{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LMKGRLETWEPKEPRDS4HWPG46M6","short_pith_number":"pith:LMKGRLET","canonical_record":{"source":{"id":"1612.05627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-12-13T00:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"63c9d307f916c4c461173fed3918a696575117f17de2d9945acfd3d22ba15c53","abstract_canon_sha256":"bd31d3109039b586a71be69a0476800ae51fd62d1404c0c9abb6d4a9805ce7ef"},"schema_version":"1.0"},"canonical_sha256":"5b1468ac93b11ea23e23970f679b9e67817a00ab0f822602ca6f096496c76aa6","source":{"kind":"arxiv","id":"1612.05627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05627","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05627v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05627","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"LMKGRLETWEPK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LMKGRLETWEPKEPRD","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LMKGRLET","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LMKGRLETWEPKEPRDS4HWPG46M6","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-12-13T00:54:03Z","cross_cats_sorted":[],"title_canon_sha256":"63c9d307f916c4c461173fed3918a696575117f17de2d9945acfd3d22ba15c53","abstract_canon_sha256":"bd31d3109039b586a71be69a0476800ae51fd62d1404c0c9abb6d4a9805ce7ef"},"schema_version":"1.0"},"canonical_sha256":"5b1468ac93b11ea23e23970f679b9e67817a00ab0f822602ca6f096496c76aa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:51.411931Z","signature_b64":"9GCIhS35mNczu3WzilJHV/ZzenPCrOcLfwvDuIrroc5OwkrLMluw2vP5DZEReOQQlkBDtnF0yf6qYDWd7rlPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1468ac93b11ea23e23970f679b9e67817a00ab0f822602ca6f096496c76aa6","last_reissued_at":"2026-05-18T00:54:51.411326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:51.411326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05627","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":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEMiRYc1Bf0X4UC+rPgPtxmJGmoWiNmPtFdAuKhBLn7dVUj4CiLIkuK8QnAq+74NC0lMFKGuOmAb5mab/cZVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:19:11.767256Z"},"content_sha256":"e7a7add777c755c6976f884d8d88114687130b731be484480bf31ab2befee73c","schema_version":"1.0","event_id":"sha256:e7a7add777c755c6976f884d8d88114687130b731be484480bf31ab2befee73c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LMKGRLETWEPKEPRDS4HWPG46M6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Models, networks and algorithmic complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Giulio Ruffini","submitted_at":"2016-12-13T00:54:03Z","abstract_excerpt":"I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs) of different kinds can be seen to implement models, b) that perturbations of inputs and nodes in NNs trained to optimally implement simple models propagate strongly, c) that there is a framework in which recurrent, deep and shallow networks can be seen to fall into a descriptive power hierarchy in agreement with notions from the theory of recursive function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05627","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":""},"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":"2026-05-18T00:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wg4GnFlUXski5VELi4lx5X4/BfIOqHzwVUSZfDfNfasrlWNMsu/d7Ctkm8FX6J0i2PFF3+5WGqC2ahf5r0hDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:19:11.767942Z"},"content_sha256":"c4e04a8a8b58639de364c8b460f023527a3e2ba4d0f2c20514a39324d70434f3","schema_version":"1.0","event_id":"sha256:c4e04a8a8b58639de364c8b460f023527a3e2ba4d0f2c20514a39324d70434f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMKGRLETWEPKEPRDS4HWPG46M6/bundle.json","state_url":"https://pith.science/pith/LMKGRLETWEPKEPRDS4HWPG46M6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMKGRLETWEPKEPRDS4HWPG46M6/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":"2026-06-11T15:19:11Z","links":{"resolver":"https://pith.science/pith/LMKGRLETWEPKEPRDS4HWPG46M6","bundle":"https://pith.science/pith/LMKGRLETWEPKEPRDS4HWPG46M6/bundle.json","state":"https://pith.science/pith/LMKGRLETWEPKEPRDS4HWPG46M6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMKGRLETWEPKEPRDS4HWPG46M6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LMKGRLETWEPKEPRDS4HWPG46M6","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":"bd31d3109039b586a71be69a0476800ae51fd62d1404c0c9abb6d4a9805ce7ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-12-13T00:54:03Z","title_canon_sha256":"63c9d307f916c4c461173fed3918a696575117f17de2d9945acfd3d22ba15c53"},"schema_version":"1.0","source":{"id":"1612.05627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05627","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05627v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05627","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"LMKGRLETWEPK","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LMKGRLETWEPKEPRD","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LMKGRLET","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:c4e04a8a8b58639de364c8b460f023527a3e2ba4d0f2c20514a39324d70434f3","target":"graph","created_at":"2026-05-18T00:54:51Z","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"},"paper":{"abstract_excerpt":"I aim to show that models, classification or generating functions, invariances and datasets are algorithmically equivalent concepts once properly defined, and provide some concrete examples of them. I then show that a) neural networks (NNs) of different kinds can be seen to implement models, b) that perturbations of inputs and nodes in NNs trained to optimally implement simple models propagate strongly, c) that there is a framework in which recurrent, deep and shallow networks can be seen to fall into a descriptive power hierarchy in agreement with notions from the theory of recursive function","authors_text":"Giulio Ruffini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-12-13T00:54:03Z","title":"Models, networks and algorithmic complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05627","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:e7a7add777c755c6976f884d8d88114687130b731be484480bf31ab2befee73c","target":"record","created_at":"2026-05-18T00:54:51Z","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":"bd31d3109039b586a71be69a0476800ae51fd62d1404c0c9abb6d4a9805ce7ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-12-13T00:54:03Z","title_canon_sha256":"63c9d307f916c4c461173fed3918a696575117f17de2d9945acfd3d22ba15c53"},"schema_version":"1.0","source":{"id":"1612.05627","kind":"arxiv","version":1}},"canonical_sha256":"5b1468ac93b11ea23e23970f679b9e67817a00ab0f822602ca6f096496c76aa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b1468ac93b11ea23e23970f679b9e67817a00ab0f822602ca6f096496c76aa6","first_computed_at":"2026-05-18T00:54:51.411326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.411326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GCIhS35mNczu3WzilJHV/ZzenPCrOcLfwvDuIrroc5OwkrLMluw2vP5DZEReOQQlkBDtnF0yf6qYDWd7rlPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.411931Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a7add777c755c6976f884d8d88114687130b731be484480bf31ab2befee73c","sha256:c4e04a8a8b58639de364c8b460f023527a3e2ba4d0f2c20514a39324d70434f3"],"state_sha256":"f8670b04105833d255c3dd97db9e230f71579d2bbce12b25d81323090808b3ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4b+wVuvIr3JSyBFTF731RxRvw9C2uWLjADtad4QJl/pdbmpFCLk1eizvBY+QVzijXzmAW8fon6HBoFpiGuCsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:19:11.771819Z","bundle_sha256":"937893ceebb854268c1613f7b5bfffac0e76819334719b95e17ead486e1a10fe"}}