{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:MFJZN6VPDXYDPGQVYLIKVGLNGK","short_pith_number":"pith:MFJZN6VP","schema_version":"1.0","canonical_sha256":"615396faaf1df0379a15c2d0aa996d32a410905a2c7c59dc97cdbf314771919f","source":{"kind":"arxiv","id":"2510.15795","version":2},"attestation_state":"computed","paper":{"title":"Synthetic perspectives on spaces and categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT","math.LO"],"primary_cat":"math.CT","authors_text":"Emily Riehl","submitted_at":"2025-10-17T16:16:55Z","abstract_excerpt":"Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2510.15795","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CT","submitted_at":"2025-10-17T16:16:55Z","cross_cats_sorted":["math.AT","math.LO"],"title_canon_sha256":"19f3155b12b19e1557e16d413c70be08f1e715611d18dd741a0ad0237dc13dda","abstract_canon_sha256":"60be3f0f60752a9b60e4b65b8f1368a2bcd63b2bc07d879f14d2e5b3f8161883"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:43.336067Z","signature_b64":"lmQtSfNlUwt2/C4Qp2nQ6mlbAd0Gzs0usVoumxJx5ok88alEn3wLgzm2mZRWGk5pflvK2km/unzBgrHxjps/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"615396faaf1df0379a15c2d0aa996d32a410905a2c7c59dc97cdbf314771919f","last_reissued_at":"2026-07-17T01:21:43.335134Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:43.335134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Synthetic perspectives on spaces and categories","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT","math.LO"],"primary_cat":"math.CT","authors_text":"Emily Riehl","submitted_at":"2025-10-17T16:16:55Z","abstract_excerpt":"Recently discovered domain-specific formal systems -- specifically homotopy type theory and simplicial type theory -- provide new perspectives on spaces and categories in a natively equivalence-invariant setting. In this note, we expose fundamental proof techniques from these parallel settings: describing induction principles over paths or arrows and constructions involving universes that are either univalent or directed univalent."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.15795","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/2510.15795/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2510.15795","created_at":"2026-07-17T01:21:43.335580+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.15795v2","created_at":"2026-07-17T01:21:43.335580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.15795","created_at":"2026-07-17T01:21:43.335580+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFJZN6VPDXYD","created_at":"2026-07-17T01:21:43.335580+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFJZN6VPDXYDPGQV","created_at":"2026-07-17T01:21:43.335580+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFJZN6VP","created_at":"2026-07-17T01:21:43.335580+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK","json":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK.json","graph_json":"https://pith.science/api/pith-number/MFJZN6VPDXYDPGQVYLIKVGLNGK/graph.json","events_json":"https://pith.science/api/pith-number/MFJZN6VPDXYDPGQVYLIKVGLNGK/events.json","paper":"https://pith.science/paper/MFJZN6VP"},"agent_actions":{"view_html":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK","download_json":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK.json","view_paper":"https://pith.science/paper/MFJZN6VP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.15795&json=true","fetch_graph":"https://pith.science/api/pith-number/MFJZN6VPDXYDPGQVYLIKVGLNGK/graph.json","fetch_events":"https://pith.science/api/pith-number/MFJZN6VPDXYDPGQVYLIKVGLNGK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK/action/storage_attestation","attest_author":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK/action/author_attestation","sign_citation":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK/action/citation_signature","submit_replication":"https://pith.science/pith/MFJZN6VPDXYDPGQVYLIKVGLNGK/action/replication_record"}},"created_at":"2026-07-17T01:21:43.335580+00:00","updated_at":"2026-07-17T01:21:43.335580+00:00"}