{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OBA546PVEAYQ3LNVXTOQIRDNNG","short_pith_number":"pith:OBA546PV","canonical_record":{"source":{"id":"1401.1420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-01-07T15:47:31Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"137bfe271547387278eba00f00c91ae9e41c9bcec03686e89ef7384265e84706","abstract_canon_sha256":"bf66a8029a05b3efbfea92230f2306d84ebc3f4237187c820ea71f6d38a337ab"},"schema_version":"1.0"},"canonical_sha256":"7041de79f520310dadb5bcdd04446d69959d000f268829839893c53772ab481c","source":{"kind":"arxiv","id":"1401.1420","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1420","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1420v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1420","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"OBA546PVEAYQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OBA546PVEAYQ3LNV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OBA546PV","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OBA546PVEAYQ3LNVXTOQIRDNNG","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-01-07T15:47:31Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"137bfe271547387278eba00f00c91ae9e41c9bcec03686e89ef7384265e84706","abstract_canon_sha256":"bf66a8029a05b3efbfea92230f2306d84ebc3f4237187c820ea71f6d38a337ab"},"schema_version":"1.0"},"canonical_sha256":"7041de79f520310dadb5bcdd04446d69959d000f268829839893c53772ab481c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:08.411625Z","signature_b64":"YRSZWmkC/JvLG1xYsAzNOStkLx5t/k+kEZqPMzFT3pJ51IWORFwH6ELohqCGKMjTw502/hWu1NLyu996I0TDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7041de79f520310dadb5bcdd04446d69959d000f268829839893c53772ab481c","last_reissued_at":"2026-05-18T03:03:08.411077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:08.411077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1420","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SR2nGdNvifDnelWdWaavrzSG8PGhKbpaf8ifJrtL3owzUyF6VT+RsKE3JsdunFxgdyUeWGX5YEnOHQp6MUhOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:39:55.486976Z"},"content_sha256":"74a41e7ea793a07aea445be65e0ebf35302ea0dd420bec853c2f5cbabf95bfe1","schema_version":"1.0","event_id":"sha256:74a41e7ea793a07aea445be65e0ebf35302ea0dd420bec853c2f5cbabf95bfe1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OBA546PVEAYQ3LNVXTOQIRDNNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mode-coupling theory for multiple decay channels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Rolf Schilling, Simon Lang, Thomas Franosch","submitted_at":"2014-01-07T15:47:31Z","abstract_excerpt":"We investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as Brownian dynamics and demonstrate that they fulfill the requirements of correlation functions, in the latter case the solutions are purely relaxational. Furthermore, we construct an effective mode-coupling functional which allows to map the theory to the case of a single decay channel, such that the covariance principle found for the mode-coupling theory for s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1420","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":"2026-05-18T03:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZwbG3rMuie4JcQcXaR9wCcMs97QAxlB4XYSdndUVr1o82rag1LA+Pfj7felZZrb2JoMDcOoduPLjJLWvaYpCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T01:39:55.487706Z"},"content_sha256":"cb091b68c7718cf8b1182e3f6ac4b40b3134ab751009aa822778df2fb3de0120","schema_version":"1.0","event_id":"sha256:cb091b68c7718cf8b1182e3f6ac4b40b3134ab751009aa822778df2fb3de0120"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/bundle.json","state_url":"https://pith.science/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/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":"2026-05-26T01:39:55Z","links":{"resolver":"https://pith.science/pith/OBA546PVEAYQ3LNVXTOQIRDNNG","bundle":"https://pith.science/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/bundle.json","state":"https://pith.science/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBA546PVEAYQ3LNVXTOQIRDNNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OBA546PVEAYQ3LNVXTOQIRDNNG","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":"bf66a8029a05b3efbfea92230f2306d84ebc3f4237187c820ea71f6d38a337ab","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-01-07T15:47:31Z","title_canon_sha256":"137bfe271547387278eba00f00c91ae9e41c9bcec03686e89ef7384265e84706"},"schema_version":"1.0","source":{"id":"1401.1420","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1420","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1420v1","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1420","created_at":"2026-05-18T03:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"OBA546PVEAYQ","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OBA546PVEAYQ3LNV","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OBA546PV","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:cb091b68c7718cf8b1182e3f6ac4b40b3134ab751009aa822778df2fb3de0120","target":"graph","created_at":"2026-05-18T03:03:08Z","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 investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as Brownian dynamics and demonstrate that they fulfill the requirements of correlation functions, in the latter case the solutions are purely relaxational. Furthermore, we construct an effective mode-coupling functional which allows to map the theory to the case of a single decay channel, such that the covariance principle found for the mode-coupling theory for s","authors_text":"Rolf Schilling, Simon Lang, Thomas Franosch","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-01-07T15:47:31Z","title":"Mode-coupling theory for multiple decay channels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1420","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":"sha256:74a41e7ea793a07aea445be65e0ebf35302ea0dd420bec853c2f5cbabf95bfe1","target":"record","created_at":"2026-05-18T03:03:08Z","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":"bf66a8029a05b3efbfea92230f2306d84ebc3f4237187c820ea71f6d38a337ab","cross_cats_sorted":["cond-mat.stat-mech"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2014-01-07T15:47:31Z","title_canon_sha256":"137bfe271547387278eba00f00c91ae9e41c9bcec03686e89ef7384265e84706"},"schema_version":"1.0","source":{"id":"1401.1420","kind":"arxiv","version":1}},"canonical_sha256":"7041de79f520310dadb5bcdd04446d69959d000f268829839893c53772ab481c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7041de79f520310dadb5bcdd04446d69959d000f268829839893c53772ab481c","first_computed_at":"2026-05-18T03:03:08.411077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:08.411077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YRSZWmkC/JvLG1xYsAzNOStkLx5t/k+kEZqPMzFT3pJ51IWORFwH6ELohqCGKMjTw502/hWu1NLyu996I0TDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:08.411625Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1420","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74a41e7ea793a07aea445be65e0ebf35302ea0dd420bec853c2f5cbabf95bfe1","sha256:cb091b68c7718cf8b1182e3f6ac4b40b3134ab751009aa822778df2fb3de0120"],"state_sha256":"93ed920b3c3529504b7770fbefa3118a7ffadbca8e01af689254413411b18e18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/fc5KlIWo+wDLbul+FS2tk4eKxmcpftDO9TaczpaG7LBQsPhcTRelee28Fo1Jw2DS22zqV1LwcM8try07G0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T01:39:55.491052Z","bundle_sha256":"ff3cba602a089f9bf14ea55a74f805667fa659e64caefeec8d286cfbf6053ad4"}}