c27e","first_computed_at":"2026-07-05T11:07:57.087927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:07:57.087927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hqRXzwR4ML73YrcmgnOopmj8a9xDsW8NPug+7yNjIjjF3SoiQKnsaeizFIjvxD7TsLcrX2FkHj/axOBneFIcBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:07:57.088485Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.07676","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c9bb004911d080f5620751d16e7476b49a8f06ec1fa0df61c2efbd66816cc9b","sha256:dd052bf88f5ccf40f123d4d4d5ad28519a5fc24920db5c8002c059def485d095"],"state_sha256":"8d2d78cdd9ddcae9a35536b12d07e34a78dd1faa6e858316f8740bca4883de50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HOmGunTYvTnRAd1VcMcmOrcaifcT1hwe92Nwo7CxT4VGPNxrNMgLNcBhi5/pnrtrAKNlVWQwR/lgIMOf8Yr3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T03:22:04.107008Z","bundle_sha256":"b9f4e08415e7700a94eec0182b34ac6e7c1be8c5c32c53f78d9698cf5d5bdbc9"}}