{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","short_pith_number":"pith:PHNPZWUA","canonical_record":{"source":{"id":"2605.08807","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-09T08:48:58Z","cross_cats_sorted":[],"title_canon_sha256":"886465ab8b5f7f8508b18a1b57705e14561df9aa01f85bb3cef0eb11f5f218e9","abstract_canon_sha256":"1a8641351351d8bb22c197599c0c64ad4f1dc941c87487b000f9353adcfa5d09"},"schema_version":"1.0"},"canonical_sha256":"79dafcda8089be0634f0ebe2780a0d1fcbf8c9dc98ff4dd88ac582bcbb228137","source":{"kind":"arxiv","id":"2605.08807","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.08807","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.08807v2","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.08807","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"PHNPZWUARG7A","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_16","alias_value":"PHNPZWUARG7AMNHQ","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_8","alias_value":"PHNPZWUA","created_at":"2026-07-14T01:20:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","target":"record","payload":{"canonical_record":{"source":{"id":"2605.08807","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-09T08:48:58Z","cross_cats_sorted":[],"title_canon_sha256":"886465ab8b5f7f8508b18a1b57705e14561df9aa01f85bb3cef0eb11f5f218e9","abstract_canon_sha256":"1a8641351351d8bb22c197599c0c64ad4f1dc941c87487b000f9353adcfa5d09"},"schema_version":"1.0"},"canonical_sha256":"79dafcda8089be0634f0ebe2780a0d1fcbf8c9dc98ff4dd88ac582bcbb228137","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:20:03.195645Z","signature_b64":"xWV793pqeRGxAPYvI0qNyBGD+R2CNHbswY0Efp13+NvIkKNdKKTK+6Rpgb+o/RhZDYIDYzcbaFmPgkRU3Pc3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79dafcda8089be0634f0ebe2780a0d1fcbf8c9dc98ff4dd88ac582bcbb228137","last_reissued_at":"2026-07-14T01:20:03.194678Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:20:03.194678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.08807","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bjrlWzZ/1rSE5oqNxj/AjTe7S63n9BJBZJNRpMGFk9mwnx2mG5kv+ZKFBuClaLA2wfmjhqZHpZHvHJmhZpKOCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:14:22.560247Z"},"content_sha256":"69168725b59d1719fbb063a3846abc6e8ffc6cf3c2ca7f68834cf2d03ead60ef","schema_version":"1.0","event_id":"sha256:69168725b59d1719fbb063a3846abc6e8ffc6cf3c2ca7f68834cf2d03ead60ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matter Maps to Geometry in Gravitational Collapse","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry.","cross_cats":[],"primary_cat":"gr-qc","authors_text":"F. Shojai, H. Khodabakhshi, H. Lu, Zhi-Chao Li","submitted_at":"2026-05-09T08:48:58Z","abstract_excerpt":"We establish an exact bidirectional map between the effective homogeneous interior density of a collapsing star and the exterior metric function in generalized Oppenheimer--Snyder collapse. The Darmois--Israel junction conditions reduce this relation to a purely algebraic form, providing a direct way to reconstruct candidate static geometries and their surface dynamics without solving the corresponding differential field equations separately. Correction powers diagnose models: integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framewor"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential matter-geometry relation to an algebraic form, generating classical or quantum-corrected metrics and dynamics without solving field equations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The assumption that the interior is exactly Friedmann and the exterior is exactly static and spherically symmetric in a generalized Oppenheimer-Snyder setup, allowing the matter-geometry relation to be reduced to an exact algebraic map without solving the Einstein equations.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"An exact bidirectional algebraic map exists between the interior Friedmann density of a collapsing star and its exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7b36914c9888f03f179c24bc71be58d0a0f3eac1df3dfc24c5706df1fb82db66"},"source":{"id":"2605.08807","kind":"arxiv","version":2},"verdict":{"id":"fed8f9a4-2d5e-43ab-9836-6f7404c223d1","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T02:41:36.821817Z","strongest_claim":"We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential matter-geometry relation to an algebraic form, generating classical or quantum-corrected metrics and dynamics without solving field equations.","one_line_summary":"An exact bidirectional algebraic map exists between the interior Friedmann density of a collapsing star and its exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The assumption that the interior is exactly Friedmann and the exterior is exactly static and spherically symmetric in a generalized Oppenheimer-Snyder setup, allowing the matter-geometry relation to be reduced to an exact algebraic map without solving the Einstein equations.","pith_extraction_headline":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry."},"integrity":{"clean":false,"summary":{"advisory":3,"critical":0,"by_detector":{"doi_compliance":{"total":3,"advisory":3,"critical":0,"informational":0}},"informational":0},"endpoint":"/pith/2605.08807/integrity.json","findings":[{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1103/physrevd.112.124057arXiv:2506.03702) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detector":"doi_compliance","severity":"advisory","ref_index":2,"audited_at":"2026-05-19T10:48:56.223581Z","detected_doi":"10.1103/physrevd.112.124057arXiv:2506.03702","finding_type":"recoverable_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null},{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/abd43carXiv:2006.09344) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detector":"doi_compliance","severity":"advisory","ref_index":9,"audited_at":"2026-05-19T10:48:56.223581Z","detected_doi":"10.1088/1361-6382/abd43carXiv:2006.09344","finding_type":"recoverable_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null},{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/ac3b41arXiv:2104.03012) was visible in the surrounding text but could not be confirmed against doi.org as printed.","detector":"doi_compliance","severity":"advisory","ref_index":16,"audited_at":"2026-05-19T10:48:56.223581Z","detected_doi":"10.1088/1361-6382/ac3b41arXiv:2104.03012","finding_type":"recoverable_identifier","verdict_class":"incontrovertible","detected_arxiv_id":null}],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T09:02:01.872768Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:34:22.371505Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T14:01:21.986124Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:48:56.223581Z","status":"completed","version":"1.0.0","findings_count":3}],"snapshot_sha256":"8def7cf583d096e758ccfb9ce84a9d3bde7d3e24bb46a9b17121d957956a9f5d"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ee200926e0c2202a53b10f6b1eb435ddf5c6124941868e0732317deec30763e5"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"fed8f9a4-2d5e-43ab-9836-6f7404c223d1"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T01:20:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QuMDvKN9OPw1ZbaoyLptqIY1vhRdAFuruXr3dacbKKavSFlD3VOx4oFliz0RXnyy/6y/XqpX4HlBL5CI6y9kBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:14:22.560875Z"},"content_sha256":"f37a7a2211641bb52388d37da47ed4834e8a907b4afc5bd4ec3e54adffb922b0","schema_version":"1.0","event_id":"sha256:f37a7a2211641bb52388d37da47ed4834e8a907b4afc5bd4ec3e54adffb922b0"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/ac3b41arXiv:2104.03012) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"R.-Q. Yang, R.-G. Cai, and L. Li, “Constraining the number of horizons with en- ergy conditions,” Class. Quant. Grav.39, 035005 (2022). doi:10.1088/1361-6382/ac3b41 arXiv:2104.03012 [gr-qc]","arxiv_id":"2605.08807","detector":"doi_compliance","evidence":{"ref_index":16,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"R.-Q. Yang, R.-G. Cai, and L. Li, “Constraining the number of horizons with en- ergy conditions,” Class. Quant. Grav.39, 035005 (2022). doi:10.1088/1361-6382/ac3b41 arXiv:2104.03012 [gr-qc]","reconstructed_doi":"10.1088/1361-6382/ac3b41arXiv:2104.03012"},"severity":"advisory","ref_index":16,"audited_at":"2026-05-19T10:48:56.223581Z","event_type":"pith.integrity.v1","detected_doi":"10.1088/1361-6382/ac3b41arXiv:2104.03012","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"5911cc547512ded89372d4aa9484f49afecfcfa1a192083ceb5e23d290a6956b","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":883,"payload_sha256":"aad113b51462137412f3caba1798b630c1ace7457dbc8b3bc7d14050bb221013","signature_b64":"Hb+HQr5iUayTUlOfLil9GxzFouPz18Jj2r1ph2berbrHnO50t5wMqsaNTan+Ek073+LlWLZ/3Gx9PHODnbHFDA==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T10:52:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IA7QM19PAuT62AqEp/OhZ/Tklb3TKsgiy3aQTKhucW6+y2B1tiJHP95m2E7m/6D2HQn9VdRGiJH25ODsv6kOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:14:22.648821Z"},"content_sha256":"2a13b3f688fde50828fb40c762adabb3db781d4dfcbc370fe2419fdfd65c8a75","schema_version":"1.0","event_id":"sha256:2a13b3f688fde50828fb40c762adabb3db781d4dfcbc370fe2419fdfd65c8a75"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/abd43carXiv:2006.09344) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"B. Kellyet al., “Loop quantum gravity corrections to black hole interiors,” Class. Quant. Grav.38, 03LT01 (2021). doi:10.1088/1361-6382/abd43c arXiv:2006.09344 [gr-qc] 16","arxiv_id":"2605.08807","detector":"doi_compliance","evidence":{"ref_index":9,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"B. Kellyet al., “Loop quantum gravity corrections to black hole interiors,” Class. Quant. Grav.38, 03LT01 (2021). doi:10.1088/1361-6382/abd43c arXiv:2006.09344 [gr-qc] 16","reconstructed_doi":"10.1088/1361-6382/abd43carXiv:2006.09344"},"severity":"advisory","ref_index":9,"audited_at":"2026-05-19T10:48:56.223581Z","event_type":"pith.integrity.v1","detected_doi":"10.1088/1361-6382/abd43carXiv:2006.09344","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"9a73806ac06352dc78c812198ba2f0811115252bc7be233773eedc176b7e4d21","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":882,"payload_sha256":"7ef78d02eee61c6225ff226dce031f283385703546fa51dc0620f458007182cc","signature_b64":"4E2BIpiFSF2KUcivwRAK1YNhnUP8zj723EsB6qUHEb9tQzIWCSL6kYgjCzr731njxrgMJP6cT3RsWMkqOoQTAQ==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T10:52:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6UkMF5Wa5JRqshe/6CRF3H6RdQunkLIuUft1x/BnBxdodDgsN6/WrOZ2/pJO3xj1jOGchDvPV52g1wqu84SCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:14:22.649124Z"},"content_sha256":"646153ee90e48175a4be6660209782a32edea8c8c7a825879ba1503831339d2c","schema_version":"1.0","event_id":"sha256:646153ee90e48175a4be6660209782a32edea8c8c7a825879ba1503831339d2c"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1103/physrevd.112.124057arXiv:2506.03702) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"H. Khodabakhshi, H. L¨ u, and F. Shojai, “Gravitational collapse: generalizing Oppenheimer–Snyder and a conjecture on horizon formation time,” Phys. Rev. D112, 124057 (2025). doi:10.1103/PhysRevD.112.124057 arXiv:2506.03702 [gr-qc]","arxiv_id":"2605.08807","detector":"doi_compliance","evidence":{"ref_index":2,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"H. Khodabakhshi, H. L¨ u, and F. Shojai, “Gravitational collapse: generalizing Oppenheimer–Snyder and a conjecture on horizon formation time,” Phys. Rev. D112, 124057 (2025). doi:10.1103/PhysRevD.112.124057 arXiv:2506.03702 [gr-qc]","reconstructed_doi":"10.1103/physrevd.112.124057arXiv:2506.03702"},"severity":"advisory","ref_index":2,"audited_at":"2026-05-19T10:48:56.223581Z","event_type":"pith.integrity.v1","detected_doi":"10.1103/physrevd.112.124057arXiv:2506.03702","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"23dea03cf732910b5a7966db81153a93a69eeecbcad329d388836e5c8a1e85f7","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":881,"payload_sha256":"fd5241dcd7b2fbfe3eb5cb411752d8fdf3c7b6d0de76c79858b82613b6a1f77b","signature_b64":"0ohk1yHuhPF8KT5J/MTw5dpb51siNKGEtkxBdpN8WuhMuONwX70Wy3q2mZRsG1k3lOJP7ePA48nXGlLlEr0vCw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-19T10:52:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+bB1+XEoVVK/zhusF6laZxzJHO4mKZ8/GSxbUJJusEeiwI9kRtDIBa6iZkayHi1+7MxRXg6WpOKxdvbjpO7cDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T10:14:22.649415Z"},"content_sha256":"cf2fec95fa0a8b25e8e33f30a822df88eb43fea5a7a3d66e8365184dcf2ce4b5","schema_version":"1.0","event_id":"sha256:cf2fec95fa0a8b25e8e33f30a822df88eb43fea5a7a3d66e8365184dcf2ce4b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/bundle.json","state_url":"https://pith.science/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-07T10:14:22Z","links":{"resolver":"https://pith.science/pith/PHNPZWUARG7AMNHQ5PRHQCQND7","bundle":"https://pith.science/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/bundle.json","state":"https://pith.science/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PHNPZWUARG7AMNHQ5PRHQCQND7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PHNPZWUARG7AMNHQ5PRHQCQND7","merge_version":"pith-open-graph-merge-v1","event_count":5,"valid_event_count":5,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1a8641351351d8bb22c197599c0c64ad4f1dc941c87487b000f9353adcfa5d09","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-09T08:48:58Z","title_canon_sha256":"886465ab8b5f7f8508b18a1b57705e14561df9aa01f85bb3cef0eb11f5f218e9"},"schema_version":"1.0","source":{"id":"2605.08807","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.08807","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"arxiv_version","alias_value":"2605.08807v2","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.08807","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_12","alias_value":"PHNPZWUARG7A","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_16","alias_value":"PHNPZWUARG7AMNHQ","created_at":"2026-07-14T01:20:03Z"},{"alias_kind":"pith_short_8","alias_value":"PHNPZWUA","created_at":"2026-07-14T01:20:03Z"}],"graph_snapshots":[{"event_id":"sha256:f37a7a2211641bb52388d37da47ed4834e8a907b4afc5bd4ec3e54adffb922b0","target":"graph","created_at":"2026-07-14T01:20:03Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential matter-geometry relation to an algebraic form, generating classical or quantum-corrected metrics and dynamics without solving field equations."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The assumption that the interior is exactly Friedmann and the exterior is exactly static and spherically symmetric in a generalized Oppenheimer-Snyder setup, allowing the matter-geometry relation to be reduced to an exact algebraic map without solving the Einstein equations."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"An exact bidirectional algebraic map exists between the interior Friedmann density of a collapsing star and its exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry."}],"snapshot_sha256":"7b36914c9888f03f179c24bc71be58d0a0f3eac1df3dfc24c5706df1fb82db66"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"ee200926e0c2202a53b10f6b1eb435ddf5c6124941868e0732317deec30763e5"},"integrity":{"available":true,"clean":false,"detectors_run":[{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-20T09:02:01.872768Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T22:34:22.371505Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T14:01:21.986124Z","status":"completed","version":"1.0.0"},{"findings_count":3,"name":"doi_compliance","ran_at":"2026-05-19T10:48:56.223581Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.08807/integrity.json","findings":[{"audited_at":"2026-05-19T10:48:56.223581Z","detected_arxiv_id":null,"detected_doi":"10.1103/physrevd.112.124057arXiv:2506.03702","detector":"doi_compliance","finding_type":"recoverable_identifier","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1103/physrevd.112.124057arXiv:2506.03702) was visible in the surrounding text but could not be confirmed against doi.org as printed.","ref_index":2,"severity":"advisory","verdict_class":"incontrovertible"},{"audited_at":"2026-05-19T10:48:56.223581Z","detected_arxiv_id":null,"detected_doi":"10.1088/1361-6382/abd43carXiv:2006.09344","detector":"doi_compliance","finding_type":"recoverable_identifier","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/abd43carXiv:2006.09344) was visible in the surrounding text but could not be confirmed against doi.org as printed.","ref_index":9,"severity":"advisory","verdict_class":"incontrovertible"},{"audited_at":"2026-05-19T10:48:56.223581Z","detected_arxiv_id":null,"detected_doi":"10.1088/1361-6382/ac3b41arXiv:2104.03012","detector":"doi_compliance","finding_type":"recoverable_identifier","note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1088/1361-6382/ac3b41arXiv:2104.03012) was visible in the surrounding text but could not be confirmed against doi.org as printed.","ref_index":16,"severity":"advisory","verdict_class":"incontrovertible"}],"snapshot_sha256":"8def7cf583d096e758ccfb9ce84a9d3bde7d3e24bb46a9b17121d957956a9f5d","summary":{"advisory":3,"by_detector":{"doi_compliance":{"advisory":3,"critical":0,"informational":0,"total":3}},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish an exact bidirectional map between the effective homogeneous interior density of a collapsing star and the exterior metric function in generalized Oppenheimer--Snyder collapse. The Darmois--Israel junction conditions reduce this relation to a purely algebraic form, providing a direct way to reconstruct candidate static geometries and their surface dynamics without solving the corresponding differential field equations separately. Correction powers diagnose models: integer exponents signal ultraviolet completions, while fractional powers identify phenomenological ones. Our framewor","authors_text":"F. Shojai, H. Khodabakhshi, H. Lu, Zhi-Chao Li","cross_cats":[],"headline":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry.","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-09T08:48:58Z","title":"Matter Maps to Geometry in Gravitational Collapse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.08807","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-12T02:41:36.821817Z","id":"fed8f9a4-2d5e-43ab-9836-6f7404c223d1","model_set":{"reader":"grok-4.3"},"one_line_summary":"An exact bidirectional algebraic map exists between the interior Friedmann density of a collapsing star and its exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Exact bidirectional map connects collapsing star density directly to exterior spacetime geometry.","strongest_claim":"We establish an exact bidirectional map between interior Friedmann density of a collapsing star and exterior static spherically symmetric metric in generalized Oppenheimer-Snyder collapse. This reduces Einstein's differential matter-geometry relation to an algebraic form, generating classical or quantum-corrected metrics and dynamics without solving field equations.","weakest_assumption":"The assumption that the interior is exactly Friedmann and the exterior is exactly static and spherically symmetric in a generalized Oppenheimer-Snyder setup, allowing the matter-geometry relation to be reduced to an exact algebraic map without solving the Einstein equations."}},"verdict_id":"fed8f9a4-2d5e-43ab-9836-6f7404c223d1"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:69168725b59d1719fbb063a3846abc6e8ffc6cf3c2ca7f68834cf2d03ead60ef","target":"record","created_at":"2026-07-14T01:20:03Z","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":"1a8641351351d8bb22c197599c0c64ad4f1dc941c87487b000f9353adcfa5d09","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-05-09T08:48:58Z","title_canon_sha256":"886465ab8b5f7f8508b18a1b57705e14561df9aa01f85bb3cef0eb11f5f218e9"},"schema_version":"1.0","source":{"id":"2605.08807","kind":"arxiv","version":2}},"canonical_sha256":"79dafcda8089be0634f0ebe2780a0d1fcbf8c9dc98ff4dd88ac582bcbb228137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79dafcda8089be0634f0ebe2780a0d1fcbf8c9dc98ff4dd88ac582bcbb228137","first_computed_at":"2026-07-14T01:20:03.194678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:20:03.194678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWV793pqeRGxAPYvI0qNyBGD+R2CNHbswY0Efp13+NvIkKNdKKTK+6Rpgb+o/RhZDYIDYzcbaFmPgkRU3Pc3Bw==","signature_status":"signed_v1","signed_at":"2026-07-14T01:20:03.195645Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.08807","source_kind":"arxiv","source_version":2}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:2a13b3f688fde50828fb40c762adabb3db781d4dfcbc370fe2419fdfd65c8a75","sha256:646153ee90e48175a4be6660209782a32edea8c8c7a825879ba1503831339d2c","sha256:cf2fec95fa0a8b25e8e33f30a822df88eb43fea5a7a3d66e8365184dcf2ce4b5"]}],"invalid_events":[],"applied_event_ids":["sha256:69168725b59d1719fbb063a3846abc6e8ffc6cf3c2ca7f68834cf2d03ead60ef","sha256:f37a7a2211641bb52388d37da47ed4834e8a907b4afc5bd4ec3e54adffb922b0"],"state_sha256":"43e055aeca736d0f3c5130b74510b571ecb416665e0123eaaf6801e632bd293b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoMdadzkRc7r2Qo9bpcm1wthu9WZRtWrGFmCtUCyuiptw8j7xN/H9I3wFqLjlqsGUn81mOxcwLsEgp1Yq580BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T10:14:22.652098Z","bundle_sha256":"4868047d7dba166585a2921dafd780f9c1bae18f033ba9640c6e4f1f2b00ef17"}}