{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TPJ6TSYBRI3KKG3WKJXVPOEC3C","short_pith_number":"pith:TPJ6TSYB","canonical_record":{"source":{"id":"1312.4532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-16T21:00:00Z","cross_cats_sorted":["astro-ph.HE","astro-ph.SR"],"title_canon_sha256":"2105294443c9720328a9805b59c6c8178d66d06b5e379fa33d4aaba1bfbf986c","abstract_canon_sha256":"84d7bcfb1a0e66a8b3d8b3cb96245bcd9f92c87f65b39b6c0a52f0528844d6d8"},"schema_version":"1.0"},"canonical_sha256":"9bd3e9cb018a36a51b76526f57b882d8a92c99878571d9c9781c4d32dd33447b","source":{"kind":"arxiv","id":"1312.4532","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4532","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4532v2","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4532","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"TPJ6TSYBRI3K","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TPJ6TSYBRI3KKG3W","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TPJ6TSYB","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TPJ6TSYBRI3KKG3WKJXVPOEC3C","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-16T21:00:00Z","cross_cats_sorted":["astro-ph.HE","astro-ph.SR"],"title_canon_sha256":"2105294443c9720328a9805b59c6c8178d66d06b5e379fa33d4aaba1bfbf986c","abstract_canon_sha256":"84d7bcfb1a0e66a8b3d8b3cb96245bcd9f92c87f65b39b6c0a52f0528844d6d8"},"schema_version":"1.0"},"canonical_sha256":"9bd3e9cb018a36a51b76526f57b882d8a92c99878571d9c9781c4d32dd33447b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:41.861621Z","signature_b64":"xwFGWDrHS6wjuBjVbhVZYrLc6BjoXJikoi4G9bKctlnLxZgg6l3V34DmMcFbFoLDVDbiS/WVw5DJtGRRYSKmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9bd3e9cb018a36a51b76526f57b882d8a92c99878571d9c9781c4d32dd33447b","last_reissued_at":"2026-05-18T02:51:41.861115Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:41.861115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4532","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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jo5YtGFDRgptRQ0UjDSxxVXd8U+/qBW6mBAAC+tBY5eymFd7/lk6KXi+84xdIFaSqXmrzkgJl2kBDhh6hUGABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:28:17.579032Z"},"content_sha256":"150bb85aea54951c4629f0848aa753d57d2b0d29c51b5a9982fd6c9392d5e82e","schema_version":"1.0","event_id":"sha256:150bb85aea54951c4629f0848aa753d57d2b0d29c51b5a9982fd6c9392d5e82e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TPJ6TSYBRI3KKG3WKJXVPOEC3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-Hair Relations for Rotating Stars: Nonrelativistic Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE","astro-ph.SR"],"primary_cat":"gr-qc","authors_text":"Kent Yagi, Leo C. Stein, Nicolas Yunes","submitted_at":"2013-12-16T21:00:00Z","abstract_excerpt":"The gravitational field outside of astrophysical black holes is completely described by their mass and spin frequency, as expressed by the no-hair theorems. These theorems assume vacuum spacetimes, and thus they apply only to black holes and not to stars. Despite this, we analytically find that the gravitational potential of arbitrarily rapid rigidly rotating stars can still be described completely by only their mass, spin angular momentum, and quadrupole moment. Although these results are obtained in the nonrelativistic limit (to leading order in a weak-field expansion of general relativity, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4532","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":""},"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":"2026-05-18T02:51:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Odly3Vj5ceLSL7BuRcQaGfjDvrIeKBNMn/TYUHsM7WhXmMCS2Dug709T7gx09MS1wbkmQj9zeNE3kjTlb3iAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:28:17.579389Z"},"content_sha256":"4bc2f34cd932c02dbb8b349e45b86aa8f4df24391e81ca51d0cb3530f87cf581","schema_version":"1.0","event_id":"sha256:4bc2f34cd932c02dbb8b349e45b86aa8f4df24391e81ca51d0cb3530f87cf581"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/bundle.json","state_url":"https://pith.science/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/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":"2026-05-30T05:28:17Z","links":{"resolver":"https://pith.science/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C","bundle":"https://pith.science/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/bundle.json","state":"https://pith.science/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TPJ6TSYBRI3KKG3WKJXVPOEC3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TPJ6TSYBRI3KKG3WKJXVPOEC3C","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":"84d7bcfb1a0e66a8b3d8b3cb96245bcd9f92c87f65b39b6c0a52f0528844d6d8","cross_cats_sorted":["astro-ph.HE","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-16T21:00:00Z","title_canon_sha256":"2105294443c9720328a9805b59c6c8178d66d06b5e379fa33d4aaba1bfbf986c"},"schema_version":"1.0","source":{"id":"1312.4532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4532","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4532v2","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4532","created_at":"2026-05-18T02:51:41Z"},{"alias_kind":"pith_short_12","alias_value":"TPJ6TSYBRI3K","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TPJ6TSYBRI3KKG3W","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TPJ6TSYB","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:4bc2f34cd932c02dbb8b349e45b86aa8f4df24391e81ca51d0cb3530f87cf581","target":"graph","created_at":"2026-05-18T02:51:41Z","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":"The gravitational field outside of astrophysical black holes is completely described by their mass and spin frequency, as expressed by the no-hair theorems. These theorems assume vacuum spacetimes, and thus they apply only to black holes and not to stars. Despite this, we analytically find that the gravitational potential of arbitrarily rapid rigidly rotating stars can still be described completely by only their mass, spin angular momentum, and quadrupole moment. Although these results are obtained in the nonrelativistic limit (to leading order in a weak-field expansion of general relativity, ","authors_text":"Kent Yagi, Leo C. Stein, Nicolas Yunes","cross_cats":["astro-ph.HE","astro-ph.SR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-16T21:00:00Z","title":"Three-Hair Relations for Rotating Stars: Nonrelativistic Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4532","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":"sha256:150bb85aea54951c4629f0848aa753d57d2b0d29c51b5a9982fd6c9392d5e82e","target":"record","created_at":"2026-05-18T02:51:41Z","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":"84d7bcfb1a0e66a8b3d8b3cb96245bcd9f92c87f65b39b6c0a52f0528844d6d8","cross_cats_sorted":["astro-ph.HE","astro-ph.SR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2013-12-16T21:00:00Z","title_canon_sha256":"2105294443c9720328a9805b59c6c8178d66d06b5e379fa33d4aaba1bfbf986c"},"schema_version":"1.0","source":{"id":"1312.4532","kind":"arxiv","version":2}},"canonical_sha256":"9bd3e9cb018a36a51b76526f57b882d8a92c99878571d9c9781c4d32dd33447b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9bd3e9cb018a36a51b76526f57b882d8a92c99878571d9c9781c4d32dd33447b","first_computed_at":"2026-05-18T02:51:41.861115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:41.861115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xwFGWDrHS6wjuBjVbhVZYrLc6BjoXJikoi4G9bKctlnLxZgg6l3V34DmMcFbFoLDVDbiS/WVw5DJtGRRYSKmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:41.861621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:150bb85aea54951c4629f0848aa753d57d2b0d29c51b5a9982fd6c9392d5e82e","sha256:4bc2f34cd932c02dbb8b349e45b86aa8f4df24391e81ca51d0cb3530f87cf581"],"state_sha256":"93576deead9bb7b0832d520c4569ee307bd27c569387db37b2e7fba340bbfe3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qhOLi1cFAy9eWvaKEf3c3uR6z+ca2qEGMW9z2DlJO6oSH+kO0I7mQ6h9rBzBZ3ax7XUZpES+R3xiSSMOcUAXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:28:17.581396Z","bundle_sha256":"2d8440faca5de644c2ec37a1b4dc9b6bbb69e7cbb60761166eccf7e618ee6709"}}