{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:I7OWZ4ORCDA4RS4RC4NPUJE2KS","short_pith_number":"pith:I7OWZ4OR","schema_version":"1.0","canonical_sha256":"47dd6cf1d110c1c8cb91171afa249a548caf73ebbc28896d686aa91e82ab336f","source":{"kind":"arxiv","id":"2605.20534","version":1},"attestation_state":"computed","paper":{"title":"Axiomatizing Neural Networks via Pursuit of Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Felix Rojas Casadiego, Marcel van Gerven, Mehmet Yamac, Mert Duman, Moncef Gabbouj, Serkan Kiranyaz, Ugur Akpinar","submitted_at":"2026-05-19T22:12:58Z","abstract_excerpt":"While deep neural networks have achieved remarkable success across a wide range of domains, their underlying mechanisms remain poorly understood, and they are often regarded as black boxes. This gap between empirical performance and theoretical understanding poses a challenge analogous to the pre-axiomatic stage of classical geometry. In this work, we introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic framework that formulates neural network behavior through a set of geometric postulates. These axioms, together with their derived consequences, provide a unified perspective on re"},"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":"2605.20534","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-19T22:12:58Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"dc2b78f7ae0f28a852a438246e10c50743916becd7baebf3df4cdc7df8671a91","abstract_canon_sha256":"e29a9207f4085b6acbb994e661337d77729b2e19eb8ba24877590ff160bb62ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:04:41.421921Z","signature_b64":"mHDF8qt5bXzwwu+UyRLcxqjYDoZTTdPzCGIaCbh5nTcXnevWp4h96c4RGpSIxEg3Fb//cnVELxGXs4N5noygAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47dd6cf1d110c1c8cb91171afa249a548caf73ebbc28896d686aa91e82ab336f","last_reissued_at":"2026-05-21T01:04:41.421379Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:04:41.421379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Axiomatizing Neural Networks via Pursuit of Subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Felix Rojas Casadiego, Marcel van Gerven, Mehmet Yamac, Mert Duman, Moncef Gabbouj, Serkan Kiranyaz, Ugur Akpinar","submitted_at":"2026-05-19T22:12:58Z","abstract_excerpt":"While deep neural networks have achieved remarkable success across a wide range of domains, their underlying mechanisms remain poorly understood, and they are often regarded as black boxes. This gap between empirical performance and theoretical understanding poses a challenge analogous to the pre-axiomatic stage of classical geometry. In this work, we introduce the Pursuit of Subspaces (PoS) hypothesis, an axiomatic framework that formulates neural network behavior through a set of geometric postulates. These axioms, together with their derived consequences, provide a unified perspective on re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.20534","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/2605.20534/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":"2605.20534","created_at":"2026-05-21T01:04:41.421464+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.20534v1","created_at":"2026-05-21T01:04:41.421464+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.20534","created_at":"2026-05-21T01:04:41.421464+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7OWZ4ORCDA4","created_at":"2026-05-21T01:04:41.421464+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7OWZ4ORCDA4RS4R","created_at":"2026-05-21T01:04:41.421464+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7OWZ4OR","created_at":"2026-05-21T01:04:41.421464+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/I7OWZ4ORCDA4RS4RC4NPUJE2KS","json":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS.json","graph_json":"https://pith.science/api/pith-number/I7OWZ4ORCDA4RS4RC4NPUJE2KS/graph.json","events_json":"https://pith.science/api/pith-number/I7OWZ4ORCDA4RS4RC4NPUJE2KS/events.json","paper":"https://pith.science/paper/I7OWZ4OR"},"agent_actions":{"view_html":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS","download_json":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS.json","view_paper":"https://pith.science/paper/I7OWZ4OR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.20534&json=true","fetch_graph":"https://pith.science/api/pith-number/I7OWZ4ORCDA4RS4RC4NPUJE2KS/graph.json","fetch_events":"https://pith.science/api/pith-number/I7OWZ4ORCDA4RS4RC4NPUJE2KS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS/action/storage_attestation","attest_author":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS/action/author_attestation","sign_citation":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS/action/citation_signature","submit_replication":"https://pith.science/pith/I7OWZ4ORCDA4RS4RC4NPUJE2KS/action/replication_record"}},"created_at":"2026-05-21T01:04:41.421464+00:00","updated_at":"2026-05-21T01:04:41.421464+00:00"}