{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:75GCQXBKAXM4NO723T3R4NLBHN","short_pith_number":"pith:75GCQXBK","canonical_record":{"source":{"id":"2212.11420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"33acfd6dd491b619cd73371b104da0ea2623e08478fc0004b357a229d1ca7044","abstract_canon_sha256":"397167ea9f530bc1c538c286a63915ac1aff01faebe3f13c4f9a96258e387354"},"schema_version":"1.0"},"canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","source":{"kind":"arxiv","id":"2212.11420","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11420","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11420v2","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11420","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"75GCQXBKAXM4","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_16","alias_value":"75GCQXBKAXM4NO72","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_8","alias_value":"75GCQXBK","created_at":"2026-07-05T08:17:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:75GCQXBKAXM4NO723T3R4NLBHN","target":"record","payload":{"canonical_record":{"source":{"id":"2212.11420","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"33acfd6dd491b619cd73371b104da0ea2623e08478fc0004b357a229d1ca7044","abstract_canon_sha256":"397167ea9f530bc1c538c286a63915ac1aff01faebe3f13c4f9a96258e387354"},"schema_version":"1.0"},"canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:55.820135Z","signature_b64":"HQiHLxCejSKjky6rouDKdT3jM29jWl42L/+0leU15Uvrqu60LxGvJDWF91VF/MkDiicHc++55OhO30wjpzd5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","last_reissued_at":"2026-07-05T08:17:55.819533Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:55.819533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.11420","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":"2026-07-05T08:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GicrHcXVukq9f4v97hkcfetDGbDgEkHFyzgtmHwTj6OpaTQT55um7eE70i+hhuzTeCUzRGQHXWGpkCdCbfrbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:14:18.563442Z"},"content_sha256":"43cd2eb61e8b735d8c69a2a70195473d3fc23ded8a15205ce2514be52491e78c","schema_version":"1.0","event_id":"sha256:43cd2eb61e8b735d8c69a2a70195473d3fc23ded8a15205ce2514be52491e78c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:75GCQXBKAXM4NO723T3R4NLBHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonradial stability of expanding Goldreich-Weber stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Juhi Jang, King Ming Lam, Mahir Had\\v{z}i\\'c","submitted_at":"2022-12-22T00:04:28Z","abstract_excerpt":"Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $\\lambda(t)_{t\\to\\infty}\\sim t^{\\frac23}$ and linear rate $\\lambda(t)_{t\\to\\infty}\\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11420","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/2212.11420/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":"2026-07-05T08:17:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0rJ0fWaNmpyb9uw/qp2VvL5YWPT/HQiIlnhhSeUtBvT2RrKTTiBthq3yBloSE+GIUZdF+Kczwc/P4gu4jOvzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T14:14:18.564250Z"},"content_sha256":"6721ead919ab921cb9c73b17bd1034fd7129782814e52b10e1eaa198c3217cd0","schema_version":"1.0","event_id":"sha256:6721ead919ab921cb9c73b17bd1034fd7129782814e52b10e1eaa198c3217cd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75GCQXBKAXM4NO723T3R4NLBHN/bundle.json","state_url":"https://pith.science/pith/75GCQXBKAXM4NO723T3R4NLBHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75GCQXBKAXM4NO723T3R4NLBHN/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":"2026-08-13T14:14:18Z","links":{"resolver":"https://pith.science/pith/75GCQXBKAXM4NO723T3R4NLBHN","bundle":"https://pith.science/pith/75GCQXBKAXM4NO723T3R4NLBHN/bundle.json","state":"https://pith.science/pith/75GCQXBKAXM4NO723T3R4NLBHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75GCQXBKAXM4NO723T3R4NLBHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:75GCQXBKAXM4NO723T3R4NLBHN","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":"397167ea9f530bc1c538c286a63915ac1aff01faebe3f13c4f9a96258e387354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","title_canon_sha256":"33acfd6dd491b619cd73371b104da0ea2623e08478fc0004b357a229d1ca7044"},"schema_version":"1.0","source":{"id":"2212.11420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.11420","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"arxiv_version","alias_value":"2212.11420v2","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.11420","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_12","alias_value":"75GCQXBKAXM4","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_16","alias_value":"75GCQXBKAXM4NO72","created_at":"2026-07-05T08:17:55Z"},{"alias_kind":"pith_short_8","alias_value":"75GCQXBK","created_at":"2026-07-05T08:17:55Z"}],"graph_snapshots":[{"event_id":"sha256:6721ead919ab921cb9c73b17bd1034fd7129782814e52b10e1eaa198c3217cd0","target":"graph","created_at":"2026-07-05T08:17:55Z","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/2212.11420/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $\\lambda(t)_{t\\to\\infty}\\sim t^{\\frac23}$ and linear rate $\\lambda(t)_{t\\to\\infty}\\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable ","authors_text":"Juhi Jang, King Ming Lam, Mahir Had\\v{z}i\\'c","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","title":"Nonradial stability of expanding Goldreich-Weber stars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.11420","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":"sha256:43cd2eb61e8b735d8c69a2a70195473d3fc23ded8a15205ce2514be52491e78c","target":"record","created_at":"2026-07-05T08:17:55Z","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":"397167ea9f530bc1c538c286a63915ac1aff01faebe3f13c4f9a96258e387354","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-12-22T00:04:28Z","title_canon_sha256":"33acfd6dd491b619cd73371b104da0ea2623e08478fc0004b357a229d1ca7044"},"schema_version":"1.0","source":{"id":"2212.11420","kind":"arxiv","version":2}},"canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff4c285c2a05d9c6bbfadcf71e35613b4f7aee0c7da1f763e1a7d35a9fad99e9","first_computed_at":"2026-07-05T08:17:55.819533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:55.819533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HQiHLxCejSKjky6rouDKdT3jM29jWl42L/+0leU15Uvrqu60LxGvJDWF91VF/MkDiicHc++55OhO30wjpzd5Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:55.820135Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.11420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43cd2eb61e8b735d8c69a2a70195473d3fc23ded8a15205ce2514be52491e78c","sha256:6721ead919ab921cb9c73b17bd1034fd7129782814e52b10e1eaa198c3217cd0"],"state_sha256":"6e4221bb669f6b56539fc59a0652fade3ac19be6f133c1c4c5ea8225cb370f19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EnNPj4fycNCm3uT/hOmpgtsQwDGOGlTEi2TuB11BMwY93zgtVIkFrzqbwu7HZsVmaCrkZ9F3N1vt2Ll2FmXtBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T14:14:18.570704Z","bundle_sha256":"acf52ec6c1e8af7ab8df5c4afff176fe703f32eaccfde5b029ab02435573b3b6"}}