{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:PAO4CFYOEHOMLB6NQ5VBKFUBE4","short_pith_number":"pith:PAO4CFYO","canonical_record":{"source":{"id":"astro-ph/9801246","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1998-01-26T11:54:56Z","cross_cats_sorted":[],"title_canon_sha256":"17f907962ae403bf33148e7a96b28a9790f04c4951a70df94a5514b94c919986","abstract_canon_sha256":"8e7033bfdbf9e685be19471085e6ded17d07d0686e10fecf000d629c6d36f6e0"},"schema_version":"1.0"},"canonical_sha256":"781dc1170e21dcc587cd876a15168127057e204ebf46c9905a397fd54997b6ba","source":{"kind":"arxiv","id":"astro-ph/9801246","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9801246","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9801246v1","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9801246","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"PAO4CFYOEHOM","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_16","alias_value":"PAO4CFYOEHOMLB6N","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_8","alias_value":"PAO4CFYO","created_at":"2026-07-04T16:06:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:PAO4CFYOEHOMLB6NQ5VBKFUBE4","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9801246","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1998-01-26T11:54:56Z","cross_cats_sorted":[],"title_canon_sha256":"17f907962ae403bf33148e7a96b28a9790f04c4951a70df94a5514b94c919986","abstract_canon_sha256":"8e7033bfdbf9e685be19471085e6ded17d07d0686e10fecf000d629c6d36f6e0"},"schema_version":"1.0"},"canonical_sha256":"781dc1170e21dcc587cd876a15168127057e204ebf46c9905a397fd54997b6ba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:06:06.646762Z","signature_b64":"TlM6Kwr0+QkEYqhMLjn65g5DTlkGYotC1gaHXyAkZsP+rYJBibJ979hR+ksdIRlz2uG2NAU4aVJsiStS9yLeBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"781dc1170e21dcc587cd876a15168127057e204ebf46c9905a397fd54997b6ba","last_reissued_at":"2026-07-04T16:06:06.646364Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:06:06.646364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9801246","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":"2026-07-04T16:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DOGSCf1nilizNXoaYkQYnTHdvToX6EWnEO4gAGVxUlvyCvrzxhAJbkfrEuUY9txhorrjuSMJFhDshX7GCoRBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:58:35.045060Z"},"content_sha256":"ca45134e00b565f386006a7ad1bf8ee610ab4604b8149ed802a1018c3f598d1c","schema_version":"1.0","event_id":"sha256:ca45134e00b565f386006a7ad1bf8ee610ab4604b8149ed802a1018c3f598d1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:PAO4CFYOEHOMLB6NQ5VBKFUBE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Equilibrium-Tide Model for Tidal Friction","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Cambridge) Piet Hut (IAS, Ludmila G. Kiseleva (IoA, Peter P. Eggleton, Princeton)","submitted_at":"1998-01-26T11:54:56Z","abstract_excerpt":"We derive from first principles equations governing (a) the quadrupole tensor of a star distorted by both rotation and the presence of a companion in a possibly eccentric orbit, (b) a functional form for the dissipative force of tidal friction, based on the concept that the rate of energy loss from a time-dependent tide should be a positive-definite function of the rate of change of the quadrupole tensor as seen in the frame which rotates with the star, and (c) the equations governing the rates of change of the magnitude and direction of the stellar rotation, and the orbital period and eccentr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9801246","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/9801246/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":"2026-07-04T16:06:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZMOvyAltZMFOtD+47jwhFQSdGZeWC8X2y/7urfHqbp6AoikC8wzPL/wQcq6bmcMzkXNuUu26kTTv7ZsX15mrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:58:35.045550Z"},"content_sha256":"02d33daece6a65fb678055510e9bab12f9adfc90222bb8703845b42d2d1c35f8","schema_version":"1.0","event_id":"sha256:02d33daece6a65fb678055510e9bab12f9adfc90222bb8703845b42d2d1c35f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/bundle.json","state_url":"https://pith.science/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/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":"2026-08-03T16:58:35Z","links":{"resolver":"https://pith.science/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4","bundle":"https://pith.science/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/bundle.json","state":"https://pith.science/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAO4CFYOEHOMLB6NQ5VBKFUBE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:PAO4CFYOEHOMLB6NQ5VBKFUBE4","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":"8e7033bfdbf9e685be19471085e6ded17d07d0686e10fecf000d629c6d36f6e0","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1998-01-26T11:54:56Z","title_canon_sha256":"17f907962ae403bf33148e7a96b28a9790f04c4951a70df94a5514b94c919986"},"schema_version":"1.0","source":{"id":"astro-ph/9801246","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9801246","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9801246v1","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9801246","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_12","alias_value":"PAO4CFYOEHOM","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_16","alias_value":"PAO4CFYOEHOMLB6N","created_at":"2026-07-04T16:06:06Z"},{"alias_kind":"pith_short_8","alias_value":"PAO4CFYO","created_at":"2026-07-04T16:06:06Z"}],"graph_snapshots":[{"event_id":"sha256:02d33daece6a65fb678055510e9bab12f9adfc90222bb8703845b42d2d1c35f8","target":"graph","created_at":"2026-07-04T16:06:06Z","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/astro-ph/9801246/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive from first principles equations governing (a) the quadrupole tensor of a star distorted by both rotation and the presence of a companion in a possibly eccentric orbit, (b) a functional form for the dissipative force of tidal friction, based on the concept that the rate of energy loss from a time-dependent tide should be a positive-definite function of the rate of change of the quadrupole tensor as seen in the frame which rotates with the star, and (c) the equations governing the rates of change of the magnitude and direction of the stellar rotation, and the orbital period and eccentr","authors_text":"Cambridge) Piet Hut (IAS, Ludmila G. Kiseleva (IoA, Peter P. Eggleton, Princeton)","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1998-01-26T11:54:56Z","title":"The Equilibrium-Tide Model for Tidal Friction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9801246","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:ca45134e00b565f386006a7ad1bf8ee610ab4604b8149ed802a1018c3f598d1c","target":"record","created_at":"2026-07-04T16:06:06Z","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":"8e7033bfdbf9e685be19471085e6ded17d07d0686e10fecf000d629c6d36f6e0","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"1998-01-26T11:54:56Z","title_canon_sha256":"17f907962ae403bf33148e7a96b28a9790f04c4951a70df94a5514b94c919986"},"schema_version":"1.0","source":{"id":"astro-ph/9801246","kind":"arxiv","version":1}},"canonical_sha256":"781dc1170e21dcc587cd876a15168127057e204ebf46c9905a397fd54997b6ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"781dc1170e21dcc587cd876a15168127057e204ebf46c9905a397fd54997b6ba","first_computed_at":"2026-07-04T16:06:06.646364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:06:06.646364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TlM6Kwr0+QkEYqhMLjn65g5DTlkGYotC1gaHXyAkZsP+rYJBibJ979hR+ksdIRlz2uG2NAU4aVJsiStS9yLeBw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:06:06.646762Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9801246","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca45134e00b565f386006a7ad1bf8ee610ab4604b8149ed802a1018c3f598d1c","sha256:02d33daece6a65fb678055510e9bab12f9adfc90222bb8703845b42d2d1c35f8"],"state_sha256":"6eadd12e250ecd1bad4d34f2a809a8733cf46066c875e6866e6314bad3f9b8b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGEzDd9n96Zf/UwxXA4YSlfo3XuGWBjwxxoTKbrB3Nt9pdr+Z4DCeYY9+3sG/IF0sMrWZAX+h7bJ0Ov+egF/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:58:35.050458Z","bundle_sha256":"2bf860d9c8830456a694d07e1eccee2ef174df9e935edae3947bffc17ecf5b65"}}