{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LP7G2G77ADBAXVGN4L6TGH4TAL","short_pith_number":"pith:LP7G2G77","canonical_record":{"source":{"id":"1411.0197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2014-11-02T02:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"d36ada226c9bbfff01cb472c931a7e60fa71612f3c1c4c2147bf12018466b136","abstract_canon_sha256":"417be00a0a83a276e9ccb77ef12066178eca6f463a1e2a89d743c0bfc2f2490c"},"schema_version":"1.0"},"canonical_sha256":"5bfe6d1bff00c20bd4cde2fd331f9302fb6e97ec63f1d538c4839b037608437c","source":{"kind":"arxiv","id":"1411.0197","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0197","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0197v3","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0197","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"LP7G2G77ADBA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LP7G2G77ADBAXVGN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LP7G2G77","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LP7G2G77ADBAXVGN4L6TGH4TAL","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0197","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2014-11-02T02:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"d36ada226c9bbfff01cb472c931a7e60fa71612f3c1c4c2147bf12018466b136","abstract_canon_sha256":"417be00a0a83a276e9ccb77ef12066178eca6f463a1e2a89d743c0bfc2f2490c"},"schema_version":"1.0"},"canonical_sha256":"5bfe6d1bff00c20bd4cde2fd331f9302fb6e97ec63f1d538c4839b037608437c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:31.300605Z","signature_b64":"o2nbLdExo8uT2bEqD6GFHcM9NWMmjdIPo6LrBroR3dNVDjN3v/7X0wgOnPRZQt1jgur4iZyQyU3pUFW1YJOZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bfe6d1bff00c20bd4cde2fd331f9302fb6e97ec63f1d538c4839b037608437c","last_reissued_at":"2026-05-18T01:37:31.299841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:31.299841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0197","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mJqU2R/o0zBziqo6zAVrLQ6nVkXJUDTty2MyKc1hFSw3uHwlKRFAwXszzLoqGziS9vPRDXKFPnw4sVWnMhQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:47:15.119571Z"},"content_sha256":"89a6fc4400ab11da0bc8b917869386e2a81d84763bdfe18ca37a0018a2002d49","schema_version":"1.0","event_id":"sha256:89a6fc4400ab11da0bc8b917869386e2a81d84763bdfe18ca37a0018a2002d49"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LP7G2G77ADBAXVGN4L6TGH4TAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Velocity-density twin transforms in thin disk model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Joanna Ja{\\l}ocha, {\\L}ukasz Bratek, Marek Kutschera, Szymon Sikora","submitted_at":"2014-11-02T02:54:19Z","abstract_excerpt":"Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0197","kind":"arxiv","version":3},"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":"2026-05-18T01:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oXqMeO6k+0rC3SghmZ1QIZKcAFyGWmFotf+P6GonffDTK0l90C+7itwNERmcgMDXAzlYK7knMzWliq0SkYlNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:47:15.119917Z"},"content_sha256":"569ab04226557445c3336dab8a48a27b0f5051e37a6aafca3463e5cc3049040a","schema_version":"1.0","event_id":"sha256:569ab04226557445c3336dab8a48a27b0f5051e37a6aafca3463e5cc3049040a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/bundle.json","state_url":"https://pith.science/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/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":"2026-06-05T12:47:15Z","links":{"resolver":"https://pith.science/pith/LP7G2G77ADBAXVGN4L6TGH4TAL","bundle":"https://pith.science/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/bundle.json","state":"https://pith.science/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LP7G2G77ADBAXVGN4L6TGH4TAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LP7G2G77ADBAXVGN4L6TGH4TAL","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":"417be00a0a83a276e9ccb77ef12066178eca6f463a1e2a89d743c0bfc2f2490c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2014-11-02T02:54:19Z","title_canon_sha256":"d36ada226c9bbfff01cb472c931a7e60fa71612f3c1c4c2147bf12018466b136"},"schema_version":"1.0","source":{"id":"1411.0197","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0197","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0197v3","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0197","created_at":"2026-05-18T01:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"LP7G2G77ADBA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LP7G2G77ADBAXVGN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LP7G2G77","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:569ab04226557445c3336dab8a48a27b0f5051e37a6aafca3463e5cc3049040a","target":"graph","created_at":"2026-05-18T01:37:31Z","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":"Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula.","authors_text":"Joanna Ja{\\l}ocha, {\\L}ukasz Bratek, Marek Kutschera, Szymon Sikora","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2014-11-02T02:54:19Z","title":"Velocity-density twin transforms in thin disk model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0197","kind":"arxiv","version":3},"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":"sha256:89a6fc4400ab11da0bc8b917869386e2a81d84763bdfe18ca37a0018a2002d49","target":"record","created_at":"2026-05-18T01:37:31Z","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":"417be00a0a83a276e9ccb77ef12066178eca6f463a1e2a89d743c0bfc2f2490c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.GA","submitted_at":"2014-11-02T02:54:19Z","title_canon_sha256":"d36ada226c9bbfff01cb472c931a7e60fa71612f3c1c4c2147bf12018466b136"},"schema_version":"1.0","source":{"id":"1411.0197","kind":"arxiv","version":3}},"canonical_sha256":"5bfe6d1bff00c20bd4cde2fd331f9302fb6e97ec63f1d538c4839b037608437c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bfe6d1bff00c20bd4cde2fd331f9302fb6e97ec63f1d538c4839b037608437c","first_computed_at":"2026-05-18T01:37:31.299841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:31.299841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2nbLdExo8uT2bEqD6GFHcM9NWMmjdIPo6LrBroR3dNVDjN3v/7X0wgOnPRZQt1jgur4iZyQyU3pUFW1YJOZBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:31.300605Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0197","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89a6fc4400ab11da0bc8b917869386e2a81d84763bdfe18ca37a0018a2002d49","sha256:569ab04226557445c3336dab8a48a27b0f5051e37a6aafca3463e5cc3049040a"],"state_sha256":"b5829b0c09e4ac30621d3c516676a21aa380ac981f9b5face434482283c6072a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Wg1ILaWo1cyBqoRgbuJO7DoIInIecEl7LWq/i2Hq3GHnfTb8R2rebRsy3WnD4zj/Adph7BCvbNmzX3l0KcTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:47:15.125307Z","bundle_sha256":"a0b59adfef3373a86ee5a63ecb8636bf1a919a74e0c729b8ba865e06f69a56e9"}}