{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:QN4K2YXZGIG2ZG5UDBZETYQIDR","short_pith_number":"pith:QN4K2YXZ","schema_version":"1.0","canonical_sha256":"8378ad62f9320dac9bb4187249e2081c5226953cab40ee6e333457e494276ad2","source":{"kind":"arxiv","id":"2607.15107","version":1},"attestation_state":"computed","paper":{"title":"Learning in Infinitesimal Non-Compositional Sketches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LG","authors_text":"Sridhar Mahadevan","submitted_at":"2026-07-16T15:18:58Z","abstract_excerpt":"This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting. Machine learning problems are specified as sketches: graphs with commutativity conditions $\\mathcal D$, limit cones $\\mathcal L$, and colimit cocones $\\mathcal K$, generalizing the usual scalarization of loss functions or vector space assumptions. Non-compositionality is defined purely as failure of a universal factorization problem, not as arithmetic"},"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":"2607.15107","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-16T15:18:58Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"5f14aee53264a3dcd8a87cd10ba2dbf52406ab719f29876f391ea43c1b1a333c","abstract_canon_sha256":"adc03ffd98aebf674f4dd42c10960c8100a83499de09847c1f42b7500c3b75bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:22:09.756117Z","signature_b64":"z6p7UAIJ8UQo8+GC4CzsYx1Lq43Cc+FprwVVTrwIZ8XGXR058qRC9b5SupsVs2asRiYWOfoVI6j19Z5kJOs5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8378ad62f9320dac9bb4187249e2081c5226953cab40ee6e333457e494276ad2","last_reissued_at":"2026-07-17T01:22:09.755241Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:22:09.755241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning in Infinitesimal Non-Compositional Sketches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"cs.LG","authors_text":"Sridhar Mahadevan","submitted_at":"2026-07-16T15:18:58Z","abstract_excerpt":"This paper develops a categorical framework -- Learning in Infinitesimal Non-Compositional Sketches (LINCS) -- as the repair of non-compositionality: failures of diagrams to factor through quotient sketches lifted to the tangent category setting. Machine learning problems are specified as sketches: graphs with commutativity conditions $\\mathcal D$, limit cones $\\mathcal L$, and colimit cocones $\\mathcal K$, generalizing the usual scalarization of loss functions or vector space assumptions. Non-compositionality is defined purely as failure of a universal factorization problem, not as arithmetic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15107","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/2607.15107/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":"2607.15107","created_at":"2026-07-17T01:22:09.755697+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.15107v1","created_at":"2026-07-17T01:22:09.755697+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.15107","created_at":"2026-07-17T01:22:09.755697+00:00"},{"alias_kind":"pith_short_12","alias_value":"QN4K2YXZGIG2","created_at":"2026-07-17T01:22:09.755697+00:00"},{"alias_kind":"pith_short_16","alias_value":"QN4K2YXZGIG2ZG5U","created_at":"2026-07-17T01:22:09.755697+00:00"},{"alias_kind":"pith_short_8","alias_value":"QN4K2YXZ","created_at":"2026-07-17T01:22:09.755697+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/QN4K2YXZGIG2ZG5UDBZETYQIDR","json":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR.json","graph_json":"https://pith.science/api/pith-number/QN4K2YXZGIG2ZG5UDBZETYQIDR/graph.json","events_json":"https://pith.science/api/pith-number/QN4K2YXZGIG2ZG5UDBZETYQIDR/events.json","paper":"https://pith.science/paper/QN4K2YXZ"},"agent_actions":{"view_html":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR","download_json":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR.json","view_paper":"https://pith.science/paper/QN4K2YXZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.15107&json=true","fetch_graph":"https://pith.science/api/pith-number/QN4K2YXZGIG2ZG5UDBZETYQIDR/graph.json","fetch_events":"https://pith.science/api/pith-number/QN4K2YXZGIG2ZG5UDBZETYQIDR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR/action/storage_attestation","attest_author":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR/action/author_attestation","sign_citation":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR/action/citation_signature","submit_replication":"https://pith.science/pith/QN4K2YXZGIG2ZG5UDBZETYQIDR/action/replication_record"}},"created_at":"2026-07-17T01:22:09.755697+00:00","updated_at":"2026-07-17T01:22:09.755697+00:00"}