{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FSZ6E7BK5NE7N6LZ3JQVGCPFND","short_pith_number":"pith:FSZ6E7BK","canonical_record":{"source":{"id":"1809.06940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-09-18T21:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"ba071794ecce8f128f16263d1a1a8f632107e5ec9831b8eef204d85994778461","abstract_canon_sha256":"3c99a0b1457f8ca401f1478bfe97d4dd43857a5d3ee8e49fdb01833f92b3680d"},"schema_version":"1.0"},"canonical_sha256":"2cb3e27c2aeb49f6f979da615309e568d08baad1ab929c1cab35f56fae21ea00","source":{"kind":"arxiv","id":"1809.06940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06940","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06940v1","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06940","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"FSZ6E7BK5NE7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FSZ6E7BK5NE7N6LZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FSZ6E7BK","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FSZ6E7BK5NE7N6LZ3JQVGCPFND","target":"record","payload":{"canonical_record":{"source":{"id":"1809.06940","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-09-18T21:26:05Z","cross_cats_sorted":[],"title_canon_sha256":"ba071794ecce8f128f16263d1a1a8f632107e5ec9831b8eef204d85994778461","abstract_canon_sha256":"3c99a0b1457f8ca401f1478bfe97d4dd43857a5d3ee8e49fdb01833f92b3680d"},"schema_version":"1.0"},"canonical_sha256":"2cb3e27c2aeb49f6f979da615309e568d08baad1ab929c1cab35f56fae21ea00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:21.111725Z","signature_b64":"WFxLuV23R/5kvy5Gk0TiUVwGS4LCinRBG+sJypzdoJflOENpiyaWqiTFxAYcWOhHBdj3KYr1y3YfMRTDIyL1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cb3e27c2aeb49f6f979da615309e568d08baad1ab929c1cab35f56fae21ea00","last_reissued_at":"2026-05-18T00:05:21.111333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:21.111333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.06940","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":"2026-05-18T00:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZOdw6kQ/I2fxGtneRCwL9xDr0SQVAD2MdXIXQXQgF5HYhygp2kZMxNt7fQsgwVjBPm0e2tpXVh8E/hhzyrACw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:39:05.328812Z"},"content_sha256":"774cf04af09f5fb28efd0706fb9909596cca370a743093b0cbff6ea84bea93cb","schema_version":"1.0","event_id":"sha256:774cf04af09f5fb28efd0706fb9909596cca370a743093b0cbff6ea84bea93cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FSZ6E7BK5NE7N6LZ3JQVGCPFND","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cartesian Double Categories with an Emphasis on Characterizing Spans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Evangelia Aleiferi","submitted_at":"2018-09-18T21:26:05Z","abstract_excerpt":"In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni, Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly more generalized notion of double categories allows us to set the whole theory inside the welcoming 2-category of double categories, and to overcome technical problems that were caused by working with left adjoints inside a general bicategory. Cartesian double categories that are also fibrant are of particular interest to us. After describing some important properties of Cartesian and fibrant double categories, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06940","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":"2026-05-18T00:05:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4aADiCc68F18NZd+0bcWWwXyHVtGSG1EX8pPWjQcvg9b5I93J5fTnTvaJFPAnkpxBuQgtJZiUJypPv8RGCRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T10:39:05.329149Z"},"content_sha256":"471c924a82436e387841fa4196732c23baca0dfac61896a932329eeed8e0b227","schema_version":"1.0","event_id":"sha256:471c924a82436e387841fa4196732c23baca0dfac61896a932329eeed8e0b227"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/bundle.json","state_url":"https://pith.science/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/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":"2026-07-05T10:39:05Z","links":{"resolver":"https://pith.science/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND","bundle":"https://pith.science/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/bundle.json","state":"https://pith.science/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FSZ6E7BK5NE7N6LZ3JQVGCPFND/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FSZ6E7BK5NE7N6LZ3JQVGCPFND","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":"3c99a0b1457f8ca401f1478bfe97d4dd43857a5d3ee8e49fdb01833f92b3680d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-09-18T21:26:05Z","title_canon_sha256":"ba071794ecce8f128f16263d1a1a8f632107e5ec9831b8eef204d85994778461"},"schema_version":"1.0","source":{"id":"1809.06940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.06940","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"arxiv_version","alias_value":"1809.06940v1","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.06940","created_at":"2026-05-18T00:05:21Z"},{"alias_kind":"pith_short_12","alias_value":"FSZ6E7BK5NE7","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FSZ6E7BK5NE7N6LZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FSZ6E7BK","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:471c924a82436e387841fa4196732c23baca0dfac61896a932329eeed8e0b227","target":"graph","created_at":"2026-05-18T00:05:21Z","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":"In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni, Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly more generalized notion of double categories allows us to set the whole theory inside the welcoming 2-category of double categories, and to overcome technical problems that were caused by working with left adjoints inside a general bicategory. Cartesian double categories that are also fibrant are of particular interest to us. After describing some important properties of Cartesian and fibrant double categories, ","authors_text":"Evangelia Aleiferi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-09-18T21:26:05Z","title":"Cartesian Double Categories with an Emphasis on Characterizing Spans"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06940","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":"sha256:774cf04af09f5fb28efd0706fb9909596cca370a743093b0cbff6ea84bea93cb","target":"record","created_at":"2026-05-18T00:05:21Z","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":"3c99a0b1457f8ca401f1478bfe97d4dd43857a5d3ee8e49fdb01833f92b3680d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2018-09-18T21:26:05Z","title_canon_sha256":"ba071794ecce8f128f16263d1a1a8f632107e5ec9831b8eef204d85994778461"},"schema_version":"1.0","source":{"id":"1809.06940","kind":"arxiv","version":1}},"canonical_sha256":"2cb3e27c2aeb49f6f979da615309e568d08baad1ab929c1cab35f56fae21ea00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cb3e27c2aeb49f6f979da615309e568d08baad1ab929c1cab35f56fae21ea00","first_computed_at":"2026-05-18T00:05:21.111333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:21.111333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WFxLuV23R/5kvy5Gk0TiUVwGS4LCinRBG+sJypzdoJflOENpiyaWqiTFxAYcWOhHBdj3KYr1y3YfMRTDIyL1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:21.111725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.06940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:774cf04af09f5fb28efd0706fb9909596cca370a743093b0cbff6ea84bea93cb","sha256:471c924a82436e387841fa4196732c23baca0dfac61896a932329eeed8e0b227"],"state_sha256":"7109aba9e3b75e60e02024d054677791f4f8f8b1759dd991b3d51db5df0cb9fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdIe/8bIWSBlSXNrYDMQjJEaYjdKMEL5f15qsqWrjb7xT7g4SElvgBXgpAlFE7NDKmO1A5n00ubO9q785acxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T10:39:05.330989Z","bundle_sha256":"10488b4e72419106cccba3f2dc8d5325cc07881dc6f70f40bfa156d26ddec06b"}}