{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:7BSFZSMA27L56ICP3QZUW355YA","short_pith_number":"pith:7BSFZSMA","canonical_record":{"source":{"id":"2606.09929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-07T14:46:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0a2863441145642b9c1a1f9b6f061dd7538a25594ac6c3662dd71e2c0c024c63","abstract_canon_sha256":"85f031f3f9de42da78bf54677f281e408d13d3089c3fa358f8d96dae4ccab975"},"schema_version":"1.0"},"canonical_sha256":"f8645cc980d7d7df204fdc334b6fbdc01e26f450fbdcee6805892d39c7c4e5b6","source":{"kind":"arxiv","id":"2606.09929","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09929","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09929v1","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09929","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"7BSFZSMA27L5","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_16","alias_value":"7BSFZSMA27L56ICP","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_8","alias_value":"7BSFZSMA","created_at":"2026-06-10T00:08:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:7BSFZSMA27L56ICP3QZUW355YA","target":"record","payload":{"canonical_record":{"source":{"id":"2606.09929","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-07T14:46:09Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"0a2863441145642b9c1a1f9b6f061dd7538a25594ac6c3662dd71e2c0c024c63","abstract_canon_sha256":"85f031f3f9de42da78bf54677f281e408d13d3089c3fa358f8d96dae4ccab975"},"schema_version":"1.0"},"canonical_sha256":"f8645cc980d7d7df204fdc334b6fbdc01e26f450fbdcee6805892d39c7c4e5b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T00:08:33.531392Z","signature_b64":"dgqzZ3fxScvfoUcM/IADwOGxCpZz9y7L7FGWKgIe+HecbKipzKy/WP4ayusyeqSowr4rvdQsSKVWQMqgbTaHCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8645cc980d7d7df204fdc334b6fbdc01e26f450fbdcee6805892d39c7c4e5b6","last_reissued_at":"2026-06-10T00:08:33.530519Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T00:08:33.530519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.09929","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":"2026-06-10T00:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7Drk7BV0R7D+fR+/9vR/4fa//xlQl+RdaYc//hLRAS2QpXB8bOrEypXgHDXaJj+/Ule6AOc/JHHQ2w7IBRRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:59:15.040122Z"},"content_sha256":"0bed08dc9307f51aa8eb03472398eae48285087021c08c9263ff843932ec08c9","schema_version":"1.0","event_id":"sha256:0bed08dc9307f51aa8eb03472398eae48285087021c08c9263ff843932ec08c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:7BSFZSMA27L56ICP3QZUW355YA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Caleb Munigety","submitted_at":"2026-06-07T14:46:09Z","abstract_excerpt":"Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable. We revisit that premise for networks of nonlinear oscillators whose mass, damping, and stiffness are learned end-to-end through a symplectic integrator. Our central result is a trilemma: memory horizon, gradient stability, and dynamical expressivity cannot be simultaneously maximized, because all three are governed by the damping. The backward gradient decays at a rate set by the damping, capping how "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09929","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/2606.09929/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":"2026-06-10T00:08:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YZyHi6vm1hHzMG7o8DJTQD8fiTlRRi7B+WwQiC1JAYQxKq6ZxgLBgGJ0Ysm7Asmlxhw6JKvQBEigBAtSeA3pDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T09:59:15.040676Z"},"content_sha256":"0c985fe0b87464c52a2ba18d84438e417582b3b1d8c7cc6380e9d097d928e6ca","schema_version":"1.0","event_id":"sha256:0c985fe0b87464c52a2ba18d84438e417582b3b1d8c7cc6380e9d097d928e6ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7BSFZSMA27L56ICP3QZUW355YA/bundle.json","state_url":"https://pith.science/pith/7BSFZSMA27L56ICP3QZUW355YA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7BSFZSMA27L56ICP3QZUW355YA/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":"2026-07-03T09:59:15Z","links":{"resolver":"https://pith.science/pith/7BSFZSMA27L56ICP3QZUW355YA","bundle":"https://pith.science/pith/7BSFZSMA27L56ICP3QZUW355YA/bundle.json","state":"https://pith.science/pith/7BSFZSMA27L56ICP3QZUW355YA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7BSFZSMA27L56ICP3QZUW355YA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7BSFZSMA27L56ICP3QZUW355YA","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":"85f031f3f9de42da78bf54677f281e408d13d3089c3fa358f8d96dae4ccab975","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-07T14:46:09Z","title_canon_sha256":"0a2863441145642b9c1a1f9b6f061dd7538a25594ac6c3662dd71e2c0c024c63"},"schema_version":"1.0","source":{"id":"2606.09929","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.09929","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"arxiv_version","alias_value":"2606.09929v1","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.09929","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_12","alias_value":"7BSFZSMA27L5","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_16","alias_value":"7BSFZSMA27L56ICP","created_at":"2026-06-10T00:08:33Z"},{"alias_kind":"pith_short_8","alias_value":"7BSFZSMA","created_at":"2026-06-10T00:08:33Z"}],"graph_snapshots":[{"event_id":"sha256:0c985fe0b87464c52a2ba18d84438e417582b3b1d8c7cc6380e9d097d928e6ca","target":"graph","created_at":"2026-06-10T00:08:33Z","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/2606.09929/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable. We revisit that premise for networks of nonlinear oscillators whose mass, damping, and stiffness are learned end-to-end through a symplectic integrator. Our central result is a trilemma: memory horizon, gradient stability, and dynamical expressivity cannot be simultaneously maximized, because all three are governed by the damping. The backward gradient decays at a rate set by the damping, capping how ","authors_text":"Caleb Munigety","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-07T14:46:09Z","title":"Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.09929","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":"sha256:0bed08dc9307f51aa8eb03472398eae48285087021c08c9263ff843932ec08c9","target":"record","created_at":"2026-06-10T00:08:33Z","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":"85f031f3f9de42da78bf54677f281e408d13d3089c3fa358f8d96dae4ccab975","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-07T14:46:09Z","title_canon_sha256":"0a2863441145642b9c1a1f9b6f061dd7538a25594ac6c3662dd71e2c0c024c63"},"schema_version":"1.0","source":{"id":"2606.09929","kind":"arxiv","version":1}},"canonical_sha256":"f8645cc980d7d7df204fdc334b6fbdc01e26f450fbdcee6805892d39c7c4e5b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8645cc980d7d7df204fdc334b6fbdc01e26f450fbdcee6805892d39c7c4e5b6","first_computed_at":"2026-06-10T00:08:33.530519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T00:08:33.530519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgqzZ3fxScvfoUcM/IADwOGxCpZz9y7L7FGWKgIe+HecbKipzKy/WP4ayusyeqSowr4rvdQsSKVWQMqgbTaHCw==","signature_status":"signed_v1","signed_at":"2026-06-10T00:08:33.531392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.09929","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bed08dc9307f51aa8eb03472398eae48285087021c08c9263ff843932ec08c9","sha256:0c985fe0b87464c52a2ba18d84438e417582b3b1d8c7cc6380e9d097d928e6ca"],"state_sha256":"69865ab88745183d8e356c6cf02a8a8dee8bfecb8a6469c0306f9d78c7031a2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcWKUVTjemPHv5o+nvbLFFh/YY8YfyNbI+PUC0XQsRaoWgE9vX6RvSxPCHQfyaxHL5HvPUZY2NZrjOBk1SHxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T09:59:15.043113Z","bundle_sha256":"5f3bbb2f66f2585d240e1651e508a52f341c89ffcee99f0d10c21fa3ffc16d74"}}