{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:K2N2NAGBGSRKTMO6RODJIZNC5Y","short_pith_number":"pith:K2N2NAGB","canonical_record":{"source":{"id":"0910.1030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-06T14:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"71da8e611559520ffcc0af6def0b24898e2e4f875a90a4346b18cc6bfeabed49","abstract_canon_sha256":"8571aa498a58b770efae89c164226dfaf0a403a5936ff4cf53085b5361603a4e"},"schema_version":"1.0"},"canonical_sha256":"569ba680c134a2a9b1de8b869465a2ee3d2c1d8296d1cd09cb767ef7c3e241ac","source":{"kind":"arxiv","id":"0910.1030","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1030","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1030v2","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1030","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"K2N2NAGBGSRK","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"K2N2NAGBGSRKTMO6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"K2N2NAGB","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:K2N2NAGBGSRKTMO6RODJIZNC5Y","target":"record","payload":{"canonical_record":{"source":{"id":"0910.1030","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-06T14:54:54Z","cross_cats_sorted":[],"title_canon_sha256":"71da8e611559520ffcc0af6def0b24898e2e4f875a90a4346b18cc6bfeabed49","abstract_canon_sha256":"8571aa498a58b770efae89c164226dfaf0a403a5936ff4cf53085b5361603a4e"},"schema_version":"1.0"},"canonical_sha256":"569ba680c134a2a9b1de8b869465a2ee3d2c1d8296d1cd09cb767ef7c3e241ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:30.957122Z","signature_b64":"1L1yP5By/GGUlavh080V8Y/cv8SQUWr0OUUZQFARLpbdqnc7YpeHAIECbiiO25uZCX2CEit3Ett3Wvo6gKUHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"569ba680c134a2a9b1de8b869465a2ee3d2c1d8296d1cd09cb767ef7c3e241ac","last_reissued_at":"2026-05-18T01:22:30.956474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:30.956474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.1030","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bims7GDdJi7iOn8B7IDTLocphn3kjGYovILP559DQ9J0SHi8bQOhJU75JxCavjsUx5B8fo2R+AaTXFoz9bonCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:07:10.648201Z"},"content_sha256":"ef05260ea8b58837a91d6ed661d0c6faf5505137ef9ff8f5fcd9298eade268c0","schema_version":"1.0","event_id":"sha256:ef05260ea8b58837a91d6ed661d0c6faf5505137ef9ff8f5fcd9298eade268c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:K2N2NAGBGSRKTMO6RODJIZNC5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic independence of generalized Morita-Miller-Mumford classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Johannes Ebert","submitted_at":"2009-10-06T14:54:54Z","abstract_excerpt":"The generalized Morita-Miller-Mumford classes of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, then all MMM-classes in rational cohomology are nonzero for some bundle. In odd dimensions, this is also true with one exception: the MMM-class associated with the Hirzebruch $\\cL$-class is always zero. We also show a similar result for holomorphic fibre bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1030","kind":"arxiv","version":2},"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":"2026-05-18T01:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjdlVng3N/VV9sJbB53Ah+P+6HvRVjaroxvyaYtdg3bHEC3Y/kC8Xnfj0vpke8lLgZB0U18EFXIyHEegEbIpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:07:10.648597Z"},"content_sha256":"3fea0f2f3c37f0c9fb62a2390eb06749231b3ab98427dcb14a4bac8f2b850b0d","schema_version":"1.0","event_id":"sha256:3fea0f2f3c37f0c9fb62a2390eb06749231b3ab98427dcb14a4bac8f2b850b0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/bundle.json","state_url":"https://pith.science/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/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":"2026-06-23T03:07:10Z","links":{"resolver":"https://pith.science/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y","bundle":"https://pith.science/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/bundle.json","state":"https://pith.science/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2N2NAGBGSRKTMO6RODJIZNC5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:K2N2NAGBGSRKTMO6RODJIZNC5Y","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":"8571aa498a58b770efae89c164226dfaf0a403a5936ff4cf53085b5361603a4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-06T14:54:54Z","title_canon_sha256":"71da8e611559520ffcc0af6def0b24898e2e4f875a90a4346b18cc6bfeabed49"},"schema_version":"1.0","source":{"id":"0910.1030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.1030","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"0910.1030v2","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.1030","created_at":"2026-05-18T01:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"K2N2NAGBGSRK","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"K2N2NAGBGSRKTMO6","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"K2N2NAGB","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:3fea0f2f3c37f0c9fb62a2390eb06749231b3ab98427dcb14a4bac8f2b850b0d","target":"graph","created_at":"2026-05-18T01:22:30Z","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":"The generalized Morita-Miller-Mumford classes of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, then all MMM-classes in rational cohomology are nonzero for some bundle. In odd dimensions, this is also true with one exception: the MMM-class associated with the Hirzebruch $\\cL$-class is always zero. We also show a similar result for holomorphic fibre bundles.","authors_text":"Johannes Ebert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-06T14:54:54Z","title":"Algebraic independence of generalized Morita-Miller-Mumford classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1030","kind":"arxiv","version":2},"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:ef05260ea8b58837a91d6ed661d0c6faf5505137ef9ff8f5fcd9298eade268c0","target":"record","created_at":"2026-05-18T01:22:30Z","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":"8571aa498a58b770efae89c164226dfaf0a403a5936ff4cf53085b5361603a4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-10-06T14:54:54Z","title_canon_sha256":"71da8e611559520ffcc0af6def0b24898e2e4f875a90a4346b18cc6bfeabed49"},"schema_version":"1.0","source":{"id":"0910.1030","kind":"arxiv","version":2}},"canonical_sha256":"569ba680c134a2a9b1de8b869465a2ee3d2c1d8296d1cd09cb767ef7c3e241ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"569ba680c134a2a9b1de8b869465a2ee3d2c1d8296d1cd09cb767ef7c3e241ac","first_computed_at":"2026-05-18T01:22:30.956474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:30.956474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1L1yP5By/GGUlavh080V8Y/cv8SQUWr0OUUZQFARLpbdqnc7YpeHAIECbiiO25uZCX2CEit3Ett3Wvo6gKUHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:30.957122Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.1030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef05260ea8b58837a91d6ed661d0c6faf5505137ef9ff8f5fcd9298eade268c0","sha256:3fea0f2f3c37f0c9fb62a2390eb06749231b3ab98427dcb14a4bac8f2b850b0d"],"state_sha256":"832bd3f17d9a260d2b2432aa209d8fc3fc978d3fe08996e67a4615a70a7ca4f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDNlLJGURqPu3NAR0dVqODf9YJORygZdVqIvK3qJ5yLvFBFV2JFjtbLWyX1vAPn9PK+mpLdrkdlyzeo22w2IAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:07:10.650946Z","bundle_sha256":"d11acb9d500cee601903b7f7cb3b3f0e2a430c18a97cd4f51635b4d05c931bf9"}}