{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:CWQISC5A2ANUQSKBPZCQ3F3WQW","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":"7ed514b69db16e9b2869dce88af9978d3e8b756d20fbfa8a4dd0da781026d678","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2002-10-31T23:18:35Z","title_canon_sha256":"bda0e9d126bc108325afbe02ffecbf3699f872c84bee6e0c49e5153de0b1ab3c"},"schema_version":"1.0","source":{"id":"gr-qc/0211001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0211001","created_at":"2026-07-04T16:33:47Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0211001v1","created_at":"2026-07-04T16:33:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0211001","created_at":"2026-07-04T16:33:47Z"},{"alias_kind":"pith_short_12","alias_value":"CWQISC5A2ANU","created_at":"2026-07-04T16:33:47Z"},{"alias_kind":"pith_short_16","alias_value":"CWQISC5A2ANUQSKB","created_at":"2026-07-04T16:33:47Z"},{"alias_kind":"pith_short_8","alias_value":"CWQISC5A","created_at":"2026-07-04T16:33:47Z"}],"graph_snapshots":[{"event_id":"sha256:624008ce148a6414b0f23c07b375acac0a6b16ab253b4888c75ab968a9ab1f12","target":"graph","created_at":"2026-07-04T16:33:47Z","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/gr-qc/0211001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a self-contained formalism for analyzing scale invariant differential equations. We first cast the scale invariant model into its equidimensional and autonomous forms, find its fixed points, and then obtain power-law background solutions. After linearizing about these fixed points, we find a second linearized solution, which provides a distinct collection of power laws characterizing the deviations from the fixed point. We prove that generically there will be a region surrounding the fixed point in which the complete general solution can be represented as a generalized Frobenius-lik","authors_text":"Matt Visser (Victoria University of Wellington), Nicolas Yunes (Washington University in Saint Louis)","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2002-10-31T23:18:35Z","title":"Power laws, scale invariance, and generalized Frobenius series: Applications to Newtonian and TOV stars near criticality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0211001","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":"sha256:18fb19f747f636b4a5e550171d64a9ab3a4aecaa59019117041dcb198e563391","target":"record","created_at":"2026-07-04T16:33:47Z","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":"7ed514b69db16e9b2869dce88af9978d3e8b756d20fbfa8a4dd0da781026d678","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2002-10-31T23:18:35Z","title_canon_sha256":"bda0e9d126bc108325afbe02ffecbf3699f872c84bee6e0c49e5153de0b1ab3c"},"schema_version":"1.0","source":{"id":"gr-qc/0211001","kind":"arxiv","version":1}},"canonical_sha256":"15a0890ba0d01b4849417e450d97768585c683896fc74bd7399d75d2d43a4e8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15a0890ba0d01b4849417e450d97768585c683896fc74bd7399d75d2d43a4e8e","first_computed_at":"2026-07-04T16:33:47.795285Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:33:47.795285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ymkHo4MV2DSsK+ZyNnL9Uv2j8jFEfWCmmSlIeS2qM+H9W4pSB16Jth9FysEOKSPAlegFK+Xo0QQ756ggcvOKDA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:33:47.795645Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0211001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18fb19f747f636b4a5e550171d64a9ab3a4aecaa59019117041dcb198e563391","sha256:624008ce148a6414b0f23c07b375acac0a6b16ab253b4888c75ab968a9ab1f12"],"state_sha256":"86642dfc23ec109c640b505d43ced357366716ac47f38c4dc35d88a3295f5cad"}