{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:5TNAM7CNPLK4CQUCJOHO2DM2H5","short_pith_number":"pith:5TNAM7CN","canonical_record":{"source":{"id":"2507.14379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-07-18T21:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"28e6b7fa44832946f6c4abb38ba75e9335d0d43188ff38885d90574ba41c5e35","abstract_canon_sha256":"12a8cc8b2618d5ca8157e3d67b8cbd1973d1150bee43714a84042b79af620bf9"},"schema_version":"1.0"},"canonical_sha256":"ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014","source":{"kind":"arxiv","id":"2507.14379","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14379","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14379v1","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14379","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"5TNAM7CNPLK4","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_16","alias_value":"5TNAM7CNPLK4CQUC","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_8","alias_value":"5TNAM7CN","created_at":"2026-07-05T11:40:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:5TNAM7CNPLK4CQUCJOHO2DM2H5","target":"record","payload":{"canonical_record":{"source":{"id":"2507.14379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-07-18T21:58:10Z","cross_cats_sorted":[],"title_canon_sha256":"28e6b7fa44832946f6c4abb38ba75e9335d0d43188ff38885d90574ba41c5e35","abstract_canon_sha256":"12a8cc8b2618d5ca8157e3d67b8cbd1973d1150bee43714a84042b79af620bf9"},"schema_version":"1.0"},"canonical_sha256":"ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:40:05.151162Z","signature_b64":"yp3JKmeiv98qbNT4mQZJ9+9g5IN/ipj+nCeBKz4wJkwUNLwipB60IRHbJM53PlAa9mJMVW4diuPZfdwcU1GQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014","last_reissued_at":"2026-07-05T11:40:05.150692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:40:05.150692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.14379","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":"2026-07-05T11:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6vhBj0rNLhaiw+gyVodvjpz4+qvJtvh673NBlQdjXI9JrbF51l/cCqMsEM66bj5Q/o9KTEUAoHCfHSn/slwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:25:22.127201Z"},"content_sha256":"9cc8cbc549c2e465fec6f78281b7f53cf8c01bf12aa9df47f5a007ce5ea93c2c","schema_version":"1.0","event_id":"sha256:9cc8cbc549c2e465fec6f78281b7f53cf8c01bf12aa9df47f5a007ce5ea93c2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:5TNAM7CNPLK4CQUCJOHO2DM2H5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local fibrations and morphisms of relative toposes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"L\\'eo Bartoli, Olivia Caramello","submitted_at":"2025-07-18T21:58:10Z","abstract_excerpt":"We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to this more general setting. As an application of this notion, we obtain a characterization of the functors between relative sites that induce a morphism between the corresponding relative toposes: these are exactly the morphisms of sites which are morphisms of local fibrations. Also, we prove a weak version of Diaconescu's theorem, providing an equivalence betwe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14379","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.14379/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":"2026-07-05T11:40:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZAP3jgfGmu1K+lyxuTQnKVQcA+CkUop5LDuzrhvxQdinRTBLS00rJro7qNXGApl90EJeneKdLfe/U/cRyEc9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:25:22.127845Z"},"content_sha256":"6d4205c670d450070b43741e277c19fe1255d60d9aca9c76f079f520e3cee283","schema_version":"1.0","event_id":"sha256:6d4205c670d450070b43741e277c19fe1255d60d9aca9c76f079f520e3cee283"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/bundle.json","state_url":"https://pith.science/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/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":"2026-08-08T17:25:22Z","links":{"resolver":"https://pith.science/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5","bundle":"https://pith.science/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/bundle.json","state":"https://pith.science/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5TNAM7CNPLK4CQUCJOHO2DM2H5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5TNAM7CNPLK4CQUCJOHO2DM2H5","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":"12a8cc8b2618d5ca8157e3d67b8cbd1973d1150bee43714a84042b79af620bf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-07-18T21:58:10Z","title_canon_sha256":"28e6b7fa44832946f6c4abb38ba75e9335d0d43188ff38885d90574ba41c5e35"},"schema_version":"1.0","source":{"id":"2507.14379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14379","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14379v1","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14379","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_12","alias_value":"5TNAM7CNPLK4","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_16","alias_value":"5TNAM7CNPLK4CQUC","created_at":"2026-07-05T11:40:05Z"},{"alias_kind":"pith_short_8","alias_value":"5TNAM7CN","created_at":"2026-07-05T11:40:05Z"}],"graph_snapshots":[{"event_id":"sha256:6d4205c670d450070b43741e277c19fe1255d60d9aca9c76f079f520e3cee283","target":"graph","created_at":"2026-07-05T11:40:05Z","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/2507.14379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the notion of local fibration, a generalization of the notion of fibration which takes into account the presence of Grothendieck topologies on the two categories, and show that the classical results about fibrations lift to this more general setting. As an application of this notion, we obtain a characterization of the functors between relative sites that induce a morphism between the corresponding relative toposes: these are exactly the morphisms of sites which are morphisms of local fibrations. Also, we prove a weak version of Diaconescu's theorem, providing an equivalence betwe","authors_text":"L\\'eo Bartoli, Olivia Caramello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-07-18T21:58:10Z","title":"Local fibrations and morphisms of relative toposes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14379","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":"sha256:9cc8cbc549c2e465fec6f78281b7f53cf8c01bf12aa9df47f5a007ce5ea93c2c","target":"record","created_at":"2026-07-05T11:40:05Z","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":"12a8cc8b2618d5ca8157e3d67b8cbd1973d1150bee43714a84042b79af620bf9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2025-07-18T21:58:10Z","title_canon_sha256":"28e6b7fa44832946f6c4abb38ba75e9335d0d43188ff38885d90574ba41c5e35"},"schema_version":"1.0","source":{"id":"2507.14379","kind":"arxiv","version":1}},"canonical_sha256":"ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecda067c4d7ad5c142824b8eed0d9a3f591cd3c37fe57fe14a391a30ddf95014","first_computed_at":"2026-07-05T11:40:05.150692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:40:05.150692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yp3JKmeiv98qbNT4mQZJ9+9g5IN/ipj+nCeBKz4wJkwUNLwipB60IRHbJM53PlAa9mJMVW4diuPZfdwcU1GQDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:40:05.151162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.14379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9cc8cbc549c2e465fec6f78281b7f53cf8c01bf12aa9df47f5a007ce5ea93c2c","sha256:6d4205c670d450070b43741e277c19fe1255d60d9aca9c76f079f520e3cee283"],"state_sha256":"e5e5dc585f60ffa388b932e4ee5d1c0a223f19b39dc8e512468b4c8382ac48dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urjs7/FdZqrTHNHSO8lHb5X8B3wGG06Ysyo6ZGxS8xk1OurgjnVpqk0AUKTMFnnwrB7gR39m0jAgR8gNZxY5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:25:22.135945Z","bundle_sha256":"80f5b74669b243aa765b40eda6b0584f2b610fa8a3904a4e7826f080adc307dc"}}