{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:MHFKVDENZZPSATMEK7Y5KJDQWM","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":"b7616432716c2df9cc42720049babdce96152df5c14b21f07b4e65f11bff272e","cross_cats_sorted":["gr-qc","hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2001-06-05T14:49:04Z","title_canon_sha256":"a778b26a48fc5e1215152858ae6ca0435f60b14803c9be3c7e82427c2518a183"},"schema_version":"1.0","source":{"id":"hep-th/0106041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0106041","created_at":"2026-05-18T04:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0106041v1","created_at":"2026-05-18T04:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0106041","created_at":"2026-05-18T04:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"MHFKVDENZZPS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"MHFKVDENZZPSATME","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"MHFKVDEN","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:53599f012c2c60f9624270edf5bb61a4d5c433e035c861447f741031397bd0ad","target":"graph","created_at":"2026-05-18T04:18:13Z","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":"A generalization of the Bardeen formalism to the case of warped geometries is presented. The system determining the gauge-invariant fluctuations of the metric induced by the scalar fluctuations of the brane is reduced to a set of Schr\\\"odinger-like equations for the Bardeen potentials and for the canonical normal modes of the scalar-tensor action. Scalar, vector and tensor modes of the geometry are classified according to four-dimensional Lorentz transformations. While the tensor modes of the geometry live on the brane determining the corrections to Newton law, the scalar and and vector fluctu","authors_text":"Lausanne University), Massimo Giovannini (Institute for Theoretical Physics","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2001-06-05T14:49:04Z","title":"Gauge-invariant fluctuations of scalar branes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0106041","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":"sha256:3eac937eecf87d041750aaa1c08b60f6ab6b7f9054ee48694dbf0496a0c8162a","target":"record","created_at":"2026-05-18T04:18:13Z","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":"b7616432716c2df9cc42720049babdce96152df5c14b21f07b4e65f11bff272e","cross_cats_sorted":["gr-qc","hep-ph"],"license":"","primary_cat":"hep-th","submitted_at":"2001-06-05T14:49:04Z","title_canon_sha256":"a778b26a48fc5e1215152858ae6ca0435f60b14803c9be3c7e82427c2518a183"},"schema_version":"1.0","source":{"id":"hep-th/0106041","kind":"arxiv","version":1}},"canonical_sha256":"61caaa8c8dce5f204d8457f1d52470b305fecf74dac2df710faa10940c46b092","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61caaa8c8dce5f204d8457f1d52470b305fecf74dac2df710faa10940c46b092","first_computed_at":"2026-05-18T04:18:13.971778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:13.971778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hocZBDcyTXH3ZciI4eRv1XrsKCblzVFWvEVn0eiDL/uis1Dd8m7d3nTNM06eE1cNh1GJU23kkGrZu9isaPqJAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:13.972427Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0106041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3eac937eecf87d041750aaa1c08b60f6ab6b7f9054ee48694dbf0496a0c8162a","sha256:53599f012c2c60f9624270edf5bb61a4d5c433e035c861447f741031397bd0ad"],"state_sha256":"47196a244850384954aa2ffe014410fe630bcfc054a838e483db55cd55402c3d"}