{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MUWNW3HAZ4GXR5WS6R3QZKECEV","short_pith_number":"pith:MUWNW3HA","canonical_record":{"source":{"id":"1307.8088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-30T19:13:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3ffad185b237c2be209a6c6540c205e77657f3afd84c41bc4067664795d769f8","abstract_canon_sha256":"49da223d25736d8d6887f5c0f266818ad5836a2d2fc06052c99c62ffeefdbaae"},"schema_version":"1.0"},"canonical_sha256":"652cdb6ce0cf0d78f6d2f4770ca882256e44bf9d0f1e0c6c89efeeacc2df3123","source":{"kind":"arxiv","id":"1307.8088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8088","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8088v1","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8088","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"MUWNW3HAZ4GX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MUWNW3HAZ4GXR5WS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MUWNW3HA","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MUWNW3HAZ4GXR5WS6R3QZKECEV","target":"record","payload":{"canonical_record":{"source":{"id":"1307.8088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-30T19:13:30Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"3ffad185b237c2be209a6c6540c205e77657f3afd84c41bc4067664795d769f8","abstract_canon_sha256":"49da223d25736d8d6887f5c0f266818ad5836a2d2fc06052c99c62ffeefdbaae"},"schema_version":"1.0"},"canonical_sha256":"652cdb6ce0cf0d78f6d2f4770ca882256e44bf9d0f1e0c6c89efeeacc2df3123","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:12.455710Z","signature_b64":"R/Ldr12GMTNfxNSKIjJ5Y/UKogxGYaUzQrIczxuAbsX+AY7PFT4SyGQwcMAxe0hqD1owinoT7IzXtFAMlRCkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652cdb6ce0cf0d78f6d2f4770ca882256e44bf9d0f1e0c6c89efeeacc2df3123","last_reissued_at":"2026-05-18T03:17:12.455007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:12.455007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.8088","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H5ts3/1/3z48GM2dSE82GquanVYfmw8GOZHK87huzW35RAEvjRM1vk2hhE9nMx0P3BTqhS5IZEzvvZdGBVWDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:41:22.799828Z"},"content_sha256":"8ca400bf26a05aeb7308b73481d03abd10817d4e0873ff5167bb7494a906628c","schema_version":"1.0","event_id":"sha256:8ca400bf26a05aeb7308b73481d03abd10817d4e0873ff5167bb7494a906628c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MUWNW3HAZ4GXR5WS6R3QZKECEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz-Schwartz extensive quantities and vector-valued integration in closed categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.FA","authors_text":"Rory B. B. Lucyshyn-Wright","submitted_at":"2013-07-30T19:13:30Z","abstract_excerpt":"We develop aspects of functional analysis in an abstract axiomatic setting, through monoidal and enriched category theory. We work in a given closed category, whose objects we call spaces, and we study R-module objects therein (or algebras of a commutative monad), which we call linear spaces. Building on ideas of Lawvere and Kock, we study functionals on the space of scalar-valued maps, including compactly-supported Radon measures and Schwartz distributions. We develop an abstract theory of vector-valued integration with respect to these scalar functionals and their relatives. We study three a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8088","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T03:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fSHQzxIbhwO08paD6/sMCZRJIzIGvSnQYjnsj01LiBN0QSfu42WSH+tAw2Oq+mGTnI0i1aRTmfsdu55b44xxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T10:41:22.800172Z"},"content_sha256":"4b712dbfc5de7a36f9f74cf00f2cf17faf118d3a0c9c0b582dd2cb3d206a52e8","schema_version":"1.0","event_id":"sha256:4b712dbfc5de7a36f9f74cf00f2cf17faf118d3a0c9c0b582dd2cb3d206a52e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/bundle.json","state_url":"https://pith.science/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/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":"2026-06-05T10:41:22Z","links":{"resolver":"https://pith.science/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV","bundle":"https://pith.science/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/bundle.json","state":"https://pith.science/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUWNW3HAZ4GXR5WS6R3QZKECEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MUWNW3HAZ4GXR5WS6R3QZKECEV","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":"49da223d25736d8d6887f5c0f266818ad5836a2d2fc06052c99c62ffeefdbaae","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-30T19:13:30Z","title_canon_sha256":"3ffad185b237c2be209a6c6540c205e77657f3afd84c41bc4067664795d769f8"},"schema_version":"1.0","source":{"id":"1307.8088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8088","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8088v1","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8088","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"MUWNW3HAZ4GX","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MUWNW3HAZ4GXR5WS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MUWNW3HA","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:4b712dbfc5de7a36f9f74cf00f2cf17faf118d3a0c9c0b582dd2cb3d206a52e8","target":"graph","created_at":"2026-05-18T03:17:12Z","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":"We develop aspects of functional analysis in an abstract axiomatic setting, through monoidal and enriched category theory. We work in a given closed category, whose objects we call spaces, and we study R-module objects therein (or algebras of a commutative monad), which we call linear spaces. Building on ideas of Lawvere and Kock, we study functionals on the space of scalar-valued maps, including compactly-supported Radon measures and Schwartz distributions. We develop an abstract theory of vector-valued integration with respect to these scalar functionals and their relatives. We study three a","authors_text":"Rory B. B. Lucyshyn-Wright","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-30T19:13:30Z","title":"Riesz-Schwartz extensive quantities and vector-valued integration in closed categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8088","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":"sha256:8ca400bf26a05aeb7308b73481d03abd10817d4e0873ff5167bb7494a906628c","target":"record","created_at":"2026-05-18T03:17:12Z","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":"49da223d25736d8d6887f5c0f266818ad5836a2d2fc06052c99c62ffeefdbaae","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-07-30T19:13:30Z","title_canon_sha256":"3ffad185b237c2be209a6c6540c205e77657f3afd84c41bc4067664795d769f8"},"schema_version":"1.0","source":{"id":"1307.8088","kind":"arxiv","version":1}},"canonical_sha256":"652cdb6ce0cf0d78f6d2f4770ca882256e44bf9d0f1e0c6c89efeeacc2df3123","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"652cdb6ce0cf0d78f6d2f4770ca882256e44bf9d0f1e0c6c89efeeacc2df3123","first_computed_at":"2026-05-18T03:17:12.455007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:12.455007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/Ldr12GMTNfxNSKIjJ5Y/UKogxGYaUzQrIczxuAbsX+AY7PFT4SyGQwcMAxe0hqD1owinoT7IzXtFAMlRCkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:12.455710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ca400bf26a05aeb7308b73481d03abd10817d4e0873ff5167bb7494a906628c","sha256:4b712dbfc5de7a36f9f74cf00f2cf17faf118d3a0c9c0b582dd2cb3d206a52e8"],"state_sha256":"0d17b66f9d52a22de8eea9b8b14d7f5bfccf89302bf3a2ac2379d6759ebd2ed3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WS0c5jl+GuX2fgv0v7HNKeOmkcJJRoW+v7S1GfxeFGQzdQfA9Ixz57IMrtlf4VsDQuSxhzNCsUIrTco7JcVWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T10:41:22.802168Z","bundle_sha256":"283afd336089aacffcdf4e61118c6007a9b00e1fe2c4525a89add6f5ff8066b2"}}