{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:A4GMXCX5ZE2VA76QYSCNSYUOTG","short_pith_number":"pith:A4GMXCX5","canonical_record":{"source":{"id":"2507.02732","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-03T15:43:54Z","cross_cats_sorted":["cs.IT","math.IT","physics.data-an","stat.ML"],"title_canon_sha256":"2c5245e81cf2869921f55f8d2c353bcee2dd63cf6e0a24f76383a6928a49bc50","abstract_canon_sha256":"7b871394ecb0aea528445fef2794d8fc0af92539815e6b3774bd15d895e73000"},"schema_version":"1.0"},"canonical_sha256":"070ccb8afdc935507fd0c484d9628e99919b936b3a354c4726df52541c71706a","source":{"kind":"arxiv","id":"2507.02732","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.02732","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"arxiv_version","alias_value":"2507.02732v1","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02732","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_12","alias_value":"A4GMXCX5ZE2V","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_16","alias_value":"A4GMXCX5ZE2VA76Q","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_8","alias_value":"A4GMXCX5","created_at":"2026-07-05T11:31:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:A4GMXCX5ZE2VA76QYSCNSYUOTG","target":"record","payload":{"canonical_record":{"source":{"id":"2507.02732","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-03T15:43:54Z","cross_cats_sorted":["cs.IT","math.IT","physics.data-an","stat.ML"],"title_canon_sha256":"2c5245e81cf2869921f55f8d2c353bcee2dd63cf6e0a24f76383a6928a49bc50","abstract_canon_sha256":"7b871394ecb0aea528445fef2794d8fc0af92539815e6b3774bd15d895e73000"},"schema_version":"1.0"},"canonical_sha256":"070ccb8afdc935507fd0c484d9628e99919b936b3a354c4726df52541c71706a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:31:33.865888Z","signature_b64":"WC6gI6WoPbfJmhPCcFj0FHhAwH7DTGj0yWp4ArTBI31dTqwGRgoX4+WUmhlnBFfFmb5pQVnoy1v2gBpwUPY3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"070ccb8afdc935507fd0c484d9628e99919b936b3a354c4726df52541c71706a","last_reissued_at":"2026-07-05T11:31:33.865394Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:31:33.865394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.02732","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:31:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPrmkQWpRC7XlTr6+WdTfgsRlH74FGjrmhaFBZE2uOHEJd3tXym7IEfINvxu14cUVTYyJxp23AjOVahP2LnVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:25:01.726006Z"},"content_sha256":"8385a81da628bafa4c3164de7493a94e469ab8ce5dcc3b8bd25cc8575cfea2ce","schema_version":"1.0","event_id":"sha256:8385a81da628bafa4c3164de7493a94e469ab8ce5dcc3b8bd25cc8575cfea2ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:A4GMXCX5ZE2VA76QYSCNSYUOTG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classification by Separating Hypersurfaces: An Entropic Approach","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.IT","math.IT","physics.data-an","stat.ML"],"primary_cat":"cs.LG","authors_text":"Argimiro Arratia, Henryk Gzyl, Mahmoud El Daou","submitted_at":"2025-07-03T15:43:54Z","abstract_excerpt":"We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\\mathbb R}^N$, the goal is to find a hyperplane in ${\\mathbb R}^N$ that separates two sets of points corresponding to two distinct classes. This problem, with a history dating back to the perceptron model, remains central to machine learning. In this paper we propose a novel approach by searching for a vector of parameters in a bounded $N$-dimensional hypercube centered at the origin and a positive vector in ${\\mathbb R}^M$, obtained through the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02732","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/2507.02732/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":"2026-07-05T11:31:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9EMy/LZayWewEi1NNllX5/G+sRSQra3HeRKEn/oYan9PF4rt0TlgCm08CVZbdggv1FiQrxDN4bq1DpayJvUKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T19:25:01.727036Z"},"content_sha256":"7bb64b6f213fd991c1974d39dcb23031fb8478662baa99de3a9b429ea0824d95","schema_version":"1.0","event_id":"sha256:7bb64b6f213fd991c1974d39dcb23031fb8478662baa99de3a9b429ea0824d95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/bundle.json","state_url":"https://pith.science/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/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":"2026-08-21T19:25:01Z","links":{"resolver":"https://pith.science/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG","bundle":"https://pith.science/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/bundle.json","state":"https://pith.science/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4GMXCX5ZE2VA76QYSCNSYUOTG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:A4GMXCX5ZE2VA76QYSCNSYUOTG","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":"7b871394ecb0aea528445fef2794d8fc0af92539815e6b3774bd15d895e73000","cross_cats_sorted":["cs.IT","math.IT","physics.data-an","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-03T15:43:54Z","title_canon_sha256":"2c5245e81cf2869921f55f8d2c353bcee2dd63cf6e0a24f76383a6928a49bc50"},"schema_version":"1.0","source":{"id":"2507.02732","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.02732","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"arxiv_version","alias_value":"2507.02732v1","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02732","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_12","alias_value":"A4GMXCX5ZE2V","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_16","alias_value":"A4GMXCX5ZE2VA76Q","created_at":"2026-07-05T11:31:33Z"},{"alias_kind":"pith_short_8","alias_value":"A4GMXCX5","created_at":"2026-07-05T11:31:33Z"}],"graph_snapshots":[{"event_id":"sha256:7bb64b6f213fd991c1974d39dcb23031fb8478662baa99de3a9b429ea0824d95","target":"graph","created_at":"2026-07-05T11:31:33Z","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/2507.02732/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\\mathbb R}^N$, the goal is to find a hyperplane in ${\\mathbb R}^N$ that separates two sets of points corresponding to two distinct classes. This problem, with a history dating back to the perceptron model, remains central to machine learning. In this paper we propose a novel approach by searching for a vector of parameters in a bounded $N$-dimensional hypercube centered at the origin and a positive vector in ${\\mathbb R}^M$, obtained through the ","authors_text":"Argimiro Arratia, Henryk Gzyl, Mahmoud El Daou","cross_cats":["cs.IT","math.IT","physics.data-an","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-03T15:43:54Z","title":"Classification by Separating Hypersurfaces: An Entropic Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02732","kind":"arxiv","version":1},"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":"sha256:8385a81da628bafa4c3164de7493a94e469ab8ce5dcc3b8bd25cc8575cfea2ce","target":"record","created_at":"2026-07-05T11:31:33Z","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":"7b871394ecb0aea528445fef2794d8fc0af92539815e6b3774bd15d895e73000","cross_cats_sorted":["cs.IT","math.IT","physics.data-an","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2025-07-03T15:43:54Z","title_canon_sha256":"2c5245e81cf2869921f55f8d2c353bcee2dd63cf6e0a24f76383a6928a49bc50"},"schema_version":"1.0","source":{"id":"2507.02732","kind":"arxiv","version":1}},"canonical_sha256":"070ccb8afdc935507fd0c484d9628e99919b936b3a354c4726df52541c71706a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"070ccb8afdc935507fd0c484d9628e99919b936b3a354c4726df52541c71706a","first_computed_at":"2026-07-05T11:31:33.865394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:31:33.865394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WC6gI6WoPbfJmhPCcFj0FHhAwH7DTGj0yWp4ArTBI31dTqwGRgoX4+WUmhlnBFfFmb5pQVnoy1v2gBpwUPY3BQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:31:33.865888Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.02732","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8385a81da628bafa4c3164de7493a94e469ab8ce5dcc3b8bd25cc8575cfea2ce","sha256:7bb64b6f213fd991c1974d39dcb23031fb8478662baa99de3a9b429ea0824d95"],"state_sha256":"431d77c9186d990991e615bd8eefe4286bdb6be812475fda86108b8067dc89a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmLR4PB52GAI84S5Xmh8i3s2V6PJ9OPJEkoksuU0Qwb77w1zNVdP5sZgfNsioDAzYMy2C9sFxby387ReQGYEDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T19:25:01.732778Z","bundle_sha256":"20d9b4475e2ef0aa8523f59224156a0d3eb7ea0856e3a62d83a770a0c9220277"}}