{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:PJWERZUFCY2WSYLNWPC3U3KYC7","short_pith_number":"pith:PJWERZUF","canonical_record":{"source":{"id":"2502.05304","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-07T20:15:07Z","cross_cats_sorted":[],"title_canon_sha256":"32c37e12a4a28756c0df32ba4251a667cd25bffdf5e70981cb6f935ed77f8c4f","abstract_canon_sha256":"bb636c188b5315235a96e0b012fb8ef62b65fcd17beeffc2caf52f53fcf69670"},"schema_version":"1.0"},"canonical_sha256":"7a6c48e685163569616db3c5ba6d5817f64d174af781ab4dab01579cb94d0cdf","source":{"kind":"arxiv","id":"2502.05304","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05304","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05304v1","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05304","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"PJWERZUFCY2W","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_16","alias_value":"PJWERZUFCY2WSYLN","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_8","alias_value":"PJWERZUF","created_at":"2026-07-05T10:11:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:PJWERZUFCY2WSYLNWPC3U3KYC7","target":"record","payload":{"canonical_record":{"source":{"id":"2502.05304","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-07T20:15:07Z","cross_cats_sorted":[],"title_canon_sha256":"32c37e12a4a28756c0df32ba4251a667cd25bffdf5e70981cb6f935ed77f8c4f","abstract_canon_sha256":"bb636c188b5315235a96e0b012fb8ef62b65fcd17beeffc2caf52f53fcf69670"},"schema_version":"1.0"},"canonical_sha256":"7a6c48e685163569616db3c5ba6d5817f64d174af781ab4dab01579cb94d0cdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:11:35.788287Z","signature_b64":"8x9PSEQxYfeHhQvLOkr5NXHhRoUTaBxVhyjifvOx1eb0Bx3r7M8/w3i2GxIjUqsLLYkCnSA3FgQQ4lJdpbRNDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a6c48e685163569616db3c5ba6d5817f64d174af781ab4dab01579cb94d0cdf","last_reissued_at":"2026-07-05T10:11:35.787903Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:11:35.787903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.05304","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":"2026-07-05T10:11:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WAoAruDGt8WitVU2q1aAPvYpf8g29hhuuKk9z0IVTGv8nlii3I3VjJ074LkJT9Sy5UU4JN4O4YHbDpXrbKZDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:52:44.707711Z"},"content_sha256":"2a986abc210579a1b4bf6007053d035a2c4f65a98faf1b6df5d056015b2a7f90","schema_version":"1.0","event_id":"sha256:2a986abc210579a1b4bf6007053d035a2c4f65a98faf1b6df5d056015b2a7f90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:PJWERZUFCY2WSYLNWPC3U3KYC7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Redefining $Q$ for multi-component discs of stars and gas","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.GA","authors_text":"Kit George, Ralph Sch\\\"onrich","submitted_at":"2025-02-07T20:15:07Z","abstract_excerpt":"We point out a fundamental mismatch in the $Q$ stability parameter for Galactic discs: Toomre's $Q = 1$ defines the boundary between axisymmetric stability/instability, while simulations, observations, and theoretical expectations apply $Q$ in the region $Q > 1$ as a measure for spiral activity (e.g. swing amplification), for which $Q$ has not been designed. We suggest to redefine $Q$ to keep $Q = 1$ as the stability boundary, but to equally yield a consistent map between $Q$ and the maximum swing amplification factor. Using the Goldreich-Lynden-Bell formalism, we find that particularly the $Q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05304","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/2502.05304/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":"2026-07-05T10:11:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tmDpiLkpOwe1I7AYl+rOkhLrvdoBhG00GwxXlj7S9FrTq/BdOKmxywcaX8+w8yvMlcIGcETL8aPu+zjvdWR7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T05:52:44.708759Z"},"content_sha256":"fecb8ab584f0d39583baee2aaf43fe065d66c2347985654a8cdf873ff020cb48","schema_version":"1.0","event_id":"sha256:fecb8ab584f0d39583baee2aaf43fe065d66c2347985654a8cdf873ff020cb48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/bundle.json","state_url":"https://pith.science/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/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":"2026-08-18T05:52:44Z","links":{"resolver":"https://pith.science/pith/PJWERZUFCY2WSYLNWPC3U3KYC7","bundle":"https://pith.science/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/bundle.json","state":"https://pith.science/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJWERZUFCY2WSYLNWPC3U3KYC7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PJWERZUFCY2WSYLNWPC3U3KYC7","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":"bb636c188b5315235a96e0b012fb8ef62b65fcd17beeffc2caf52f53fcf69670","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-07T20:15:07Z","title_canon_sha256":"32c37e12a4a28756c0df32ba4251a667cd25bffdf5e70981cb6f935ed77f8c4f"},"schema_version":"1.0","source":{"id":"2502.05304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.05304","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"2502.05304v1","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.05304","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"PJWERZUFCY2W","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_16","alias_value":"PJWERZUFCY2WSYLN","created_at":"2026-07-05T10:11:35Z"},{"alias_kind":"pith_short_8","alias_value":"PJWERZUF","created_at":"2026-07-05T10:11:35Z"}],"graph_snapshots":[{"event_id":"sha256:fecb8ab584f0d39583baee2aaf43fe065d66c2347985654a8cdf873ff020cb48","target":"graph","created_at":"2026-07-05T10:11:35Z","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/2502.05304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We point out a fundamental mismatch in the $Q$ stability parameter for Galactic discs: Toomre's $Q = 1$ defines the boundary between axisymmetric stability/instability, while simulations, observations, and theoretical expectations apply $Q$ in the region $Q > 1$ as a measure for spiral activity (e.g. swing amplification), for which $Q$ has not been designed. We suggest to redefine $Q$ to keep $Q = 1$ as the stability boundary, but to equally yield a consistent map between $Q$ and the maximum swing amplification factor. Using the Goldreich-Lynden-Bell formalism, we find that particularly the $Q","authors_text":"Kit George, Ralph Sch\\\"onrich","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-07T20:15:07Z","title":"Redefining $Q$ for multi-component discs of stars and gas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.05304","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":"sha256:2a986abc210579a1b4bf6007053d035a2c4f65a98faf1b6df5d056015b2a7f90","target":"record","created_at":"2026-07-05T10:11:35Z","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":"bb636c188b5315235a96e0b012fb8ef62b65fcd17beeffc2caf52f53fcf69670","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"astro-ph.GA","submitted_at":"2025-02-07T20:15:07Z","title_canon_sha256":"32c37e12a4a28756c0df32ba4251a667cd25bffdf5e70981cb6f935ed77f8c4f"},"schema_version":"1.0","source":{"id":"2502.05304","kind":"arxiv","version":1}},"canonical_sha256":"7a6c48e685163569616db3c5ba6d5817f64d174af781ab4dab01579cb94d0cdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a6c48e685163569616db3c5ba6d5817f64d174af781ab4dab01579cb94d0cdf","first_computed_at":"2026-07-05T10:11:35.787903Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:35.787903Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8x9PSEQxYfeHhQvLOkr5NXHhRoUTaBxVhyjifvOx1eb0Bx3r7M8/w3i2GxIjUqsLLYkCnSA3FgQQ4lJdpbRNDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:35.788287Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.05304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a986abc210579a1b4bf6007053d035a2c4f65a98faf1b6df5d056015b2a7f90","sha256:fecb8ab584f0d39583baee2aaf43fe065d66c2347985654a8cdf873ff020cb48"],"state_sha256":"1e5fa9c725aecb99a0c2d82ffdb4fb86e6a699f1470e2d1766b0c7f45654f784"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TbNSWljFRvc9ruuEVVfk5EI++bxFq4rikynoBief7MM/Yx0MNkYTreUMbr0oolqeDJpciun/p5j8GV4/O2tDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T05:52:44.715652Z","bundle_sha256":"5fb39bb9c2c6ab622f6ad423520af476e3c5adbc902e6d7fd0b3f4e611433357"}}