{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZPBST7CV53XHNT2IE4QDFP3MGC","short_pith_number":"pith:ZPBST7CV","canonical_record":{"source":{"id":"1507.02220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-07-08T16:59:22Z","cross_cats_sorted":["math.AG","math.KT"],"title_canon_sha256":"cd1c99e71301aeaf8b767104a1c1bf3977c06fbb3cc1591f029c475ac23ec56f","abstract_canon_sha256":"86b65185439df3835175fa223594540297af3c00074421b0a65ce9e0f8d793a4"},"schema_version":"1.0"},"canonical_sha256":"cbc329fc55eeee76cf48272032bf6c3086252c6be55416925311483f234596b6","source":{"kind":"arxiv","id":"1507.02220","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02220","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02220v1","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02220","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZPBST7CV53XH","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZPBST7CV53XHNT2I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZPBST7CV","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZPBST7CV53XHNT2IE4QDFP3MGC","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02220","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-07-08T16:59:22Z","cross_cats_sorted":["math.AG","math.KT"],"title_canon_sha256":"cd1c99e71301aeaf8b767104a1c1bf3977c06fbb3cc1591f029c475ac23ec56f","abstract_canon_sha256":"86b65185439df3835175fa223594540297af3c00074421b0a65ce9e0f8d793a4"},"schema_version":"1.0"},"canonical_sha256":"cbc329fc55eeee76cf48272032bf6c3086252c6be55416925311483f234596b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:09.772644Z","signature_b64":"73GiTS//yqfuEVh49QnMOv/deVusxCyCrtog2UmrBktDZXvJZE2mMYIBJWvsExmlW+hPZv5iSfiiCTKNEn3uBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbc329fc55eeee76cf48272032bf6c3086252c6be55416925311483f234596b6","last_reissued_at":"2026-05-18T01:16:09.772184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:09.772184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02220","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VxB7vPNvew6PCkOG3h0NrysyWwuVGSubC8crdsEWojEbkDgVZduP1i4bM5p6qar58G8wv4yh3ka9VgJmuKMQBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:56:28.291008Z"},"content_sha256":"a98cd9747075998f575a0fac24b11fe482902ff9a7623ea076cd55c1f6d94976","schema_version":"1.0","event_id":"sha256:a98cd9747075998f575a0fac24b11fe482902ff9a7623ea076cd55c1f6d94976"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZPBST7CV53XHNT2IE4QDFP3MGC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative symmetric monoidal closed categories I: Autoenrichment and change of base","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.CT","authors_text":"Rory B. B. Lucyshyn-Wright","submitted_at":"2015-07-08T16:59:22Z","abstract_excerpt":"Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to G. M. Kelly in the 1960s that there is a very close connection between these phenomena. In this first part of a two-part series on this subject, we show that the assignment to each symmetric monoidal closed category $V$ its associated $V$-enriched category $\\underline{V}$ extends to a 2-functor valued in an op-2-fibred 2-category of symmetric monoidal closed categories enriched over various bases. For a fixed $V$, we show that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02220","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gww0/ww66eaTOyfqb87a8G93/kL9v7fwjNGrefCb6ok7sJyViQ7zHPRgUgZfUd7wUqR/rf2Y9YADq6yLAD0kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:56:28.291380Z"},"content_sha256":"26a779f47067ed20deae9cec84e6c1de8cf2635898ea92145fe819799c6bd3a9","schema_version":"1.0","event_id":"sha256:26a779f47067ed20deae9cec84e6c1de8cf2635898ea92145fe819799c6bd3a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/bundle.json","state_url":"https://pith.science/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/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":"2026-06-05T11:56:28Z","links":{"resolver":"https://pith.science/pith/ZPBST7CV53XHNT2IE4QDFP3MGC","bundle":"https://pith.science/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/bundle.json","state":"https://pith.science/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZPBST7CV53XHNT2IE4QDFP3MGC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZPBST7CV53XHNT2IE4QDFP3MGC","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":"86b65185439df3835175fa223594540297af3c00074421b0a65ce9e0f8d793a4","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-07-08T16:59:22Z","title_canon_sha256":"cd1c99e71301aeaf8b767104a1c1bf3977c06fbb3cc1591f029c475ac23ec56f"},"schema_version":"1.0","source":{"id":"1507.02220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02220","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02220v1","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02220","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZPBST7CV53XH","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZPBST7CV53XHNT2I","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZPBST7CV","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:26a779f47067ed20deae9cec84e6c1de8cf2635898ea92145fe819799c6bd3a9","target":"graph","created_at":"2026-05-18T01:16:09Z","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":"Symmetric monoidal closed categories may be related to one another not only by the functors between them but also by enrichment of one in another, and it was known to G. M. Kelly in the 1960s that there is a very close connection between these phenomena. In this first part of a two-part series on this subject, we show that the assignment to each symmetric monoidal closed category $V$ its associated $V$-enriched category $\\underline{V}$ extends to a 2-functor valued in an op-2-fibred 2-category of symmetric monoidal closed categories enriched over various bases. For a fixed $V$, we show that th","authors_text":"Rory B. B. Lucyshyn-Wright","cross_cats":["math.AG","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-07-08T16:59:22Z","title":"Relative symmetric monoidal closed categories I: Autoenrichment and change of base"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02220","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:a98cd9747075998f575a0fac24b11fe482902ff9a7623ea076cd55c1f6d94976","target":"record","created_at":"2026-05-18T01:16:09Z","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":"86b65185439df3835175fa223594540297af3c00074421b0a65ce9e0f8d793a4","cross_cats_sorted":["math.AG","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2015-07-08T16:59:22Z","title_canon_sha256":"cd1c99e71301aeaf8b767104a1c1bf3977c06fbb3cc1591f029c475ac23ec56f"},"schema_version":"1.0","source":{"id":"1507.02220","kind":"arxiv","version":1}},"canonical_sha256":"cbc329fc55eeee76cf48272032bf6c3086252c6be55416925311483f234596b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbc329fc55eeee76cf48272032bf6c3086252c6be55416925311483f234596b6","first_computed_at":"2026-05-18T01:16:09.772184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:09.772184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"73GiTS//yqfuEVh49QnMOv/deVusxCyCrtog2UmrBktDZXvJZE2mMYIBJWvsExmlW+hPZv5iSfiiCTKNEn3uBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:09.772644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a98cd9747075998f575a0fac24b11fe482902ff9a7623ea076cd55c1f6d94976","sha256:26a779f47067ed20deae9cec84e6c1de8cf2635898ea92145fe819799c6bd3a9"],"state_sha256":"21c9048ccdbb9296512b4b7a6a39da4d71fa1c697b3e5f96363670020e61e8f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rX9jj4cksdrrWQzVQHr/MQGVsa2B3WUiqfywMlblgHrcCC0cPP7oIu/rf/M2p7YQ4zyXstzKceeGa/glM5BVAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:56:28.293392Z","bundle_sha256":"c38c1cc398e844ea85833cd84be23f42563b1e30fc47baaf421a388f929d3c84"}}