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Recent observations reveal a steep velocity dispersion-size relation with the slope $\\beta> 0.6$, which cannot be explained by a single mechanism with only gravity ($\\beta\\sim0.5$) or shear ($\\beta \\sim 1$). We present a two-component model $\\sigma_{\\rm v_{total}} = \\lambda_1 \\sigma_{\\rm v_{g}} + \\lambda_2 \\sigma_{\\rm v_{shear}} = A[(GM/R)^{\\frac{1}{2}} + f(R/t_{\\rm shear})]$ to explain the steep velocity"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.03027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-01-06T14:10:44Z","cross_cats_sorted":[],"title_canon_sha256":"ac9ebc3c44fdbea74336bb9dc8b61f4cf2a3847773d015430e68b139d003a631","abstract_canon_sha256":"3b7e8e3d3656f2928e04c78d111e5d914bb7640079279a72b4317bc7ac83dde5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:02:16.161406Z","signature_b64":"To/mTygOaZjlDRhubPwKkr3hRqGtQzkVIhiyonOX5ytPfSL/I0oQb+FCbbJmovAcmkBvQg2OhO4I3MXaxRVQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86ef3df72dd546689067c2f5c62a2b5544fa6b37f4b8d70a1b46eaacf793f5ce","last_reissued_at":"2026-07-05T11:02:16.161048Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:02:16.161048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shear-gravity transition determines the steep velocity dispersion-size relation in molecular clouds: confronting analytical formula with observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Guang-Xing Li, Yi-Heng Xie","submitted_at":"2025-01-06T14:10:44Z","abstract_excerpt":"The velocity dispersion-size relation ($\\sigma_{\\rm v}\\sim R^{\\beta}$) is a crucial indicator of the dynamic properties of interstellar gas, where the slope is considered as $\\beta \\sim 0.5$. Recent observations reveal a steep velocity dispersion-size relation with the slope $\\beta> 0.6$, which cannot be explained by a single mechanism with only gravity ($\\beta\\sim0.5$) or shear ($\\beta \\sim 1$). We present a two-component model $\\sigma_{\\rm v_{total}} = \\lambda_1 \\sigma_{\\rm v_{g}} + \\lambda_2 \\sigma_{\\rm v_{shear}} = A[(GM/R)^{\\frac{1}{2}} + f(R/t_{\\rm shear})]$ to explain the steep velocity"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03027","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.03027/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.03027","created_at":"2026-07-05T11:02:16.161102+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03027v2","created_at":"2026-07-05T11:02:16.161102+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03027","created_at":"2026-07-05T11:02:16.161102+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q3XT35ZN2VDG","created_at":"2026-07-05T11:02:16.161102+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q3XT35ZN2VDGREDH","created_at":"2026-07-05T11:02:16.161102+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q3XT35ZN","created_at":"2026-07-05T11:02:16.161102+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV","json":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV.json","graph_json":"https://pith.science/api/pith-number/Q3XT35ZN2VDGREDHYL24MKRLKV/graph.json","events_json":"https://pith.science/api/pith-number/Q3XT35ZN2VDGREDHYL24MKRLKV/events.json","paper":"https://pith.science/paper/Q3XT35ZN"},"agent_actions":{"view_html":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV","download_json":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV.json","view_paper":"https://pith.science/paper/Q3XT35ZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03027&json=true","fetch_graph":"https://pith.science/api/pith-number/Q3XT35ZN2VDGREDHYL24MKRLKV/graph.json","fetch_events":"https://pith.science/api/pith-number/Q3XT35ZN2VDGREDHYL24MKRLKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV/action/storage_attestation","attest_author":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV/action/author_attestation","sign_citation":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV/action/citation_signature","submit_replication":"https://pith.science/pith/Q3XT35ZN2VDGREDHYL24MKRLKV/action/replication_record"}},"created_at":"2026-07-05T11:02:16.161102+00:00","updated_at":"2026-07-05T11:02:16.161102+00:00"}