{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Z6E2JDIS6YI5T4Z6PEF3OGE34I","short_pith_number":"pith:Z6E2JDIS","canonical_record":{"source":{"id":"2602.17355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-02-19T13:37:10Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"e9d0abc6924f6da0452e0463d6e88db8ae9aeaf7a7145ce940458abe573a8690","abstract_canon_sha256":"98b1b1fc97592f0624d4f0bb3d20520c1920c7b44fd6d10a283c5d2e5cf5f0f4"},"schema_version":"1.0"},"canonical_sha256":"cf89a48d12f611d9f33e790bb7189be233345daebdc32a5c45480b06e298fc74","source":{"kind":"arxiv","id":"2602.17355","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.17355","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"2602.17355v2","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.17355","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"Z6E2JDIS6YI5","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_16","alias_value":"Z6E2JDIS6YI5T4Z6","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_8","alias_value":"Z6E2JDIS","created_at":"2026-06-05T00:13:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Z6E2JDIS6YI5T4Z6PEF3OGE34I","target":"record","payload":{"canonical_record":{"source":{"id":"2602.17355","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-02-19T13:37:10Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"e9d0abc6924f6da0452e0463d6e88db8ae9aeaf7a7145ce940458abe573a8690","abstract_canon_sha256":"98b1b1fc97592f0624d4f0bb3d20520c1920c7b44fd6d10a283c5d2e5cf5f0f4"},"schema_version":"1.0"},"canonical_sha256":"cf89a48d12f611d9f33e790bb7189be233345daebdc32a5c45480b06e298fc74","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T00:13:45.660943Z","signature_b64":"KjdSs964C/yf04ZodgLt6wiqcB/Cj/fWNY8XlIGcNiuLqMWmCb49wO6x088Ybum3V/cOc9Ste4480kAG5wkfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf89a48d12f611d9f33e790bb7189be233345daebdc32a5c45480b06e298fc74","last_reissued_at":"2026-06-05T00:13:45.660204Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T00:13:45.660204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.17355","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-05T00:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zoo/r0k0OhgnQNoNmZCfiK1K4MWkc/eIrHgQhuwoR+fCFY8s6wHTVsOGerzu6xhdu/tIZiAA2lMyphMblS7RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:03:20.128944Z"},"content_sha256":"2d277c3555237fcbd32752ee902f66beb13cd9092109b5dd2742f6eae050bb49","schema_version":"1.0","event_id":"sha256:2d277c3555237fcbd32752ee902f66beb13cd9092109b5dd2742f6eae050bb49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Z6E2JDIS6YI5T4Z6PEF3OGE34I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized inverse diagrams in tribes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CT","authors_text":"El Mehdi Cherradi","submitted_at":"2026-02-19T13:37:10Z","abstract_excerpt":"Starting from a generalized direct category $R$, we construct an absolutely dense functor $\\mathbf{D}_r \\to R$ with domain a strict direct category. Given any tribe $\\mathcal{T}$, we leverage this construction to provide a tribe structure on a subcategory of fibrant diagrams in $\\mathcal{T}^{R^{op}}$, assuming some finiteness condition on $R$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.17355","kind":"arxiv","version":2},"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/2602.17355/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":"2026-06-05T00:13:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TSd0A2qOBH6TzO5yvf534RNq+67Tu3gWph88bGpBF466EQe2hUCJLZibbDo1hmEVHBPsuyULqZxzCJyU7NUkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T03:03:20.129581Z"},"content_sha256":"d46ee98e56e51ce5891e8bbae706f996aff0ca5a7a56e3ca5b23f8e2f7949367","schema_version":"1.0","event_id":"sha256:d46ee98e56e51ce5891e8bbae706f996aff0ca5a7a56e3ca5b23f8e2f7949367"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/bundle.json","state_url":"https://pith.science/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/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":"2026-08-09T03:03:20Z","links":{"resolver":"https://pith.science/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I","bundle":"https://pith.science/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/bundle.json","state":"https://pith.science/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6E2JDIS6YI5T4Z6PEF3OGE34I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z6E2JDIS6YI5T4Z6PEF3OGE34I","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":"98b1b1fc97592f0624d4f0bb3d20520c1920c7b44fd6d10a283c5d2e5cf5f0f4","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-02-19T13:37:10Z","title_canon_sha256":"e9d0abc6924f6da0452e0463d6e88db8ae9aeaf7a7145ce940458abe573a8690"},"schema_version":"1.0","source":{"id":"2602.17355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.17355","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"arxiv_version","alias_value":"2602.17355v2","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.17355","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_12","alias_value":"Z6E2JDIS6YI5","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_16","alias_value":"Z6E2JDIS6YI5T4Z6","created_at":"2026-06-05T00:13:45Z"},{"alias_kind":"pith_short_8","alias_value":"Z6E2JDIS","created_at":"2026-06-05T00:13:45Z"}],"graph_snapshots":[{"event_id":"sha256:d46ee98e56e51ce5891e8bbae706f996aff0ca5a7a56e3ca5b23f8e2f7949367","target":"graph","created_at":"2026-06-05T00:13:45Z","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/2602.17355/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Starting from a generalized direct category $R$, we construct an absolutely dense functor $\\mathbf{D}_r \\to R$ with domain a strict direct category. Given any tribe $\\mathcal{T}$, we leverage this construction to provide a tribe structure on a subcategory of fibrant diagrams in $\\mathcal{T}^{R^{op}}$, assuming some finiteness condition on $R$.","authors_text":"El Mehdi Cherradi","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-02-19T13:37:10Z","title":"Generalized inverse diagrams in tribes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.17355","kind":"arxiv","version":2},"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":"sha256:2d277c3555237fcbd32752ee902f66beb13cd9092109b5dd2742f6eae050bb49","target":"record","created_at":"2026-06-05T00:13:45Z","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":"98b1b1fc97592f0624d4f0bb3d20520c1920c7b44fd6d10a283c5d2e5cf5f0f4","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2026-02-19T13:37:10Z","title_canon_sha256":"e9d0abc6924f6da0452e0463d6e88db8ae9aeaf7a7145ce940458abe573a8690"},"schema_version":"1.0","source":{"id":"2602.17355","kind":"arxiv","version":2}},"canonical_sha256":"cf89a48d12f611d9f33e790bb7189be233345daebdc32a5c45480b06e298fc74","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf89a48d12f611d9f33e790bb7189be233345daebdc32a5c45480b06e298fc74","first_computed_at":"2026-06-05T00:13:45.660204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T00:13:45.660204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KjdSs964C/yf04ZodgLt6wiqcB/Cj/fWNY8XlIGcNiuLqMWmCb49wO6x088Ybum3V/cOc9Ste4480kAG5wkfBA==","signature_status":"signed_v1","signed_at":"2026-06-05T00:13:45.660943Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.17355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d277c3555237fcbd32752ee902f66beb13cd9092109b5dd2742f6eae050bb49","sha256:d46ee98e56e51ce5891e8bbae706f996aff0ca5a7a56e3ca5b23f8e2f7949367"],"state_sha256":"0b5e45ff3871d00691eb36a5aaaed3b20a507a95b7741c0c53a6fd3c9d4ce4c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTHizhFKjRO0QeDVnG0GHlMdsNh1jIKZcoQqKX2xQhBO8B0yLgmglGbPlFUbDAc63vWuGOT34QlrnPzHnzbZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T03:03:20.133581Z","bundle_sha256":"69b52970f96f6fcf94182404bf32fa82acd1f02be5fc6a2c4887669faea5d3e2"}}