{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:D7DOJLGPTAHUQTTIJ4A4UJQSAC","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":"ee7be0c8198cf9f7926dc1ec1f4736a1b1f0c667e90fb1bc15aa2e588564c784","cross_cats_sorted":["cs.AI","math.DS","math.RT","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-27T18:38:23Z","title_canon_sha256":"fc31415dd6dd8a7921ce034dd2dee536fec381177b3169726cd3298c8a965a45"},"schema_version":"1.0","source":{"id":"2605.28983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.28983","created_at":"2026-05-29T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.28983v1","created_at":"2026-05-29T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.28983","created_at":"2026-05-29T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"D7DOJLGPTAHU","created_at":"2026-05-29T01:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"D7DOJLGPTAHUQTTI","created_at":"2026-05-29T01:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"D7DOJLGP","created_at":"2026-05-29T01:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:7603cde9ba23ddcb980b38c4216f819333d4b3362c70cb709e208694e48f8be6","target":"graph","created_at":"2026-05-29T01:04:42Z","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/2605.28983/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights. The correspondence is exact for log-sum-exp layers and structural for broader architectures: residual networks, transformers, and recurrent architectures (RNNs, LSTMs, SSMs) each discretize the","authors_text":"Christopher P. Monterola, Erika Fille T. Legara, Jose Marie Antonio Mi\\~noza","cross_cats":["cs.AI","math.DS","math.RT","physics.comp-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-27T18:38:23Z","title":"The Hamilton-Jacobi Theory of Deep Learning"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28983","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":"sha256:4406cfec4d2399020b4ad13ded466ee51677226e2a60ea883bddcae3418a3164","target":"record","created_at":"2026-05-29T01:04:42Z","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":"ee7be0c8198cf9f7926dc1ec1f4736a1b1f0c667e90fb1bc15aa2e588564c784","cross_cats_sorted":["cs.AI","math.DS","math.RT","physics.comp-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-27T18:38:23Z","title_canon_sha256":"fc31415dd6dd8a7921ce034dd2dee536fec381177b3169726cd3298c8a965a45"},"schema_version":"1.0","source":{"id":"2605.28983","kind":"arxiv","version":1}},"canonical_sha256":"1fc6e4accf980f484e684f01ca2612008934f3c2db7db8e45c9586fe33530653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fc6e4accf980f484e684f01ca2612008934f3c2db7db8e45c9586fe33530653","first_computed_at":"2026-05-29T01:04:42.389489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:42.389489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fq8DmNqEiPP7G8oVvrue6WaQgXNuoGRptqoePu5xNTAFvpOUIH7gk7a9w/5GzGc5cuZrxBjk3FCaMy2cQzm+Bg==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:42.389952Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.28983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4406cfec4d2399020b4ad13ded466ee51677226e2a60ea883bddcae3418a3164","sha256:7603cde9ba23ddcb980b38c4216f819333d4b3362c70cb709e208694e48f8be6"],"state_sha256":"89d54479ff476442ebc160ed3b64fb27f7c3deecee0ef044a80f662647ff99bd"}