{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2E2VDAKTR2GPSDEKVOABFCZDMA","short_pith_number":"pith:2E2VDAKT","canonical_record":{"source":{"id":"2505.02537","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T10:18:48Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"e214a55ad8c1f8458aca97d1837a924e472383bba4e6ccad2a5e0bce8e1cb5ea","abstract_canon_sha256":"d6584c4b43f918681ace2835093a6630b88a61ba53de9182faa0fb2945178dfc"},"schema_version":"1.0"},"canonical_sha256":"d1355181538e8cf90c8aab80128b2360382d8c39f8f40a2065133468f0122371","source":{"kind":"arxiv","id":"2505.02537","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02537","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02537v2","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02537","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"2E2VDAKTR2GP","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"2E2VDAKTR2GPSDEK","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"2E2VDAKT","created_at":"2026-07-05T10:59:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2E2VDAKTR2GPSDEKVOABFCZDMA","target":"record","payload":{"canonical_record":{"source":{"id":"2505.02537","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T10:18:48Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"e214a55ad8c1f8458aca97d1837a924e472383bba4e6ccad2a5e0bce8e1cb5ea","abstract_canon_sha256":"d6584c4b43f918681ace2835093a6630b88a61ba53de9182faa0fb2945178dfc"},"schema_version":"1.0"},"canonical_sha256":"d1355181538e8cf90c8aab80128b2360382d8c39f8f40a2065133468f0122371","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:10.358518Z","signature_b64":"9xH2NgPwG64sZNOwCT7+4d7muYNPmbZEgxMnJR1q8hvnHcsZTuDIJ06+g5i35kz29j5mnUAgztLgLh6nMB9CBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1355181538e8cf90c8aab80128b2360382d8c39f8f40a2065133468f0122371","last_reissued_at":"2026-07-05T10:59:10.358031Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:10.358031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.02537","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":"2026-07-05T10:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5btCkXi3GK7ZetxmY2kUPvo/AU+0fopa7rh3LUJIift9kGPtf2pT2EsDjQ0iFXMW6t2GhXYbfanAFVVKa3mVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-14T10:36:17.789809Z"},"content_sha256":"4549694591b957c9d40e9d76765510e131279e8963a7afb93e94604950b56c54","schema_version":"1.0","event_id":"sha256:4549694591b957c9d40e9d76765510e131279e8963a7afb93e94604950b56c54"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2E2VDAKTR2GPSDEKVOABFCZDMA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Advancing Constrained Monotonic Neural Networks: Achieving Universal Approximation Beyond Bounded Activations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alberto Sinigaglia, Davide Sartor, Gian Antonio Susto","submitted_at":"2025-05-05T10:18:48Z","abstract_excerpt":"Conventional techniques for imposing monotonicity in MLPs by construction involve the use of non-negative weight constraints and bounded activation functions, which pose well-known optimization challenges. In this work, we generalize previous theoretical results, showing that MLPs with non-negative weight constraint and activations that saturate on alternating sides are universal approximators for monotonic functions. Additionally, we show an equivalence between the saturation side in the activations and the sign of the weight constraint. This connection allows us to prove that MLPs with conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02537","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/2505.02537/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":"2026-07-05T10:59:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tVkFRzC0rp1B5IH6hcX32yw1ikaTXaU8jeYLVueuZujrxPfYKQKMJXdb2S3T533lQsjjQPRGqJKugv98x2qMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-14T10:36:17.790178Z"},"content_sha256":"822156fe63b1f47d70bc595d89dd94222000f001d3b547e7350e8b7b09eda7d6","schema_version":"1.0","event_id":"sha256:822156fe63b1f47d70bc595d89dd94222000f001d3b547e7350e8b7b09eda7d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/bundle.json","state_url":"https://pith.science/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/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":"2026-07-14T10:36:17Z","links":{"resolver":"https://pith.science/pith/2E2VDAKTR2GPSDEKVOABFCZDMA","bundle":"https://pith.science/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/bundle.json","state":"https://pith.science/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2E2VDAKTR2GPSDEKVOABFCZDMA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2E2VDAKTR2GPSDEKVOABFCZDMA","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":"d6584c4b43f918681ace2835093a6630b88a61ba53de9182faa0fb2945178dfc","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T10:18:48Z","title_canon_sha256":"e214a55ad8c1f8458aca97d1837a924e472383bba4e6ccad2a5e0bce8e1cb5ea"},"schema_version":"1.0","source":{"id":"2505.02537","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.02537","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"arxiv_version","alias_value":"2505.02537v2","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.02537","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_12","alias_value":"2E2VDAKTR2GP","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_16","alias_value":"2E2VDAKTR2GPSDEK","created_at":"2026-07-05T10:59:10Z"},{"alias_kind":"pith_short_8","alias_value":"2E2VDAKT","created_at":"2026-07-05T10:59:10Z"}],"graph_snapshots":[{"event_id":"sha256:822156fe63b1f47d70bc595d89dd94222000f001d3b547e7350e8b7b09eda7d6","target":"graph","created_at":"2026-07-05T10:59:10Z","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/2505.02537/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Conventional techniques for imposing monotonicity in MLPs by construction involve the use of non-negative weight constraints and bounded activation functions, which pose well-known optimization challenges. In this work, we generalize previous theoretical results, showing that MLPs with non-negative weight constraint and activations that saturate on alternating sides are universal approximators for monotonic functions. Additionally, we show an equivalence between the saturation side in the activations and the sign of the weight constraint. This connection allows us to prove that MLPs with conve","authors_text":"Alberto Sinigaglia, Davide Sartor, Gian Antonio Susto","cross_cats":["cs.AI","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T10:18:48Z","title":"Advancing Constrained Monotonic Neural Networks: Achieving Universal Approximation Beyond Bounded Activations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.02537","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":"sha256:4549694591b957c9d40e9d76765510e131279e8963a7afb93e94604950b56c54","target":"record","created_at":"2026-07-05T10:59:10Z","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":"d6584c4b43f918681ace2835093a6630b88a61ba53de9182faa0fb2945178dfc","cross_cats_sorted":["cs.AI","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-05T10:18:48Z","title_canon_sha256":"e214a55ad8c1f8458aca97d1837a924e472383bba4e6ccad2a5e0bce8e1cb5ea"},"schema_version":"1.0","source":{"id":"2505.02537","kind":"arxiv","version":2}},"canonical_sha256":"d1355181538e8cf90c8aab80128b2360382d8c39f8f40a2065133468f0122371","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1355181538e8cf90c8aab80128b2360382d8c39f8f40a2065133468f0122371","first_computed_at":"2026-07-05T10:59:10.358031Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:10.358031Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xH2NgPwG64sZNOwCT7+4d7muYNPmbZEgxMnJR1q8hvnHcsZTuDIJ06+g5i35kz29j5mnUAgztLgLh6nMB9CBw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:10.358518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.02537","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4549694591b957c9d40e9d76765510e131279e8963a7afb93e94604950b56c54","sha256:822156fe63b1f47d70bc595d89dd94222000f001d3b547e7350e8b7b09eda7d6"],"state_sha256":"2674d003ce8481dbd636ad605607e78d9b26038407be5c9adb56b6e14639d41e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kCnypwZNTpThnqjFzs311HflrAC9/qhvRdlXoI4wZ/O16N6fzInzKAZPPlG1eZ7HdP+G2D0ZLPd63fxxOKyqCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-14T10:36:17.792586Z","bundle_sha256":"0c607b786537e3ab0af76ba0baca0261326ec42a0a324f7b9a7a7152a81ec80e"}}