{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:UFQVPD3TQJDLLP64QWIDJ33YW5","short_pith_number":"pith:UFQVPD3T","canonical_record":{"source":{"id":"2310.20360","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-10-31T11:01:23Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"title_canon_sha256":"2a0e360bb832d8b0c72d7cd9540def2a7af3340162a1a44dac850588fbaee9ee","abstract_canon_sha256":"fec3a6230dccf78fdb3b66c007285cf3ba1501e8216108868625dfa087d5557a"},"schema_version":"1.0"},"canonical_sha256":"a161578f738246b5bfdc859034ef78b745c7ad2b1e496c031d1e09ee6b46780f","source":{"kind":"arxiv","id":"2310.20360","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.20360","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"2310.20360v3","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20360","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"UFQVPD3TQJDL","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_16","alias_value":"UFQVPD3TQJDLLP64","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_8","alias_value":"UFQVPD3T","created_at":"2026-07-05T11:37:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:UFQVPD3TQJDLLP64QWIDJ33YW5","target":"record","payload":{"canonical_record":{"source":{"id":"2310.20360","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-10-31T11:01:23Z","cross_cats_sorted":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"title_canon_sha256":"2a0e360bb832d8b0c72d7cd9540def2a7af3340162a1a44dac850588fbaee9ee","abstract_canon_sha256":"fec3a6230dccf78fdb3b66c007285cf3ba1501e8216108868625dfa087d5557a"},"schema_version":"1.0"},"canonical_sha256":"a161578f738246b5bfdc859034ef78b745c7ad2b1e496c031d1e09ee6b46780f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:41.394653Z","signature_b64":"NT9XWnDkbyQVAcW6YkteZbXs/zXVdQEtJ8owcdgV5ASu0tPVZHcDnIdadaUrNidicitHtL4dsFrGv/tWuob0Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a161578f738246b5bfdc859034ef78b745c7ad2b1e496c031d1e09ee6b46780f","last_reissued_at":"2026-07-05T11:37:41.394140Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:41.394140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.20360","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lxPAOqIpc/5gjNPdWzaeMT1nZCXSVv7/tjI/TxkE90yuv3tUfW7ofvGTcwx56TNQ2KwRIKMbX5Nbg226WRFfBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:58:26.498274Z"},"content_sha256":"7d5bfb2bbc4c4644a505a4c06f3a21e960bce8f17d3b0e0673a65fb969e9bf07","schema_version":"1.0","event_id":"sha256:7d5bfb2bbc4c4644a505a4c06f3a21e960bce8f17d3b0e0673a65fb969e9bf07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:UFQVPD3TQJDLLP64QWIDJ33YW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger","submitted_at":"2023-10-31T11:01:23Z","abstract_excerpt":"This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20360","kind":"arxiv","version":3},"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/2310.20360/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":"2026-07-05T11:37:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ylWFPtPvdzpJsj3nv58NC9dN3zg9IE3gyMi3lPRDwMxwSYd2SPOaYfgUQsyfrTtvuEBKXX5YjCbLqCR6mlrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:58:26.499412Z"},"content_sha256":"ec0839ceb8e6055d47d3079c48d209afd40442ac61e904e8c82581d6da118cc6","schema_version":"1.0","event_id":"sha256:ec0839ceb8e6055d47d3079c48d209afd40442ac61e904e8c82581d6da118cc6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/bundle.json","state_url":"https://pith.science/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/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":"2026-08-09T00:58:26Z","links":{"resolver":"https://pith.science/pith/UFQVPD3TQJDLLP64QWIDJ33YW5","bundle":"https://pith.science/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/bundle.json","state":"https://pith.science/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFQVPD3TQJDLLP64QWIDJ33YW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:UFQVPD3TQJDLLP64QWIDJ33YW5","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":"fec3a6230dccf78fdb3b66c007285cf3ba1501e8216108868625dfa087d5557a","cross_cats_sorted":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-10-31T11:01:23Z","title_canon_sha256":"2a0e360bb832d8b0c72d7cd9540def2a7af3340162a1a44dac850588fbaee9ee"},"schema_version":"1.0","source":{"id":"2310.20360","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.20360","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"arxiv_version","alias_value":"2310.20360v3","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20360","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_12","alias_value":"UFQVPD3TQJDL","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_16","alias_value":"UFQVPD3TQJDLLP64","created_at":"2026-07-05T11:37:41Z"},{"alias_kind":"pith_short_8","alias_value":"UFQVPD3T","created_at":"2026-07-05T11:37:41Z"}],"graph_snapshots":[{"event_id":"sha256:ec0839ceb8e6055d47d3079c48d209afd40442ac61e904e8c82581d6da118cc6","target":"graph","created_at":"2026-07-05T11:37:41Z","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/2310.20360/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This book aims to provide an introduction to the topic of deep learning algorithms. We review essential components of deep learning algorithms in full mathematical detail including different artificial neural network (ANN) architectures (such as fully-connected feedforward ANNs, convolutional ANNs, recurrent ANNs, residual ANNs, and ANNs with batch normalization) and different optimization algorithms (such as the basic stochastic gradient descent (SGD) method, accelerated methods, and adaptive methods). We also cover several theoretical aspects of deep learning algorithms such as approximation","authors_text":"Arnulf Jentzen, Benno Kuckuck, Philippe von Wurstemberger","cross_cats":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-10-31T11:01:23Z","title":"Mathematical Introduction to Deep Learning: Methods, Implementations, and Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20360","kind":"arxiv","version":3},"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":"sha256:7d5bfb2bbc4c4644a505a4c06f3a21e960bce8f17d3b0e0673a65fb969e9bf07","target":"record","created_at":"2026-07-05T11:37:41Z","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":"fec3a6230dccf78fdb3b66c007285cf3ba1501e8216108868625dfa087d5557a","cross_cats_sorted":["cs.AI","cs.NA","math.NA","math.PR","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-10-31T11:01:23Z","title_canon_sha256":"2a0e360bb832d8b0c72d7cd9540def2a7af3340162a1a44dac850588fbaee9ee"},"schema_version":"1.0","source":{"id":"2310.20360","kind":"arxiv","version":3}},"canonical_sha256":"a161578f738246b5bfdc859034ef78b745c7ad2b1e496c031d1e09ee6b46780f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a161578f738246b5bfdc859034ef78b745c7ad2b1e496c031d1e09ee6b46780f","first_computed_at":"2026-07-05T11:37:41.394140Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:41.394140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NT9XWnDkbyQVAcW6YkteZbXs/zXVdQEtJ8owcdgV5ASu0tPVZHcDnIdadaUrNidicitHtL4dsFrGv/tWuob0Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:41.394653Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.20360","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d5bfb2bbc4c4644a505a4c06f3a21e960bce8f17d3b0e0673a65fb969e9bf07","sha256:ec0839ceb8e6055d47d3079c48d209afd40442ac61e904e8c82581d6da118cc6"],"state_sha256":"9a35d32530d7e9c2aabbca699c09f35dd296e538d34bee0de50df8f8b55695e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+5hqvs1+r94ZuZ4q7gkbG4SUyIYqKlfHWpiKBWz12079aY0zXPmoameIk6DJxhred9NJFh5CGxI+t1H9m5bgDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:58:26.505742Z","bundle_sha256":"2bbaafa0403683ad88ad62524dd192c9c5204ff3d53474144713bddece3a0540"}}