{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V27JTMCQ3G67WVRRTPMDNHGPEA","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":"d1a00270585c5d9c69b902c3dfe4b4e9178a8e480794b3b6117ea5ffc4281fdc","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2018-03-08T19:00:12Z","title_canon_sha256":"f60acd9587f29c34d814a0b5b1d11e929e2890d040167cde06c228b377b574ef"},"schema_version":"1.0","source":{"id":"1803.03273","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.03273","created_at":"2026-05-18T00:15:51Z"},{"alias_kind":"arxiv_version","alias_value":"1803.03273v2","created_at":"2026-05-18T00:15:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.03273","created_at":"2026-05-18T00:15:51Z"},{"alias_kind":"pith_short_12","alias_value":"V27JTMCQ3G67","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"V27JTMCQ3G67WVRR","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"V27JTMCQ","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:c040c22f41f322897f3698dee657909652beb2d7b6d021a3e0f4c9a17cf27fbe","target":"graph","created_at":"2026-05-18T00:15:51Z","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":"Astrophysical systems, such as clumps that form star clusters share a density profile that is close to $\\rho \\sim r^{-2}$. We prove analytically this density profile is the result of the scale-free nature of the gravitational collapse. Therefore, it should emerge in many different situations as long as gravity is dominating the evolution for a period that is comparable or longer than the free-fall time, and this does not necessarily imply an isothermal model, as many have previously believed.\n  To describe the collapse process, we construct a model called the turbulence-regulated gravitational","authors_text":"Guang-Xing Li","cross_cats":["astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2018-03-08T19:00:12Z","title":"Scale-free gravitational collapse as the origin of $\\rho \\sim r^{-2}$ density profile -- a possible role of turbulence in regulating gravitational collapse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03273","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:c738e47cefe209fa0f1ffd5b5d882fa6b5830931d1518a93cb9fbda8affc8f03","target":"record","created_at":"2026-05-18T00:15:51Z","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":"d1a00270585c5d9c69b902c3dfe4b4e9178a8e480794b3b6117ea5ffc4281fdc","cross_cats_sorted":["astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2018-03-08T19:00:12Z","title_canon_sha256":"f60acd9587f29c34d814a0b5b1d11e929e2890d040167cde06c228b377b574ef"},"schema_version":"1.0","source":{"id":"1803.03273","kind":"arxiv","version":2}},"canonical_sha256":"aebe99b050d9bdfb56319bd8369ccf20082c7cc9fdb867be9d6fdcbfd3ea4ab3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aebe99b050d9bdfb56319bd8369ccf20082c7cc9fdb867be9d6fdcbfd3ea4ab3","first_computed_at":"2026-05-18T00:15:51.770959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:51.770959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Oymv/dBfS2EDdyJ2OYhqfVuwCrw3k7xvoJglIwK6akwLE+EAmCgDSp4YgxvcGShVC1FDIfWmgTN1o5jlpX6vAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:51.771706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.03273","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c738e47cefe209fa0f1ffd5b5d882fa6b5830931d1518a93cb9fbda8affc8f03","sha256:c040c22f41f322897f3698dee657909652beb2d7b6d021a3e0f4c9a17cf27fbe"],"state_sha256":"99720b45ac9dd168450f65c9ba3a4826f6421d9aa4a2c4140a824554f8a48e57"}