{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6NB4ZW23PSNTIIF27EO5OVJRX6","short_pith_number":"pith:6NB4ZW23","canonical_record":{"source":{"id":"1008.4084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-24T16:56:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"928bb66cfe43e08b539a6592df08a63e8946aae8f25d2dbadef780b51ecdcfde","abstract_canon_sha256":"19ef25782087f81837a6e9946bd48fb58e6555ba19a2370c636477ada49a666b"},"schema_version":"1.0"},"canonical_sha256":"f343ccdb5b7c9b3420baf91dd75531bfa2b71128ecebcb57cdf14bfc53ba30d6","source":{"kind":"arxiv","id":"1008.4084","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4084","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4084v1","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4084","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"6NB4ZW23PSNT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6NB4ZW23PSNTIIF2","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6NB4ZW23","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6NB4ZW23PSNTIIF27EO5OVJRX6","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-24T16:56:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"928bb66cfe43e08b539a6592df08a63e8946aae8f25d2dbadef780b51ecdcfde","abstract_canon_sha256":"19ef25782087f81837a6e9946bd48fb58e6555ba19a2370c636477ada49a666b"},"schema_version":"1.0"},"canonical_sha256":"f343ccdb5b7c9b3420baf91dd75531bfa2b71128ecebcb57cdf14bfc53ba30d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:54.183969Z","signature_b64":"+ePH5joQhIhh1tL0Gu0c6Z2Fz8vBrMcyHhWkclFnbWcORieNtrfNDmQeHnplmdUNJwbVF4XC0PXBU8pSfwr+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f343ccdb5b7c9b3420baf91dd75531bfa2b71128ecebcb57cdf14bfc53ba30d6","last_reissued_at":"2026-05-18T04:41:54.183330Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:54.183330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4084","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVtCuDZENIx/jUUWTk3j64weRz9LdthhifCApi7oHO/lAqlNE9f8MXdJofwJjouT0bB1WIyR0Fe2JSnVtbBZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:17:11.909593Z"},"content_sha256":"7ce49e65f832532b1b3e36297c0b4d40955ed3514a36db46c478524ef3520dd5","schema_version":"1.0","event_id":"sha256:7ce49e65f832532b1b3e36297c0b4d40955ed3514a36db46c478524ef3520dd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6NB4ZW23PSNTIIF27EO5OVJRX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the General Problem of Structure-Preserving Submersions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ziyang Hu","submitted_at":"2010-08-24T16:56:50Z","abstract_excerpt":"In this paper we give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate familiar problems arsing from physics in our framework. Then, as an application of this framework we derive the new results of generalisations of the classical Herglotz-Noether theorem to arbitrary dimensions and to all conformally-flat ambient spaces. Possible further directions for research are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4084","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":"2026-05-18T04:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7pNTUw1e9287SrxYV5xjwgocdP8TNn+x7q+MXklxdQ6VGckqu2/mGSdckbcl8wMicpkaF5PxkZX1q2MO6YfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T03:17:11.910103Z"},"content_sha256":"45f43ea62edf0319425cd125814dc7c7839cd365de540d629a7586f1bc668430","schema_version":"1.0","event_id":"sha256:45f43ea62edf0319425cd125814dc7c7839cd365de540d629a7586f1bc668430"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/bundle.json","state_url":"https://pith.science/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/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":"2026-08-24T03:17:11Z","links":{"resolver":"https://pith.science/pith/6NB4ZW23PSNTIIF27EO5OVJRX6","bundle":"https://pith.science/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/bundle.json","state":"https://pith.science/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6NB4ZW23PSNTIIF27EO5OVJRX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6NB4ZW23PSNTIIF27EO5OVJRX6","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":"19ef25782087f81837a6e9946bd48fb58e6555ba19a2370c636477ada49a666b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-24T16:56:50Z","title_canon_sha256":"928bb66cfe43e08b539a6592df08a63e8946aae8f25d2dbadef780b51ecdcfde"},"schema_version":"1.0","source":{"id":"1008.4084","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4084","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4084v1","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4084","created_at":"2026-05-18T04:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"6NB4ZW23PSNT","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6NB4ZW23PSNTIIF2","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6NB4ZW23","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:45f43ea62edf0319425cd125814dc7c7839cd365de540d629a7586f1bc668430","target":"graph","created_at":"2026-05-18T04:41:54Z","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 give a general geometrical framework for working with problems that can be described as a structure-preserving submersion defined on a suitable space with a geometrical structure. We give many examples of how to formulate familiar problems arsing from physics in our framework. Then, as an application of this framework we derive the new results of generalisations of the classical Herglotz-Noether theorem to arbitrary dimensions and to all conformally-flat ambient spaces. Possible further directions for research are also discussed.","authors_text":"Ziyang Hu","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-24T16:56:50Z","title":"On the General Problem of Structure-Preserving Submersions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4084","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":"sha256:7ce49e65f832532b1b3e36297c0b4d40955ed3514a36db46c478524ef3520dd5","target":"record","created_at":"2026-05-18T04:41:54Z","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":"19ef25782087f81837a6e9946bd48fb58e6555ba19a2370c636477ada49a666b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-08-24T16:56:50Z","title_canon_sha256":"928bb66cfe43e08b539a6592df08a63e8946aae8f25d2dbadef780b51ecdcfde"},"schema_version":"1.0","source":{"id":"1008.4084","kind":"arxiv","version":1}},"canonical_sha256":"f343ccdb5b7c9b3420baf91dd75531bfa2b71128ecebcb57cdf14bfc53ba30d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f343ccdb5b7c9b3420baf91dd75531bfa2b71128ecebcb57cdf14bfc53ba30d6","first_computed_at":"2026-05-18T04:41:54.183330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:54.183330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ePH5joQhIhh1tL0Gu0c6Z2Fz8vBrMcyHhWkclFnbWcORieNtrfNDmQeHnplmdUNJwbVF4XC0PXBU8pSfwr+DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:54.183969Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4084","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ce49e65f832532b1b3e36297c0b4d40955ed3514a36db46c478524ef3520dd5","sha256:45f43ea62edf0319425cd125814dc7c7839cd365de540d629a7586f1bc668430"],"state_sha256":"0b188c2953c675a6c6f5fba2c883f35e7b05f96bf2d2bfa9220bd61a8f06874a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mytj9rlTwncmHl9xTpn0vwYpXNips/eXj4AYiqw9e1udKr7sL5O3IfpYhoViMrI9MAtRWQQkuKdkOV8xK8GJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T03:17:11.914824Z","bundle_sha256":"5d8e57ce9f3dd5d717a56483c68844bbe8c7a2333ba6f75831313da69cb5873c"}}