{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:XB2NRGSBP34QIGZ7VQEHCFB2TW","short_pith_number":"pith:XB2NRGSB","canonical_record":{"source":{"id":"2311.00955","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-02T02:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"3e3134353c96c1623d41a3eba5075ba3c6943d79c36de7c68f7a13364dbe78ba","abstract_canon_sha256":"cb4f803dd84c7488cac060c66cf2a36c4bf2e8bb85642d1fb4cd840cabd2ec9d"},"schema_version":"1.0"},"canonical_sha256":"b874d89a417ef9041b3fac0871143a9da9c25abb4c4c698a8456f1d083c2161f","source":{"kind":"arxiv","id":"2311.00955","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00955","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00955v2","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00955","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_12","alias_value":"XB2NRGSBP34Q","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_16","alias_value":"XB2NRGSBP34QIGZ7","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_8","alias_value":"XB2NRGSB","created_at":"2026-07-05T08:22:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:XB2NRGSBP34QIGZ7VQEHCFB2TW","target":"record","payload":{"canonical_record":{"source":{"id":"2311.00955","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-02T02:47:06Z","cross_cats_sorted":[],"title_canon_sha256":"3e3134353c96c1623d41a3eba5075ba3c6943d79c36de7c68f7a13364dbe78ba","abstract_canon_sha256":"cb4f803dd84c7488cac060c66cf2a36c4bf2e8bb85642d1fb4cd840cabd2ec9d"},"schema_version":"1.0"},"canonical_sha256":"b874d89a417ef9041b3fac0871143a9da9c25abb4c4c698a8456f1d083c2161f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:34.571506Z","signature_b64":"dauFbTp5pdCatTXXXjq7jprOiIBOwmEr+2X7h5rr8f8IMpsSAQRCedHvNa7WO4xe07Y3zvXszTyYCpPrLkYhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b874d89a417ef9041b3fac0871143a9da9c25abb4c4c698a8456f1d083c2161f","last_reissued_at":"2026-07-05T08:22:34.570897Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:34.570897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.00955","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":"2026-07-05T08:22:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76r54JtT3Ve1g+hUyY7SY938ACw2/ZK8UseG5mOy1KgprJy1UlnLeLRsTIdp3FsybP4Ck919wdS5IgLrG60YCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:16:47.919547Z"},"content_sha256":"40fcca148e427822314a475b7d4e906b04036a8014a875962d4049a3451b8699","schema_version":"1.0","event_id":"sha256:40fcca148e427822314a475b7d4e906b04036a8014a875962d4049a3451b8699"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:XB2NRGSBP34QIGZ7VQEHCFB2TW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On stability analysis for steady states of the free boundary hard phase model in general relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shuang Miao, Zeming Hao","submitted_at":"2023-11-02T02:47:06Z","abstract_excerpt":"The hard phase model describes a relativistic barotropic fluid with sound speed equal to the speed of light. In the framework of general relativity, the motion of the fluid is coupled to the Einstein equations which describe the structure of the underlying spacetime. This model with free boundary admits a $1$-parameter family of steady states with spherical symmetry. In this work, for perturbations within spherical symmetry, we study the stability and instability of this family. We prove that the linearized operator around steady states with large central densities admits a growing mode, while"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00955","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/2311.00955/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:22:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rETEnqR/f3t7vKWa0UCMG89NGEKEymxT9dShnfhgUlaVDBjz3GhOi1sMSJRwXSr5jzwHnXwi5IAn3bYjIUukBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T23:16:47.920080Z"},"content_sha256":"963144c75bdbd3c5f26e5e5c7b1eada655f691660cfe29bb1cc679cbf4572a5f","schema_version":"1.0","event_id":"sha256:963144c75bdbd3c5f26e5e5c7b1eada655f691660cfe29bb1cc679cbf4572a5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/bundle.json","state_url":"https://pith.science/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/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":"2026-08-15T23:16:47Z","links":{"resolver":"https://pith.science/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW","bundle":"https://pith.science/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/bundle.json","state":"https://pith.science/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XB2NRGSBP34QIGZ7VQEHCFB2TW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:XB2NRGSBP34QIGZ7VQEHCFB2TW","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":"cb4f803dd84c7488cac060c66cf2a36c4bf2e8bb85642d1fb4cd840cabd2ec9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-02T02:47:06Z","title_canon_sha256":"3e3134353c96c1623d41a3eba5075ba3c6943d79c36de7c68f7a13364dbe78ba"},"schema_version":"1.0","source":{"id":"2311.00955","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.00955","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"arxiv_version","alias_value":"2311.00955v2","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.00955","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_12","alias_value":"XB2NRGSBP34Q","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_16","alias_value":"XB2NRGSBP34QIGZ7","created_at":"2026-07-05T08:22:34Z"},{"alias_kind":"pith_short_8","alias_value":"XB2NRGSB","created_at":"2026-07-05T08:22:34Z"}],"graph_snapshots":[{"event_id":"sha256:963144c75bdbd3c5f26e5e5c7b1eada655f691660cfe29bb1cc679cbf4572a5f","target":"graph","created_at":"2026-07-05T08:22:34Z","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/2311.00955/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The hard phase model describes a relativistic barotropic fluid with sound speed equal to the speed of light. In the framework of general relativity, the motion of the fluid is coupled to the Einstein equations which describe the structure of the underlying spacetime. This model with free boundary admits a $1$-parameter family of steady states with spherical symmetry. In this work, for perturbations within spherical symmetry, we study the stability and instability of this family. We prove that the linearized operator around steady states with large central densities admits a growing mode, while","authors_text":"Shuang Miao, Zeming Hao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-02T02:47:06Z","title":"On stability analysis for steady states of the free boundary hard phase model in general relativity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.00955","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":"sha256:40fcca148e427822314a475b7d4e906b04036a8014a875962d4049a3451b8699","target":"record","created_at":"2026-07-05T08:22:34Z","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":"cb4f803dd84c7488cac060c66cf2a36c4bf2e8bb85642d1fb4cd840cabd2ec9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-11-02T02:47:06Z","title_canon_sha256":"3e3134353c96c1623d41a3eba5075ba3c6943d79c36de7c68f7a13364dbe78ba"},"schema_version":"1.0","source":{"id":"2311.00955","kind":"arxiv","version":2}},"canonical_sha256":"b874d89a417ef9041b3fac0871143a9da9c25abb4c4c698a8456f1d083c2161f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b874d89a417ef9041b3fac0871143a9da9c25abb4c4c698a8456f1d083c2161f","first_computed_at":"2026-07-05T08:22:34.570897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:22:34.570897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dauFbTp5pdCatTXXXjq7jprOiIBOwmEr+2X7h5rr8f8IMpsSAQRCedHvNa7WO4xe07Y3zvXszTyYCpPrLkYhDA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:22:34.571506Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.00955","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40fcca148e427822314a475b7d4e906b04036a8014a875962d4049a3451b8699","sha256:963144c75bdbd3c5f26e5e5c7b1eada655f691660cfe29bb1cc679cbf4572a5f"],"state_sha256":"d35b03e39c7abbf2be05a95a5004fb1248ae43768c8e465f9ec110a88025079a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xocIZ0a+gVbcv3QWgl2pqHc9Cogd4KKbxAR4bdhil595TBmCkVY1XUAnDRN5Dr5FGVkQoirfc9WsnAvX8F6+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T23:16:47.924378Z","bundle_sha256":"5a808db147e0a9bca14153ed21526fc61a0a6cc0773882c0a92075262b1758aa"}}