{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GOT6YTAMEFLLK23KOFVHLKUP2T","short_pith_number":"pith:GOT6YTAM","canonical_record":{"source":{"id":"1112.6155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T17:21:23Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"e7eb54bc316ceabac40c05b85be476ea5c48aca5f1d74ea196e8ea5fc653b067","abstract_canon_sha256":"c4296eaa9ac2d3c88f5b11d7f667bc8872197af2e9c4e57665a8460a413c07c7"},"schema_version":"1.0"},"canonical_sha256":"33a7ec4c0c2156b56b6a716a75aa8fd4cb0e48287891ad4d3c22a10d28fed3f7","source":{"kind":"arxiv","id":"1112.6155","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6155","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6155v1","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6155","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"GOT6YTAMEFLL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GOT6YTAMEFLLK23K","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GOT6YTAM","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GOT6YTAMEFLLK23KOFVHLKUP2T","target":"record","payload":{"canonical_record":{"source":{"id":"1112.6155","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T17:21:23Z","cross_cats_sorted":["gr-qc","math.MP"],"title_canon_sha256":"e7eb54bc316ceabac40c05b85be476ea5c48aca5f1d74ea196e8ea5fc653b067","abstract_canon_sha256":"c4296eaa9ac2d3c88f5b11d7f667bc8872197af2e9c4e57665a8460a413c07c7"},"schema_version":"1.0"},"canonical_sha256":"33a7ec4c0c2156b56b6a716a75aa8fd4cb0e48287891ad4d3c22a10d28fed3f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:36.647126Z","signature_b64":"SSXowfjaPXBH++C/2OP+wQqXI1Wd5ffSN/PaE+op1bYkqxj8BhfiXzSZBfrlKo6JOeke15G5lQBY1jBxJuprBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33a7ec4c0c2156b56b6a716a75aa8fd4cb0e48287891ad4d3c22a10d28fed3f7","last_reissued_at":"2026-05-18T04:05:36.646450Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:36.646450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.6155","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":"2026-05-18T04:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAlq2OSzWIX8Qy49kDfpmlScq607iguhYh5EjAESVSU5O/Lu6uNNVYLC+80ANpRd08uqhry1F6XV1OWf7ZctBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:10:51.630189Z"},"content_sha256":"7c6ac8edd1b311a6bbce950513d9655151edddd09c6f908a66e1e6af1d318324","schema_version":"1.0","event_id":"sha256:7c6ac8edd1b311a6bbce950513d9655151edddd09c6f908a66e1e6af1d318324"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GOT6YTAMEFLLK23KOFVHLKUP2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A framework for structure-preserving submersions and some theorems in relativistic flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Ziyang Hu","submitted_at":"2011-12-28T17:21:23Z","abstract_excerpt":"In this paper we first propose a framework of structure-preserving submersions, which generalises the concept of a Riemannian submersion, and dualises the concept of subgeometry, or \"structure-preserving immersions\". The emphasis of our approach is on making precise the free variables and the degree of freedom in a given system, thus making the messy calculations in such problems more bearable and, more importantly, algorithmic. In particular, we derive the degrees of freedom of Riemannian submersions and of Weyl submersions. Then we apply our framework to the study of relativistic dissipation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6155","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":"2026-05-18T04:05:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EcGNVWf0Na5ASPM8jmW3H9IYmln6BMBAyYNO91yqg3ePIYO9HNbXPovHOsvcE6LfloJr+EZyG6A6PEwDSVuWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T04:10:51.630701Z"},"content_sha256":"b25a71540682a168c94229f0619b00058010dab8034dca8e9814bbe6451ce704","schema_version":"1.0","event_id":"sha256:b25a71540682a168c94229f0619b00058010dab8034dca8e9814bbe6451ce704"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/bundle.json","state_url":"https://pith.science/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/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":"2026-08-24T04:10:51Z","links":{"resolver":"https://pith.science/pith/GOT6YTAMEFLLK23KOFVHLKUP2T","bundle":"https://pith.science/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/bundle.json","state":"https://pith.science/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOT6YTAMEFLLK23KOFVHLKUP2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GOT6YTAMEFLLK23KOFVHLKUP2T","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":"c4296eaa9ac2d3c88f5b11d7f667bc8872197af2e9c4e57665a8460a413c07c7","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T17:21:23Z","title_canon_sha256":"e7eb54bc316ceabac40c05b85be476ea5c48aca5f1d74ea196e8ea5fc653b067"},"schema_version":"1.0","source":{"id":"1112.6155","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6155","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6155v1","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6155","created_at":"2026-05-18T04:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"GOT6YTAMEFLL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GOT6YTAMEFLLK23K","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GOT6YTAM","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:b25a71540682a168c94229f0619b00058010dab8034dca8e9814bbe6451ce704","target":"graph","created_at":"2026-05-18T04:05:36Z","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":"In this paper we first propose a framework of structure-preserving submersions, which generalises the concept of a Riemannian submersion, and dualises the concept of subgeometry, or \"structure-preserving immersions\". The emphasis of our approach is on making precise the free variables and the degree of freedom in a given system, thus making the messy calculations in such problems more bearable and, more importantly, algorithmic. In particular, we derive the degrees of freedom of Riemannian submersions and of Weyl submersions. Then we apply our framework to the study of relativistic dissipation","authors_text":"Ziyang Hu","cross_cats":["gr-qc","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T17:21:23Z","title":"A framework for structure-preserving submersions and some theorems in relativistic flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6155","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":"sha256:7c6ac8edd1b311a6bbce950513d9655151edddd09c6f908a66e1e6af1d318324","target":"record","created_at":"2026-05-18T04:05:36Z","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":"c4296eaa9ac2d3c88f5b11d7f667bc8872197af2e9c4e57665a8460a413c07c7","cross_cats_sorted":["gr-qc","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T17:21:23Z","title_canon_sha256":"e7eb54bc316ceabac40c05b85be476ea5c48aca5f1d74ea196e8ea5fc653b067"},"schema_version":"1.0","source":{"id":"1112.6155","kind":"arxiv","version":1}},"canonical_sha256":"33a7ec4c0c2156b56b6a716a75aa8fd4cb0e48287891ad4d3c22a10d28fed3f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33a7ec4c0c2156b56b6a716a75aa8fd4cb0e48287891ad4d3c22a10d28fed3f7","first_computed_at":"2026-05-18T04:05:36.646450Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:36.646450Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SSXowfjaPXBH++C/2OP+wQqXI1Wd5ffSN/PaE+op1bYkqxj8BhfiXzSZBfrlKo6JOeke15G5lQBY1jBxJuprBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:36.647126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6155","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c6ac8edd1b311a6bbce950513d9655151edddd09c6f908a66e1e6af1d318324","sha256:b25a71540682a168c94229f0619b00058010dab8034dca8e9814bbe6451ce704"],"state_sha256":"6aca398d8315052aa88cfda5790098e080e80be2d89abc9e5083bba8593b2aac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LqkvbzB9LY5PpAQJ1KWpaw0EP3dWwJJpWpEUapP56eanSclrzAiA+zF54PyT+qNLWTwg3iDpH8b3fwapljy7Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T04:10:51.635166Z","bundle_sha256":"3f917e2b5cc2967bdc636bf1016294e12e2cbf729480a953eb42558461d9a8c7"}}