{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NZ5SI53AWSQGTYOBZEP3XR7M7P","short_pith_number":"pith:NZ5SI53A","canonical_record":{"source":{"id":"1601.07983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-29T06:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"cc86be08315f123d0a60123d7666e7a8ef705df109d2449a1d7eb64d98defeb2","abstract_canon_sha256":"4311e32a0916eaecefa5e9e4899502be73992ed433625b7b3a1d578023d89c50"},"schema_version":"1.0"},"canonical_sha256":"6e7b247760b4a069e1c1c91fbbc7ecfbd77a24ab8c464ad3f309937009ade4ac","source":{"kind":"arxiv","id":"1601.07983","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07983","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07983v2","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07983","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"NZ5SI53AWSQG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NZ5SI53AWSQGTYOB","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NZ5SI53A","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NZ5SI53AWSQGTYOBZEP3XR7M7P","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-29T06:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"cc86be08315f123d0a60123d7666e7a8ef705df109d2449a1d7eb64d98defeb2","abstract_canon_sha256":"4311e32a0916eaecefa5e9e4899502be73992ed433625b7b3a1d578023d89c50"},"schema_version":"1.0"},"canonical_sha256":"6e7b247760b4a069e1c1c91fbbc7ecfbd77a24ab8c464ad3f309937009ade4ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:08.139097Z","signature_b64":"aRV2UA2FI59esF8+xwH+TD7w9jgi4/r7sQmjecREo8sZfK8ItyID9nL6pwYArhoHi6l+N8kKkZOCZ/ubsCbjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e7b247760b4a069e1c1c91fbbc7ecfbd77a24ab8c464ad3f309937009ade4ac","last_reissued_at":"2026-05-18T01:20:08.138585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:08.138585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07983","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bK6G0sT4rJlYsUW7I4AaR84xrWlfRdMRm9LMq8bkvURHhaL/X9H025pJDO9ZJv0F4KrFMbgmZ4TUglNCEx/sBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:14:19.255460Z"},"content_sha256":"0abfde2513c9469da0b9e9db0da65134a5070ad96fae7abe554335470344a68f","schema_version":"1.0","event_id":"sha256:0abfde2513c9469da0b9e9db0da65134a5070ad96fae7abe554335470344a68f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NZ5SI53AWSQGTYOBZEP3XR7M7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yoshio Uwano","submitted_at":"2016-01-29T06:25:30Z","abstract_excerpt":"In this paper, two families of trajectories on the quantum state space (QSS) originating from a synaptic-neuron model and from quantum information geometry meet together. The extended averaged Hebbian learning equation (EAHLE) on the QSS developed by the author and Yuya (Far East Journal of Applied Mathematics, vol.47, pp.149-167, 2010) from a Hebbian synaptic-neuron model is studied from a quantum-information-geometric point of view. It is shown that all the trajectories of the EAHLE are the e-geodesics, the autoparallel curves with respect to the exponential-type parallel transport, on the Q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07983","kind":"arxiv","version":2},"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":"2026-05-18T01:20:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vBkJ0dGu9msYKAPT2e7q9573bn35hFHfzyYmrV+MRsAlk9Jr6B8r1iF97vMwnpRmkN9wcbNOap626HRwLsc5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:14:19.255824Z"},"content_sha256":"90b5b16a120738c39bb8033ee007346b0077877c7ed0ea414c5ff13297bd4e71","schema_version":"1.0","event_id":"sha256:90b5b16a120738c39bb8033ee007346b0077877c7ed0ea414c5ff13297bd4e71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/bundle.json","state_url":"https://pith.science/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/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":"2026-06-26T17:14:19Z","links":{"resolver":"https://pith.science/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P","bundle":"https://pith.science/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/bundle.json","state":"https://pith.science/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NZ5SI53AWSQGTYOBZEP3XR7M7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NZ5SI53AWSQGTYOBZEP3XR7M7P","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":"4311e32a0916eaecefa5e9e4899502be73992ed433625b7b3a1d578023d89c50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-29T06:25:30Z","title_canon_sha256":"cc86be08315f123d0a60123d7666e7a8ef705df109d2449a1d7eb64d98defeb2"},"schema_version":"1.0","source":{"id":"1601.07983","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07983","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07983v2","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07983","created_at":"2026-05-18T01:20:08Z"},{"alias_kind":"pith_short_12","alias_value":"NZ5SI53AWSQG","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NZ5SI53AWSQGTYOB","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NZ5SI53A","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:90b5b16a120738c39bb8033ee007346b0077877c7ed0ea414c5ff13297bd4e71","target":"graph","created_at":"2026-05-18T01:20:08Z","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":"In this paper, two families of trajectories on the quantum state space (QSS) originating from a synaptic-neuron model and from quantum information geometry meet together. The extended averaged Hebbian learning equation (EAHLE) on the QSS developed by the author and Yuya (Far East Journal of Applied Mathematics, vol.47, pp.149-167, 2010) from a Hebbian synaptic-neuron model is studied from a quantum-information-geometric point of view. It is shown that all the trajectories of the EAHLE are the e-geodesics, the autoparallel curves with respect to the exponential-type parallel transport, on the Q","authors_text":"Yoshio Uwano","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-29T06:25:30Z","title":"All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07983","kind":"arxiv","version":2},"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":"sha256:0abfde2513c9469da0b9e9db0da65134a5070ad96fae7abe554335470344a68f","target":"record","created_at":"2026-05-18T01:20:08Z","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":"4311e32a0916eaecefa5e9e4899502be73992ed433625b7b3a1d578023d89c50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-01-29T06:25:30Z","title_canon_sha256":"cc86be08315f123d0a60123d7666e7a8ef705df109d2449a1d7eb64d98defeb2"},"schema_version":"1.0","source":{"id":"1601.07983","kind":"arxiv","version":2}},"canonical_sha256":"6e7b247760b4a069e1c1c91fbbc7ecfbd77a24ab8c464ad3f309937009ade4ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e7b247760b4a069e1c1c91fbbc7ecfbd77a24ab8c464ad3f309937009ade4ac","first_computed_at":"2026-05-18T01:20:08.138585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:08.138585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aRV2UA2FI59esF8+xwH+TD7w9jgi4/r7sQmjecREo8sZfK8ItyID9nL6pwYArhoHi6l+N8kKkZOCZ/ubsCbjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:08.139097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07983","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0abfde2513c9469da0b9e9db0da65134a5070ad96fae7abe554335470344a68f","sha256:90b5b16a120738c39bb8033ee007346b0077877c7ed0ea414c5ff13297bd4e71"],"state_sha256":"5bdf3c270032c0d2ee6b87be161120200bc9e13551f57a68041f3d411c2b3b90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fqZPCcGlNwqk4lDdpub25mVrUc6bJ012FNCGptlWMKpT4DH5OGx+nYheaJuRlgUy9VWk9lgC1iZJMpYFXqCMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:14:19.257855Z","bundle_sha256":"a2894065f157b5ca607dd4ba5a2b4ee93913c9c05d44217e87cc3a101c1de596"}}