{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:EIZ2KSX2GZFLFU4TV7NR54HIZS","short_pith_number":"pith:EIZ2KSX2","canonical_record":{"source":{"id":"2606.03067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-02T02:56:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"606ff52cb59716015e404659f43a15dcbd80a60a6d56b75bb371baa2e6eab1b9","abstract_canon_sha256":"b5f97aed948b97b575a3495598a3c1cf1af99ecc6fa77e06afe1fa0fe0444e4c"},"schema_version":"1.0"},"canonical_sha256":"2233a54afa364ab2d393afdb1ef0e8cca63ba4fb16bac3c0795256e7a3367a4f","source":{"kind":"arxiv","id":"2606.03067","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03067","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03067v1","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03067","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"EIZ2KSX2GZFL","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"EIZ2KSX2GZFLFU4T","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"EIZ2KSX2","created_at":"2026-06-03T01:05:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:EIZ2KSX2GZFLFU4TV7NR54HIZS","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03067","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-02T02:56:36Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"606ff52cb59716015e404659f43a15dcbd80a60a6d56b75bb371baa2e6eab1b9","abstract_canon_sha256":"b5f97aed948b97b575a3495598a3c1cf1af99ecc6fa77e06afe1fa0fe0444e4c"},"schema_version":"1.0"},"canonical_sha256":"2233a54afa364ab2d393afdb1ef0e8cca63ba4fb16bac3c0795256e7a3367a4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:30.791830Z","signature_b64":"UeKtDdJpo7oNyG4BJG2166kAtVkyIEQtGFI7JqyygJCFWLzrawdZDzKZtHvJDECsiHbdDrHbUHa/D8594rrEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2233a54afa364ab2d393afdb1ef0e8cca63ba4fb16bac3c0795256e7a3367a4f","last_reissued_at":"2026-06-03T01:05:30.791363Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:30.791363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03067","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":"2026-06-03T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IH5pvQksk48CEng682excvoLCk5sjQcot06kr5FoQwoTL++/qCT+d3rHhfDT8DkIZsrIFrHLKV/2ha9/jQUXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:08:00.255078Z"},"content_sha256":"82c5fc3ddfeccd37e7fecec99d53e2f689474b2f66e0aa4aa6823d8786e18d60","schema_version":"1.0","event_id":"sha256:82c5fc3ddfeccd37e7fecec99d53e2f689474b2f66e0aa4aa6823d8786e18d60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:EIZ2KSX2GZFLFU4TV7NR54HIZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trajectory-Aware Node Contributions and the Limits of Static Controllability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Dmitry Zaytsev, Michael Coppedge, Valentina Kuskova","submitted_at":"2026-06-02T02:56:36Z","abstract_excerpt":"A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior. Existing approaches rely on either static-graph centralities or control-theoretic quantities such as controllability Gramians, which assume linear, time-invariant dynamics. Estimated systems, however, are typically nonlinear and time-varying. We define \"emergent contribution (EC),\" a finite-horizon measure of a node's dynamical leverage: the metric-weighted energy of its impulse response accumulated along the system trajectory. Computed from the Jacobians of any differentiable m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03067","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/2606.03067/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":"2026-06-03T01:05:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JnY4cYpAGek/UuQYNTZCIF77ri+OBbokmbd/Dvicc2GU1YkkaEi/5W4craro/v4yvv29ZRW6v1r5y+7GsLWkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:08:00.255795Z"},"content_sha256":"530dfea0f39c62aa558342289a46f5f8f1d2ceae06e49043600d8035f310a729","schema_version":"1.0","event_id":"sha256:530dfea0f39c62aa558342289a46f5f8f1d2ceae06e49043600d8035f310a729"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/bundle.json","state_url":"https://pith.science/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/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":"2026-06-07T04:08:00Z","links":{"resolver":"https://pith.science/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS","bundle":"https://pith.science/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/bundle.json","state":"https://pith.science/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EIZ2KSX2GZFLFU4TV7NR54HIZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EIZ2KSX2GZFLFU4TV7NR54HIZS","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":"b5f97aed948b97b575a3495598a3c1cf1af99ecc6fa77e06afe1fa0fe0444e4c","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-02T02:56:36Z","title_canon_sha256":"606ff52cb59716015e404659f43a15dcbd80a60a6d56b75bb371baa2e6eab1b9"},"schema_version":"1.0","source":{"id":"2606.03067","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03067","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03067v1","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03067","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"EIZ2KSX2GZFL","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"EIZ2KSX2GZFLFU4T","created_at":"2026-06-03T01:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"EIZ2KSX2","created_at":"2026-06-03T01:05:30Z"}],"graph_snapshots":[{"event_id":"sha256:530dfea0f39c62aa558342289a46f5f8f1d2ceae06e49043600d8035f310a729","target":"graph","created_at":"2026-06-03T01:05:30Z","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/2606.03067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior. Existing approaches rely on either static-graph centralities or control-theoretic quantities such as controllability Gramians, which assume linear, time-invariant dynamics. Estimated systems, however, are typically nonlinear and time-varying. We define \"emergent contribution (EC),\" a finite-horizon measure of a node's dynamical leverage: the metric-weighted energy of its impulse response accumulated along the system trajectory. Computed from the Jacobians of any differentiable m","authors_text":"Dmitry Zaytsev, Michael Coppedge, Valentina Kuskova","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-02T02:56:36Z","title":"Trajectory-Aware Node Contributions and the Limits of Static Controllability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03067","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":"sha256:82c5fc3ddfeccd37e7fecec99d53e2f689474b2f66e0aa4aa6823d8786e18d60","target":"record","created_at":"2026-06-03T01:05:30Z","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":"b5f97aed948b97b575a3495598a3c1cf1af99ecc6fa77e06afe1fa0fe0444e4c","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-06-02T02:56:36Z","title_canon_sha256":"606ff52cb59716015e404659f43a15dcbd80a60a6d56b75bb371baa2e6eab1b9"},"schema_version":"1.0","source":{"id":"2606.03067","kind":"arxiv","version":1}},"canonical_sha256":"2233a54afa364ab2d393afdb1ef0e8cca63ba4fb16bac3c0795256e7a3367a4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2233a54afa364ab2d393afdb1ef0e8cca63ba4fb16bac3c0795256e7a3367a4f","first_computed_at":"2026-06-03T01:05:30.791363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:30.791363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UeKtDdJpo7oNyG4BJG2166kAtVkyIEQtGFI7JqyygJCFWLzrawdZDzKZtHvJDECsiHbdDrHbUHa/D8594rrEBw==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:30.791830Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03067","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82c5fc3ddfeccd37e7fecec99d53e2f689474b2f66e0aa4aa6823d8786e18d60","sha256:530dfea0f39c62aa558342289a46f5f8f1d2ceae06e49043600d8035f310a729"],"state_sha256":"2d3fb3f70d6d3e818ea76e35edd75876f94a4d875ca4404471c7951ebac34e78"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"So+e9jPIHil0uT4Eg8LgridT6/YHSubzupXqTRqTT96ZxoX+/aK3i2X+wyfu0BRKSpOkthPRu9Zn573HVD6NBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:08:00.259282Z","bundle_sha256":"1fc5144e46c7e97f70099e444f0494c444850e895ea3427ebe705f5b9f6e5e2e"}}