{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:LWVVJA2CKPW4MQ7PJ6RRGDPWDO","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":"a3bfd7ecc0d60e2ea53dcfa1ad5076b3db4faea4aa6e2bc4de3c237362d8eb32","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T06:09:54Z","title_canon_sha256":"ec93c0bf638886e6d55095d136aa254378bfaff5e53eb5179ebd74ac75563246"},"schema_version":"1.0","source":{"id":"2607.07035","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.07035","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.07035v1","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.07035","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_12","alias_value":"LWVVJA2CKPW4","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_16","alias_value":"LWVVJA2CKPW4MQ7P","created_at":"2026-07-09T01:20:12Z"},{"alias_kind":"pith_short_8","alias_value":"LWVVJA2C","created_at":"2026-07-09T01:20:12Z"}],"graph_snapshots":[{"event_id":"sha256:2a7152f9eb0068111dab9b6fd97ab2e65e34bf7396c002eabc58a624c748db2c","target":"graph","created_at":"2026-07-09T01:20:12Z","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/2607.07035/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The architecture of deep feedforward neural networks is ubiquitous in deep learning, either as a whole system or as a subnetwork of other architectures, and thus its mechanism is a key ingredient of the black box of neural networks. On the basis of the simplest two-layer ReLU network, this paper systematically studies the mechanism of deep feedforward ReLU networks with multiple hidden layers and successfully explains the training solution obtained by the back-propagation algorithm. The concept of a path, especially in terms of the relationships between paths, plays a central role in uncoverin","authors_text":"Changcun Huang","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T06:09:54Z","title":"On the Principles of Deep Feedforward ReLU Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07035","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":"sha256:734352c6311bb9b7f9e514b58462c9063272c2f7a2dec2f865b75e4bfb279fdb","target":"record","created_at":"2026-07-09T01:20:12Z","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":"a3bfd7ecc0d60e2ea53dcfa1ad5076b3db4faea4aa6e2bc4de3c237362d8eb32","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-07-08T06:09:54Z","title_canon_sha256":"ec93c0bf638886e6d55095d136aa254378bfaff5e53eb5179ebd74ac75563246"},"schema_version":"1.0","source":{"id":"2607.07035","kind":"arxiv","version":1}},"canonical_sha256":"5dab54834253edc643ef4fa3130df61bb9fb68fcbd64380cfbe9a235d8d4e980","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dab54834253edc643ef4fa3130df61bb9fb68fcbd64380cfbe9a235d8d4e980","first_computed_at":"2026-07-09T01:20:12.904805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:12.904805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djQDP1FbybeqFJAGOD6K6KxSQd3tuPFvRszXbZreH+LSG9wAJT+BKz1AZSLOIV8411VsHNMwWVrO6ctynrntBQ==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:12.905142Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.07035","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:734352c6311bb9b7f9e514b58462c9063272c2f7a2dec2f865b75e4bfb279fdb","sha256:2a7152f9eb0068111dab9b6fd97ab2e65e34bf7396c002eabc58a624c748db2c"],"state_sha256":"af4647e40a971f8234f0c830a14ef3bffacfb19a522d8730db222ed02248563c"}