{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BO6OHSTUVC5QDKMM3FMPY3V64F","short_pith_number":"pith:BO6OHSTU","canonical_record":{"source":{"id":"1205.6689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-05-30T14:31:03Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"64ba0f7bed06223231cc2e3b6917e7d764bb2520b41a79c6949c77e625294ade","abstract_canon_sha256":"d7e7a467f4c97665207bca479a280e4ed8c85046a47fb1aabf70ac5423bfe9a5"},"schema_version":"1.0"},"canonical_sha256":"0bbce3ca74a8bb01a98cd958fc6ebee149ed9f2b23c8237b7ddc02e5fd110fff","source":{"kind":"arxiv","id":"1205.6689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6689","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6689v1","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6689","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"BO6OHSTUVC5Q","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BO6OHSTUVC5QDKMM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BO6OHSTU","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BO6OHSTUVC5QDKMM3FMPY3V64F","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-05-30T14:31:03Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"64ba0f7bed06223231cc2e3b6917e7d764bb2520b41a79c6949c77e625294ade","abstract_canon_sha256":"d7e7a467f4c97665207bca479a280e4ed8c85046a47fb1aabf70ac5423bfe9a5"},"schema_version":"1.0"},"canonical_sha256":"0bbce3ca74a8bb01a98cd958fc6ebee149ed9f2b23c8237b7ddc02e5fd110fff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:47.008595Z","signature_b64":"NrRTdLus2BlLg27ti47V6QF3F5mhLKzwz8tWAilyMwVKpHw8Cxm6VesCtsaWY73vjsywy4j4rcVRKSCcyjj4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbce3ca74a8bb01a98cd958fc6ebee149ed9f2b23c8237b7ddc02e5fd110fff","last_reissued_at":"2026-05-18T03:44:47.007671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:47.007671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6689","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMbrvarbawz+pz0XSQc/MPNSFjMVZg01AnJsxME3wPnc+eur/Sl9fT2QOJEPUgMK/HkSosRPfR2jrqUNndFTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:58:37.398146Z"},"content_sha256":"942be3d5b8c07fca1f212b4859516a1a0b13fdc44ba2eb3f67b84517bdf14554","schema_version":"1.0","event_id":"sha256:942be3d5b8c07fca1f212b4859516a1a0b13fdc44ba2eb3f67b84517bdf14554"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BO6OHSTUVC5QDKMM3FMPY3V64F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Regular Oscillation Sub-spectrum of Rapidly Rotating Stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"astro-ph.SR","authors_text":"Bertrand Georgeot, Daniel R. Reese, Fran\\c{c}ois Ligni\\`eres, Michael Pasek","submitted_at":"2012-05-30T14:31:03Z","abstract_excerpt":"We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6689","kind":"arxiv","version":1},"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":"2026-05-18T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3xEOH5OWLI69ssj9kxbv/HD+ioFcGwW5Lyw7RUw4/nJwFBNvcuGtf8hLlTeazcc4lHzFByZEETij4lwQY2gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T04:58:37.398518Z"},"content_sha256":"274f2a6c42e9d8062689d0acb56eeb6705a59e74c649f1752ea7d878e28982a8","schema_version":"1.0","event_id":"sha256:274f2a6c42e9d8062689d0acb56eeb6705a59e74c649f1752ea7d878e28982a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/bundle.json","state_url":"https://pith.science/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/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":"2026-05-30T04:58:37Z","links":{"resolver":"https://pith.science/pith/BO6OHSTUVC5QDKMM3FMPY3V64F","bundle":"https://pith.science/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/bundle.json","state":"https://pith.science/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BO6OHSTUVC5QDKMM3FMPY3V64F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BO6OHSTUVC5QDKMM3FMPY3V64F","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":"d7e7a467f4c97665207bca479a280e4ed8c85046a47fb1aabf70ac5423bfe9a5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-05-30T14:31:03Z","title_canon_sha256":"64ba0f7bed06223231cc2e3b6917e7d764bb2520b41a79c6949c77e625294ade"},"schema_version":"1.0","source":{"id":"1205.6689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6689","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6689v1","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6689","created_at":"2026-05-18T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"BO6OHSTUVC5Q","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BO6OHSTUVC5QDKMM","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BO6OHSTU","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:274f2a6c42e9d8062689d0acb56eeb6705a59e74c649f1752ea7d878e28982a8","target":"graph","created_at":"2026-05-18T03:44:47Z","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":"We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agr","authors_text":"Bertrand Georgeot, Daniel R. Reese, Fran\\c{c}ois Ligni\\`eres, Michael Pasek","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-05-30T14:31:03Z","title":"Regular Oscillation Sub-spectrum of Rapidly Rotating Stars"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6689","kind":"arxiv","version":1},"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":"sha256:942be3d5b8c07fca1f212b4859516a1a0b13fdc44ba2eb3f67b84517bdf14554","target":"record","created_at":"2026-05-18T03:44:47Z","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":"d7e7a467f4c97665207bca479a280e4ed8c85046a47fb1aabf70ac5423bfe9a5","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.SR","submitted_at":"2012-05-30T14:31:03Z","title_canon_sha256":"64ba0f7bed06223231cc2e3b6917e7d764bb2520b41a79c6949c77e625294ade"},"schema_version":"1.0","source":{"id":"1205.6689","kind":"arxiv","version":1}},"canonical_sha256":"0bbce3ca74a8bb01a98cd958fc6ebee149ed9f2b23c8237b7ddc02e5fd110fff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bbce3ca74a8bb01a98cd958fc6ebee149ed9f2b23c8237b7ddc02e5fd110fff","first_computed_at":"2026-05-18T03:44:47.007671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:47.007671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NrRTdLus2BlLg27ti47V6QF3F5mhLKzwz8tWAilyMwVKpHw8Cxm6VesCtsaWY73vjsywy4j4rcVRKSCcyjj4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:47.008595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:942be3d5b8c07fca1f212b4859516a1a0b13fdc44ba2eb3f67b84517bdf14554","sha256:274f2a6c42e9d8062689d0acb56eeb6705a59e74c649f1752ea7d878e28982a8"],"state_sha256":"87a421b9e3db4d34edd9e0e179618f8e4a7bf602335ca5c59f5486c3db8b4d89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fgjiLAPKC9jZ9unBbclo5Fgp3+bhjgnZucc7krUeZqi64Lsn2UrLxtKheiFlbWJSt3qcZArimIwOuwGdmFDyAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T04:58:37.400480Z","bundle_sha256":"a7726b593a0264a263354adcb5e51059f17b8c4f77f3e342c831146e3d08915e"}}