{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:BBMN3CZG5EMSZUSCV6VE4LXTXO","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":"04a2d35c32a11bd031213b14736371c21845495c1eca1bfbde63726b72297ea1","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2006-05-17T10:41:29Z","title_canon_sha256":"6bee87b371b7ca6fdf450d8d1a94f44a903060a0f7b80978638a756676e203c4"},"schema_version":"1.0","source":{"id":"gr-qc/0605097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0605097","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0605097v2","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0605097","created_at":"2026-05-18T04:16:21Z"},{"alias_kind":"pith_short_12","alias_value":"BBMN3CZG5EMS","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"BBMN3CZG5EMSZUSC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"BBMN3CZG","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:d2e44289b6840d95a2dbe1fa73a5e19af4facd924e6d213c8887bee78f411975","target":"graph","created_at":"2026-05-18T04:16:21Z","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 classical result by Buchdahl \\cite{Bu1} shows that for static solutions of the spherically symmetric Einstein-matter system, the total ADM mass M and the area radius R of the boundary of the body, obey the inequality $2M/R\\leq 8/9.$ The proof of this inequality rests on the hypotheses that the energy density is non-increasing outwards and that the pressure is isotropic. In this work neither of Buchdahl's hypotheses are assumed. We consider non-isotropic spherically symmetric shells, supported in $[R_0,R_1], R_0>0,$ of matter models for which the energy density $\\rho\\geq 0,$ and the radial- a","authors_text":"Hakan Andreasson","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2006-05-17T10:41:29Z","title":"On the Buchdahl inequality for spherically symmetric static shells"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0605097","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:e062df875bca9043d7bc736fe24d45bcbf7b8d1bcb570c901d9ffaf461baa553","target":"record","created_at":"2026-05-18T04:16:21Z","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":"04a2d35c32a11bd031213b14736371c21845495c1eca1bfbde63726b72297ea1","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"gr-qc","submitted_at":"2006-05-17T10:41:29Z","title_canon_sha256":"6bee87b371b7ca6fdf450d8d1a94f44a903060a0f7b80978638a756676e203c4"},"schema_version":"1.0","source":{"id":"gr-qc/0605097","kind":"arxiv","version":2}},"canonical_sha256":"0858dd8b26e9192cd242afaa4e2ef3bb9f08b2b7ad8da957845424bc418e91af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0858dd8b26e9192cd242afaa4e2ef3bb9f08b2b7ad8da957845424bc418e91af","first_computed_at":"2026-05-18T04:16:21.697827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:21.697827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hjmd/dYgak5SsJBfpeT5fxRtq8gQQ0mVxlxbVf8QJxJU6aoRw8tgx46v16+jBHv4/OWhWnbBc70/qBmJUY0dBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:21.698516Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0605097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e062df875bca9043d7bc736fe24d45bcbf7b8d1bcb570c901d9ffaf461baa553","sha256:d2e44289b6840d95a2dbe1fa73a5e19af4facd924e6d213c8887bee78f411975"],"state_sha256":"0a7c093fdaec4f4686f174535f98f84098227fe49958871b36419938265dcaa0"}