{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WGXSD2TT4BMP52DCVX7QNITVGX","short_pith_number":"pith:WGXSD2TT","canonical_record":{"source":{"id":"1705.00288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-04-30T09:21:07Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"0db5c96bc4d90d58b37ded23c45fa2c9af9eaf34487863caa227bf732ef2c118","abstract_canon_sha256":"1910f3154f159e392dc9f7c3d21c27cfb0ced926b7e4af46d3715f55569d39ff"},"schema_version":"1.0"},"canonical_sha256":"b1af21ea73e058fee862adff06a27535c24b16d698134395622de61c823ef406","source":{"kind":"arxiv","id":"1705.00288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00288","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00288v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00288","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"WGXSD2TT4BMP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WGXSD2TT4BMP52DC","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WGXSD2TT","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WGXSD2TT4BMP52DCVX7QNITVGX","target":"record","payload":{"canonical_record":{"source":{"id":"1705.00288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-04-30T09:21:07Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"0db5c96bc4d90d58b37ded23c45fa2c9af9eaf34487863caa227bf732ef2c118","abstract_canon_sha256":"1910f3154f159e392dc9f7c3d21c27cfb0ced926b7e4af46d3715f55569d39ff"},"schema_version":"1.0"},"canonical_sha256":"b1af21ea73e058fee862adff06a27535c24b16d698134395622de61c823ef406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:20.867193Z","signature_b64":"7QT3ufcuZQDotTtFfnbrUX5JLu6UdtzytDrJoxHthumFDPKTq6O1ikPy6qdfme0RVrh4RpJzMD+0gFhRPVhbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1af21ea73e058fee862adff06a27535c24b16d698134395622de61c823ef406","last_reissued_at":"2026-05-18T00:45:20.866486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:20.866486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.00288","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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pp/zRcnDTVedR7HkARuy83zcWmEDIOmAbXnTKB56EvYc4SXWaHmL0W7K0Z9HTUNi4UwpR4UCJw5gPL/cSrCaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:16:47.028594Z"},"content_sha256":"178213dfea63691a698283392b9223d39510c387fad2bbad188ec32cf4c36983","schema_version":"1.0","event_id":"sha256:178213dfea63691a698283392b9223d39510c387fad2bbad188ec32cf4c36983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WGXSD2TT4BMP52DCVX7QNITVGX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An analytical model for the evolution of the protoplanetary discs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"astro-ph.EP","authors_text":"Fazeleh Khajenabi, Kimia Kazrani, Mohsen Shadmehri","submitted_at":"2017-04-30T09:21:07Z","abstract_excerpt":"We obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00288","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":"2026-05-18T00:45:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uauv7Kb8Q+oC4NyuQkK91UAxZfjODXT9FUZWLwaIrsQixzH9dEkYXlTLkJaW3uHerjK/8f5QXwwfcMD07o3mDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:16:47.028937Z"},"content_sha256":"35719783fe2b777f43b3f423f09691d8cfef7d6ea37cf630925f2f88a9478c1e","schema_version":"1.0","event_id":"sha256:35719783fe2b777f43b3f423f09691d8cfef7d6ea37cf630925f2f88a9478c1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WGXSD2TT4BMP52DCVX7QNITVGX/bundle.json","state_url":"https://pith.science/pith/WGXSD2TT4BMP52DCVX7QNITVGX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WGXSD2TT4BMP52DCVX7QNITVGX/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":"2026-06-25T23:16:47Z","links":{"resolver":"https://pith.science/pith/WGXSD2TT4BMP52DCVX7QNITVGX","bundle":"https://pith.science/pith/WGXSD2TT4BMP52DCVX7QNITVGX/bundle.json","state":"https://pith.science/pith/WGXSD2TT4BMP52DCVX7QNITVGX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WGXSD2TT4BMP52DCVX7QNITVGX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WGXSD2TT4BMP52DCVX7QNITVGX","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":"1910f3154f159e392dc9f7c3d21c27cfb0ced926b7e4af46d3715f55569d39ff","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-04-30T09:21:07Z","title_canon_sha256":"0db5c96bc4d90d58b37ded23c45fa2c9af9eaf34487863caa227bf732ef2c118"},"schema_version":"1.0","source":{"id":"1705.00288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.00288","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.00288v1","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.00288","created_at":"2026-05-18T00:45:20Z"},{"alias_kind":"pith_short_12","alias_value":"WGXSD2TT4BMP","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WGXSD2TT4BMP52DC","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WGXSD2TT","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:35719783fe2b777f43b3f423f09691d8cfef7d6ea37cf630925f2f88a9478c1e","target":"graph","created_at":"2026-05-18T00:45:20Z","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 obtain a new set of analytical solutions for the evolution of a self-gravitating accretion disc by holding the Toomre parameter close to its threshold, and obtaining the stress parameter from the cooling rate. In agreement with the previous numerical solutions, furthermore, the accretion rate is assumed to be independent of the disc radius. Extreme situations where the entire disc is either optically thick or optically thin are studied independently and the obtained solutions can be used for exploring the early or the final phases of a protoplanetary disc evolution. Our solutions exhibit de","authors_text":"Fazeleh Khajenabi, Kimia Kazrani, Mohsen Shadmehri","cross_cats":["astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-04-30T09:21:07Z","title":"An analytical model for the evolution of the protoplanetary discs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00288","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":"sha256:178213dfea63691a698283392b9223d39510c387fad2bbad188ec32cf4c36983","target":"record","created_at":"2026-05-18T00:45:20Z","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":"1910f3154f159e392dc9f7c3d21c27cfb0ced926b7e4af46d3715f55569d39ff","cross_cats_sorted":["astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.EP","submitted_at":"2017-04-30T09:21:07Z","title_canon_sha256":"0db5c96bc4d90d58b37ded23c45fa2c9af9eaf34487863caa227bf732ef2c118"},"schema_version":"1.0","source":{"id":"1705.00288","kind":"arxiv","version":1}},"canonical_sha256":"b1af21ea73e058fee862adff06a27535c24b16d698134395622de61c823ef406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1af21ea73e058fee862adff06a27535c24b16d698134395622de61c823ef406","first_computed_at":"2026-05-18T00:45:20.866486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:20.866486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7QT3ufcuZQDotTtFfnbrUX5JLu6UdtzytDrJoxHthumFDPKTq6O1ikPy6qdfme0RVrh4RpJzMD+0gFhRPVhbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:20.867193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.00288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:178213dfea63691a698283392b9223d39510c387fad2bbad188ec32cf4c36983","sha256:35719783fe2b777f43b3f423f09691d8cfef7d6ea37cf630925f2f88a9478c1e"],"state_sha256":"0e4c61f62dae9288f40608ad9e3e222ccc6bf60a296361e621b0abce2c175716"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wlvDwZTPYP0zFe4vRwlmSPJlVZVNVuX9A3zL6iE78joSlNq5qi4sGBqBTALJeB2pJa+eTWhBJWJA+xZPhajGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:16:47.031029Z","bundle_sha256":"5d65d70538c40e90a295df62e339a0d36604dfb3c53657ca8016853a01ab7329"}}